This results when you flip the numerator and denominator of a fraction. what do you call this?

To determine how many plants Ms. Holmes had, divide the total amount of water she had by the amount of water she gave each plant. The expression that can be used is (2 1/2 gallons) divided by (1/4 gallon per plant). Simplifying the expression gives the answer of 10 plants.

To determine how many plants Ms. Holmes had, we can divide the total amount of water she had (2 1/2 gallons) by the amount of water she gave each plant (1/4 gallon per plant).

So, the expression that can be used is (2 ½ gallons) ÷ (1/4 gallon per plant). To divide a fraction by a fraction, we multiply the first fraction by the reciprocal of the second fraction. Therefore, the expression simplifies to (2 ½ gallons) × (4 gallons per plant).

Simplifying further, we get 10 gallons. This means that Ms. Holmes had 10 plants.

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The probability that a container with 2 defective diesel engines will be shipped when 8 engines are chosen at random is 1/45, calculated using combinations in Mathematics.

The subject of this question is Mathematics, specifically involving probability and combinatorics. A container has 10 diesel engines, with 2 being defective. The company will only ship the container if none of the randomly selected 8 engines are defective. The probability that the container is shipped can be found by considering the number of ways to choose 8 engines that are not defective out of the 10 engines, relative to the total number of ways to choose 8 engines out of 10 without any restrictions. Since there are 2 defective engines, there are 8 non-defective engines in total.

To calculate this, we use combinations: The number of ways to choose 8 non-defective engines from the 8 available is given by 8 choose 8 (which is 1 way), while the total number of ways to choose any 8 engines from the 10 is given by 10 choose 8. The probability is the ratio of these two numbers.

Using the combination formula which is n choose k = n! / (k!(n - k)!), we can calculate:

The probability is therefore 1/45. Hence, the probability that a container will be shipped, even though it contains 2 defective engines, when 8 engines are chosen at random is 1/45.

Answer:

[tex]\frac{9}{64}[/tex] π in²

Step-by-step explanation:

The area (A) of the circle is calculated using the formula

A = πr² ← r is the radius

here the diameter = [tex]\frac{3}{4}[/tex]

and radius is half the diameter, hence

r = [tex]\frac{3}{8}[/tex], so

A = π × ([tex]\frac{3}{8}[/tex] )² = [tex]\frac{9}{64}[/tex] π in²

Answer:

23.78

Step-by-step explanation:

CAH

x/25

cos18=x/25

25cos18=x

x=23.78

Answer:

23.78 cm

Step-by-step explanation:

Since, We know that,

In a right angle triangle,

[tex]cos \theta=\frac{B}{H}[/tex]

Where, B represents base adjacent to [tex]\theta[/tex]

H represents the hypotenuse adjacent to [tex]\theta[/tex]

Thus, by the given diagram,

[tex]cos 18^{\circ}=\frac{x}{25}[/tex]

[tex]\implies x = 25\times cos 18^{\circ}=23.7764129074\approx 23.78\text{ cm}[/tex]

Hence, Last option is correct.

Answer:

  see below

Step-by-step explanation:

The denominator quadratic of each of the rational functions has two real roots, so the rational function would ordinarily have two vertical asymptotes. If there is one vertical asymptote, it is because the other one has been canceled by a numerator factor, creating a "hole."

A graph of the first rational function shows it to have only one vertical asymptote, at x=3. The product of zeros of the denominator quadratic is the constant term, -12, so the other denominator zero must be at x=-4. That is where the hole is found. (See the graph in the second attachment.)

_____

Without a graphing calculator, you would determine the zeros of each quadratic, and identify the rational function that had numerator and denominator zeros that were the same.

[tex]f(x)=\dfrac{x^2+5x+4}{x^2+x-12}\\\\=\dfrac{(x+4)(x+1)}{(x+4)(x-3)} \qquad\text{has a common factor in numerator and denominator, a hole}[/tex]

Answer:

y=-1/2x+2 start at y-intercept 2 and go down by 1 and right by 2

Step-by-step explanation:

The slope-intercept form of the equation −2x−4y=−8 is y = 0.5x + 2. Starting from the y-intercept (0,2), the graph of this line is drawn by moving a half unit up and one unit to the right from the intercept.

The given mathematical equation is −2x−4y=−8. To convert this equation into slope-intercept form (y=mx+b), we want to isolate y. Start by dividing every term by -4, which simplifies the equation to 0.5x + y = 2. In this equation, the slope (m) is 0.5, and the y-intercept (b) is 2.

To graph this line, start by plotting the y-intercept (b) at the point (0, 2) on the y-axis. The slope (m) is 0.5, which we can interpret as a rise of 0.5 units for every run of 1 unit. So, from the y-intercept, move up half a unit and right one unit to plot your second point. Drawing a straight line through these points will give you the graph of your equation.

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ANSWER

[tex](4n - 1)\sqrt{3 n} + 3\sqrt{n}[/tex]

EXPLANATION

The given expression is

[tex] \sqrt{48 {n}^{3} } + \sqrt{9n} - \sqrt{3n} [/tex]

We remove the perfect squares under the radical sign.

[tex]\sqrt{16 {n}^{2} \times3 n} + \sqrt{9n} - \sqrt{3n} [/tex]

We can now take square root of the perfect squares and simplify them further.

[tex] \sqrt{16 {n}^{2}} \times \sqrt{3 n} + \sqrt{9} \times \sqrt{n} - \sqrt{3n} [/tex]

This simplifies to:

[tex]4n\sqrt{3 n} + 3\sqrt{n} - \sqrt{3n} [/tex]

This further simplifies to:

[tex](4n - 1)\sqrt{3 n} + 3\sqrt{n} [/tex]

Answer:

Option B is Correct

Step-by-step explanation:

[tex]\sqrt{48n^3}+\sqrt{9n} - \sqrt{3n}[/tex]

We need to solve the above expression.

48 can be written as: 2x2x2x2x3

9 can be written as : 3x3

Putting values

[tex]\sqrt{2*2*2*2*3*n*n*n} +\sqrt{3*3*n}-\sqrt{3n}[/tex]

2*2 = 2^2 and n*n = n^2 and 3*3 = 3^2

we also know √ = 1/2

so, putting these values we get,

[tex]\sqrt{2^2*2^2*3*n^2*n} +\sqrt{3^2*n}-\sqrt{3n}\\(2^2)^{1/2} * (2^2)^{1/2} * (3)^{1/2} * (n^2)^{1/2} * n ^{1/2} + ((3^2)^{1/2} *n^{1/2}) -(\sqrt{3n})\\2*2*n * (3^{1/2} *n ^{1/2}) +(3 +n^{1/2}) -(\sqrt{3n})\\4n (\sqrt{3n})+(3 \sqrt{n}) -(\sqrt{3n})\\Rearraninging\\4n(\sqrt{3n}) - (\sqrt{3n})+(3 \sqrt{n})\\Taking \,\,\sqrt{3n} \,\,common\,\, from\,\, 1st\,\, and\,\, 2nd\,\, term\\\sqrt{3n}(4n-1)+(3 \sqrt{n})\\or \,\,it\,\,can\,\,be\,\,written\,\,as\,\,\\(4n-1)\sqrt{3n}+(3 \sqrt{n})[/tex]

So, Option B is Correct.

Answer:

8 seconds

Step-by-step explanation:

Set the equation equal to 0.  You do this because h(0) means that there is no height of the object, and that then implies that the object is on the ground (where there is no height).  Then factor using the quadratic formula:

[tex]0=-5t^2+40t[/tex]

Factor out the common constant and variable between the terms:

[tex]0=-5t(t-8)[/tex]

Solving for t, you get that t = 0 and t = 8.  The t = 0 is indicative of the fact that at zero seconds (in other words before the object was launched) it was still on the ground.  At t = 8, it had completed its parabolic travels and landed on the ground again.  

The object launched in the air described by the quadratic equation [tex]-5t^2 + 40t[/tex] will hit the ground after 8 seconds. This is found by solving the quadratic equation [tex]0 = -5t^2 + 40t[/tex] for t.

The expression [tex]-5t^2 + 40t[/tex] predicts the height of an object at a given time after it is launched into the air. To find out when the object will hit the ground, we set the height to zero and solve for t. This results in a quadratic equation that we need to solve:

[tex]0 = -5t^2 + 40t[/tex]

Dividing each term by -5 to simplify, we get:

[tex]t^2 - 8t = 0[/tex]

We can factor this to:

t(t - 8) = 0

Setting each factor equal to zero gives us two solutions, t = 0 and t = 8. The solution t = 0 represents the object at launch. The solution t = 8 seconds represents the time when the object hits the ground.

f(x) = 2(x+8)

replace f(x) with 12 and then solve for x:

12 = 2(x +8)

Use the distributive Property on the right side:

12 = 2x +16

Subtract 16 from each side:

-4 - 2x

Divide both sides by 2:

x = -4 / 2

x = -2

Answer:

−2

Step-by-step explanation:

f(x) = 2(x+8)

f(x) = 12

12 = 2(x+8)

Divide each side by 2

12/2 = 2/2(x+8)

6 = x+8

Subtract 8 from each side

6-8 =x+8-8

-2 = x

Answer:

the first function, y = (x + 1)^2, does pass through the points (1, 4), (2, 9), and (3, 16).

Step-by-step explanation:

Note that 4, 9 and 16 are squares of 2, 3 and 4.  So it's likely that the parent function is of the form f(x) = x^2.  Note that f(1) = 1, f(2) = 4, f(3) = 9 and f(4) = 16.

Let's now determine whether these three points satisfy the first given equation, y = (x + 1)^2:  Does 4 = (1 + 1)^2?  Does 4 = 2^2?  YES.

Does 9 = (2 + 1)^2?  Does 9 = 3^2?  YES

Does 16 = (3 + 1)^2?  YES

So the first function, y = (x + 1)^2, does pass through the points (1, 4), (2, 9), and (3, 16).

Final answer:

The detailed answers cover questions related to functions, sequences, equations of lines, slopes, and graphing lines.

Explanation:

Question 1:

The function that passes through the points (1, 4), (2, 9), and (3, 16) is y = (x + 1)^2.

Question 2:

The equation representing the total number of laps swum y in terms of hours x is y(x) = 10x + 1.

Question 3:

The sequence {4, 2, 0, -2, -4, -6, …} is an arithmetic sequence with a common difference of -2.

Question 5:

The slope of the line containing (3, 5) and (2, 7) is m = -2.

Question 6:

For a line passing through (-3, 2) with a slope of 4, the equation of the line is y = 4x + 14.

Answer:

[tex]10x^{2}-34[/tex]

Step-by-step explanation:

Because we are told equivalent expressions for y and z we can plug those in to 2(y+z).

[tex]2((3x^{2}+x^{2}-5)+(x^{2}-12))[/tex]

Then simplify by combining like terms of the expressions. Values ending in x^2 can be combined with each other.

[tex]2(5x^{2}-17)[/tex]

Now we can distribute the 2 by multiplying each value in the parentheses by 2.

[tex]10x^{2}-34[/tex]

Answer: last option

Step-by-step explanation:

You need to remember the identity:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

You need to find the cosine of angle P, then, you can identify in the figure that:

[tex]adjacent=PR=21\\hypotenuse=PQ=29\\\alpha=P[/tex]

Therefore, the next step is substitute these values into  [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex], then you get:

 [tex]cos(P)=\frac{21}{29}[/tex]

You can observe that this matches with the last option.

The answer is  D, (x + 1) (x + 2) (x - 3)

Answer:  D) (x + 1))x + 2)(x - 3)

Step-by-step explanation:

The x-intercepts help us to form the equation of the curve:

           (-2, 0)            (-1, 0)             and (3, 0)

-->  x = -2,            x = -1,                    x = 3

--> x + 2 = 0         x + 1 = 0               x - 3 = 0

--> (x + 2)       ×     (x + 1)          ×       (x - 3) = 0

This is the reverse order for the Zero Product Property

Answer:

  x = 1

Step-by-step explanation:

The base is 3. The value of 3^x will be 3 only when x=1.

_____

The value of any exponential term will be equal to the base when the exponent is 1.

You didn't post any option, but the ration roots theorem states that all possible rational roots of a polynomial come in the form

[tex]\pm\dfrac{p}{q}[/tex]

where p divides the constant term and q divides the leading term of the polynomial. So, in your case, p divides 3 (i.e. it is 1 or 3), and q divides 5 (i.e. it is 1 or 5).

So, the possible roots are

[tex]\pm 1,\quad \pm 3,\quad \pm\dfrac{1}{5},\quad \pm\dfrac{3}{5}[/tex]

For the record, this parabola has no real roots.

The possible rational roots of the polynomial function f(x) = 5x² - 3x + 3 are;

±1/5, ±3/5, ±1, ±3

      We are given the polynomial function;

f(x) = 5x² - 3x + 3

       The rational root theorem states that for a polynomial to have any rational roots, then the roots must be of the form;

±(Factors of coefficient of constant term/factors of the coefficient of the highest power)

       Now, the coefficient of the highest power is 5 and the constant term is 3.

Factors of 5 = 1, 5

Factors of 3 = 1, 3

Thus, the possible rational roots are;

±1/5, ±3/5, ±1, ±3

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The approximate probability that the person will win at least $15 is 0.255.

To solve this problem, we need to calculate the probability of winning at least $15 after playing the game 30 times. Winning at least $15 means that the player must win on at least 6 rolls because winning once pays $5, and $5 times 6 is $30, which is the minimum needed to have a net gain of $15 ($30 won - $15 lost).

First, let's calculate the probability of winning in a single roll. The player wins if they roll a 3 or a 5, which are two favorable outcomes out of six possible outcomes.

[tex]\[ P(\text{win on a single roll}) = \frac{2}{6} = \frac{1}{3} \][/tex]

The probability of losing in a single roll is the complement of the probability of winning:

[tex][ P(\text{lose on a single roll}) = 1 - P(\text{win on a single roll}) = 1 - \frac{1}{3} = \frac{2}{3} \][/tex]

Now, we need to find the probability of winning at least 6 times in 30 rolls. This can be modeled using the binomial probability formula:

[tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \][/tex]

where [tex]\( n \)[/tex]  is the number of trials (30 in this case), [tex]\( k \)[/tex] is the number of successes (at least 6), [tex]\( p \)[/tex] is the probability of success on a single trial [tex](\( \frac{1}{3} \)), and \( \binom{n}{k} \)[/tex]  is the binomial coefficient.

We want to calculate the probability of winning at least 6 times, which is the sum of the probabilities of winning exactly 6, 7, .. up to 30 times:

[tex]\[ P(X \geq 6) = \sum_{k=6}^{30} \binom{30}{k} \left(\frac{1}{3}\right)^k \left(\frac{2}{3}\right)^{30-k} \][/tex]

[tex]\[ P(X \geq 6) \approx 0.255 \][/tex]

Answer:

Part 1) The system of equations that represent this situation is equal to

b+p=42  and 5b+2p=144

Part 2) 20 binders were sold

Step-by-step explanation:

Let

b -----> the number of binders sold

p -----> the number of pencil pouches sold

Part 1)

we know that

The system of equations that represent this situation is equal to

b+p=42

5b+2p=144

Part 2) How many binders were sold?

we have

b+p=42

p=42-b ------> equation A

5b+2p=144 -----> equation B

substitute equation A in equation B

5b+2(42-b)=144

5b+84-2b=144

3b=144-84

3b=60

b=20 binders

Answer:

option B

2

Step-by-step explanation:

Given in the question

DO,h(7, 9) → (14, 18)

Formula to use

distance formula = √((7-0)²+(9-0)²) = √(7²+9²) = √130

distance formula = √((14-0)²+(18-0)²) = √(14²+18²) = 2√130

Scale factor

√130 = 2√130

d = 2d

Answer:

b = 8√3 and c = 16

Step-by-step explanation:

Points to remember

If the angles of a right angled triangle with angles are 30°, 60, and 90 the their sides are in the ratio 1 : √3 : 2

To find the unknown side lengths

From the given figure we can see a right angled triangle

Angles are 30°, 60° and 90°

sides are in the ratio 1 : √3 : 2

1 : √3 : 2 = 8 : b : c

b = 8√3 and c = 8 * 2 = 16

Therefore b = 8√3 and c = 16

Answer:

Your answer is D.

Step-by-step explanation:

Although A and C are also correct, according to a graph using the free online program Desmos

Answer:

•0.5

Step-by-step explanation:

We'll assume the dilation was done at the origin point, so it was done evenly.

Since the k point went from (10,0) to (5,0), we know it was reduced... so the scale factor has to be below 1. A scale factor means the size wasn't changed and a dilation/scale factor larger than 1 means it was enlarged.

So, we take the new X-value (5) and divide it by the original X-value (10).

Scale factor = 5/10 = 1/2... so 0.5

Answer:

Height ( h) = 12 units.

Step-by-step explanation:

Given  : An equilateral triangle with side = 8 √3.

To find : What us the length of the altitude of the equilateral triangle .

Solution : We have given equilateral triangle with side = 8 √3.

By taking the half triangle,

By the Pythagorean theorem :

(Hypotenuse)² = ( adjacent)² + (opposite)².

Plug the values Hypotenuse = 8√3 , adjacent = 4√3 , opposite = h.

(8√3)² = ( 4√3)² + (h)².

192 = 48 +  (h)².

On subtracting by 48 both sides.

192 -48 =  (h)².

144 =  (h)².

On taking square root .

h = 12 .

Therefore, Height ( h) = 12 units.

The guy is right trust me mate

Answer:

[tex]f(3)=1.9[/tex]

Step-by-step explanation:

we have

[tex]f(x)=\frac{14}{7+2e^{-0.6x}}[/tex]

we know that

f(3) is the value of the function for the value of x equal to 3

so

substitute the value of x=3 in the function

[tex]f(3)=\frac{14}{7+2e^{-0.6(3)}}=1.9[/tex]

Answer:

16 Boxes

Step-by-step explanation:

Total Bottles:125

Amount of Bottles A Box Is Able To Hold:8

125/8=15.625

Round Up To Nearest Whole Number

16 Boxes Are Needed To Hold 125 Bottles

Final answer:

62.5% of those surveyed prefer hamburgers.

Explanation:

The question is asking to find the percentage of people who prefer hamburgers over hot dogs when given the ratio of 5 to 3.

To calculate this, you would add the two parts of the ratio together to get the total number of parts, which is 5 + 3 = 8.

The number of parts that represent hamburgers is 5.

To find the percentage, you would divide the hamburger part by the total number of parts and then multiply by 100.

This gives you (5/8) × 100, which equals 62.5%.

Therefore, 62.5% of those surveyed prefer hamburgers.

Answer:

6/1

Step-by-step explanation:

So we are looking for a ratio of flour which is 4 and brown sugar which is 2/3.

So we divide 4 by 2/3.

4÷2/3 since we are diving by a fraction we keep 4÷2/3 change 4*2/3 flip 4*3/2. So now we are multiplying 4 and 3/2.

So that is 4/1*3/2= 12/2 that simplies to 6/1

Answer:

⁶/₁

Step-by-step explanation:

4 cups of flour, ⅔ cup of brown sugar.  The ratio of flour to brown sugar is:

4 / ⅔

We need to simplify this.  First, write 4 as a fraction:

⁴/₁ / ⅔

To divide by a fraction, multiply by the reciprocal:

⁴/₁ × ³/₂

¹²/₂

⁶/₁

Answer:

3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]

Step-by-step explanation:

Given that the explicit rule for a sequence is [tex]a_n=5(-2)^{n-1}[/tex].

Now we need to find about what is the recursive rule for the sequence and match with the given choices to find the correct choice.

1) [tex]a_n=-2a_{n+1}[/tex], [tex]a_1=5[/tex]

2) [tex]a_n=-5a_{n+1}[/tex], [tex]a_1=2[/tex]

3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]

4) [tex]a_n=-5a_{n-1}[/tex], [tex]a_1=2[/tex]

Plug n=1 into given formula to get first term

[tex]a_n=5(-2)^{n-1}[/tex]

[tex]a_1=5(-2)^{1-1}=5(-2)^{0}=5(1)=5[/tex]

base of the exponent part is (-2) so that means we need to multiply -2 to the previous term to get nth term

Hence correct choice is: 3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]

Answer:

3) an=−2(an−1)

a1=5

Step-by-step explanation:

Answer:

  [tex]\boxed{18}[/tex]

Step-by-step explanation:

One of the rules of logarithms is ...

  log(a^b) = b·log(a)

So ...

[tex]6\log_5{x^3}=6(3\log_5{x})=\bf{18}\log_5{x}[/tex]

Answer:

D

Step-by-step explanation:

Let the following point represent the first job:  (4, $144).  Let (6, $188) represent the second.  Then we find the equation of the line through these two points.  As we go from (4, $144) to (6, $188), x increases by 2 and y increases by $44.  Thus, the slope of this line is m = rise/run = $44/(2 hrs), or $22/hr.

Using the slope-intercept formula for a  straight line, y = mx + b, we find the equation of this line by finding the y-intercept, b:

Subbing the given info ($22/hr for m, 4 hr for x and $144 for y), we get:

$144 = ($22/hr)(4 hr) + b, or

$144 = $88 + b, which yields b = $56.

Thus, the desired equation is y = mx + b, or y = ($22/hr)x + $56.  This matches the last answer (D)

Answer:

A. Lucy Only

Step-by-step explanation:

Got it right on Khan Academy

The possible sample space is: FV, WV, SV, FB, WB, and SB

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes

As, the sample space with all possibilities in which lucy and katy register a sports League.

Now, they have 2 sports and 3 seasons for the Sample space.

Mow let us consider, V is registered for Volleyball and B is registered for basketball .

and, F is registered Fall, W is registered for Winter and S is for Spring.

so, that the sample space is:

FV, WV, SV, FB, WB, and SB

where, FV is the  registered possibility for fall and in volleyball.

WV is the  registered possibility for Winter and in volleyball.

SV is the  registered possibility for Spring and in volleyball.

and so on..

Therefore, the correctly representation for the sample space is the one that has all these possibilities.

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