Which of the following is a correct interpretation of the expression 6-13

The required geometric mean between 1 and 16 is 4.

The geometric mean between two numbers is the square root of their product.

As per the question, we have to determine the geometric mean between 1 and 16.

So, we first need to find the product of 1 and 16, which is:

1 x 16 = 16

Next, we take the square root of the product:

√16 = 4

Therefore, the geometric mean between 1 and 16 is 4.

This means that if we were to have a sequence of numbers with the same ratio as 1 and 16, the average number of that sequence would be 4.

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Answer:

Step-by-step explanation:

See image

Answer:

x^3+8

Step-by-step explanation:

Answer:

x=0

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

5x(x+3)=x(5x-3)+36

5x^2+15x=5x^2-3x+36

-18x+36=0

36=18x

x=2

Answer: A and C

Step-by-step explanation:

Options A and C are errors David made while adding the numbers on the number line.

Given that, David added 2 and -3 using the number line tool.

We need to check which of the given errors did he make.

In order to add two integers on a number line, we follow the following step procedure:

Step 1: Draw a number line and mark integers on it.

Step 2: Start from the point representing the first number on the number line.

Step 3: Move as many units as the second number to the

Step 4: Obtain the number representing the point reached in the previous step. This number represents the required sum of the given integers.

Adding 2 and -3 on number line:

We begin at zero and first move 3 units to the left of zero to arrive at -3. The second number is positive 2. So we move 2 units to the right of -3 to arrive at -1.

Therefore, options A and C are errors David made while adding the numbers on the number line.

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Answer:

her is a screenshot fot the answer and step by step they all in side the screenshot please check it

The weighted average of the points on the number line is -0.75

The weighted average of a set of numbers is the average taken into consideration the contribution of each weight.

The weighted average is given by W = ∑wx/∑w where

To find the weighted average of the points on the number line, the ratio of weights of A to Bto C is 3:3:2. Note: Point A is at -7, point B is at -1, and point C is at 9.

So, the weighted average W =  ∑wx/∑w = (w₁x₁ + w₂x₂ + w₃x₃)/(w₁ + w₂ + w₃) where

So, substituting the values of the variables into the equation, we have that

the weighted average W = (w₁x₁ + w₂x₂ + w₃x₃)/(w₁ + w₂ + w₃)

= [3 × (-7) + 3 × (-1) + 2 × 9]/(3 + 3 + 2)

= [-21 - 3 + 18]/8

= [-24 + 18]/8

= -6/8

= -3/4

= -0.75

So, the weighted average is -0.75

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Answer:

11x + 5y

Step-by-step explanation:

To find the product,

simplify the expression.

Thus, you will get 11x + 5y as your answer.

Therefore, After 20 minutes, there are approximately 11.9 kg (rounded to one decimal place) of salt in the tank.

To solve this problem, we need to consider the rate of change of the amount of salt in the tank over time.

(a) Let's denote the amount of salt in the tank after t minutes as y (in kg). We can set up a differential equation to represent the rate of change of salt:

dy/dt = (rate of salt in) - (rate of salt out)

The rate of salt in is given by the concentration of salt in the incoming water (0 kg/L) multiplied by the rate at which water enters the tank (90 L/min). Therefore, the rate of salt in is 0 kg/L * 90 L/min = 0 kg/min.

The rate of salt out is given by the concentration of salt in the tank (y kg/9000 L) multiplied by the rate at which water leaves the tank (90 L/min). Therefore, the rate of salt out is (y/9000) kg/min.

Setting up the differential equation:

dy/dt = 0 - (y/9000)

dy/dt + (1/9000)y = 0

This is a first-order linear homogeneous differential equation. We can solve it by separation of variables:

dy/y = -(1/9000)dt

Integrating both sides:

ln|y| = -(1/9000)t + C

Solving for y:

y = Ce^(-t/9000)

To find the particular solution, we need an initial condition. We know that at t = 0, y = 12 kg (the initial amount of salt in the tank). Substituting these values into the equation:

12 = Ce^(0/9000)

12 = Ce^0

12 = C

Therefore, the particular solution is:

y = 12e^(-t/9000)

(b) To find the amount of salt in the tank after 20 minutes, we substitute t = 20 into the particular solution:

y = 12e^(-20/9000)

y ≈ 11.8767 kg (rounded to one decimal place)

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Answer:

-3.44

Step-by-step explanation:

The expression will equal 28.1 when x= -3.44. Any value of x , except when x= -3.44 , will make the expression equal to 28.1

Answer:

x = − 5 + 1/2 √ 21 or x = − 5 + − 1/2 √ 21

Step-by-step explanation:

Let's solve your equation step-by-step.

4(x+5)^2=21

Step 1: Simplify both sides of the equation.

4x^2+40x+100=21

Step 2: Subtract 21 from both sides.

4x^2+40x+100−21 =21−21 4x^2+40x+79=0

For this equation: a=4, b=40, c=79

4x^2+40x+79=0

Step 3: Use quadratic formula with a=4, b=40, c=79.

x= −b±√ b^2−4ac/2ax

= −(40)+√ (40)^2−4(4)(79)/2(4)

x = 40^2±√ 336/8

x= −5+1/2 √ 21 or x = −5+ − 1/2√ 21

Answer: x = − 5 + 1/2 √ 21 or x = − 5 + − 1/2 √ 21

( I hope this was helpful) >;D

Step-by-step explanation:

let's think about it logically :

|x| can only be positive, from 0 to +infinity.

but the second part "- 4" will bring the result for small x values into the negative realm.

x = 0 gives us f(x) = -4.

x = 4 gives us f(x) = 0

x = -4 gives us f(x) = 0

so, if is the 3rd graph (bottom left).

Answer:

C

Step-by-step explanation:

Answer:

0.84

Step-by-step explanation:

Answer:

0.84>0.74

Step-by-step explanation:

0.84 is 0.1 more than 0.74

Answer:

0.5L

Step-by-step explanation:

0.5L

I only know the first one :/

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Sum of the interior angles of any triangle is 180° .

Thus ;

\(y + 48° + 90° = 180°\)

\(y + 138° = 180°\)

Subtract sides 138°

\(y + 138° - 138° = 180° - 138° \\ \)

\(y = 42°\)

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Answer:

Third term is 36

Step-by-step explanation:

According to the definition of proportion, if two sets of given numbers are  in the same ratio, then the ratios are said to be directly proportional to each other

We use the symbol :: to denote proportion

So if

a:b :: c:d

Then a/b = c/d

We are given that first number = 16, second is 24 and the last is 54

Let the third number be x

We have that
16:24 :: x : 54

In other words

16/24 = x/ 54

Simplifying left side

2/3 = x/54

x = 2/3 x 54 = 36

Answer:

1/5 and 9/4

Step-by-step explanation:

Reciprocal is basically the vertically flipped version of the original number. To find the reciprocal, rewrite the numbers in fractions and then swap the numerator and the denominator. So 5/1 becomes 1/5, 4/9 becomes 9/4.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The reciprocal of a number [x] is given by [1/x].

We have the following numbers -

5 and 4/9

We can write -

x = 5

y = 4/9

So, the reciprocal of [x] would be [1/x]. Therefore, the reciprocal of 5 will be 1/5.

The reciprocal of [y] would be [1/y]. Therefore, the reciprocal of 4/9 will be 9/4.

Therefore -

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Answer: 300

Step-by-step explanation:

From the question, we are informed that Mr Gaines is catering his company picnic and that he will pay $18.45 for 3 people to eat the barbecue lunch. This means each person spends:

= $18.45/3

= $6.15

With a budget of $1850.00, the number of people that he'll be able to feed will be:

= $1850/$6.15

= $300 people

\( \boxed{(x - a)(x - b) = 0}\)

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

\(x = - \frac{1}{3} \\ x = 5\)

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

\((x + \frac{1}{3} )(x - 5) = 0\)

Here we can convert the expression x+1/3 to this.

\(x + \frac{1}{3} = 0 \\ 3x + 1 = 0\)

Rewrite the equation.

\((3x + 1)(x - 5) = 0\)

Simplify by multiplying both expressions.

\(3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0\)

Answer Check

Substitute the given roots in the equation.

\(3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0\)

\(3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0\)

The equation is true for both roots.

Answer

\( \large \boxed {3 {x}^{2} - 14x - 5 = 0}\)

the slope is how many units its goes up and how many it goes right basically rise/run

Answer:

I think the answer is x<2/7

Step-by-step explanation:

That's what i got.

Answer:

Step-by-step explanation:

x<2/7

Answer:

udzufzgodyosogsogsogdgozoyd

Step-by-step explanation:

giigdgdooydogdkgddyoyddigdifocic sorry

\( \sqrt{78866666999} \)

The measures of angles 4 and 5 are:

∠5 = 104°

∠4 =76°

On the image we can see that angles 1 and 2 are next to eachother, that means that the sum of their measures must be a plane angle, that is an angle of 180°.

Then we can write the sum:

∠1 + ∠2 = 180°

(3x + 5) + (2x + 10) = 180

5x + 15 = 180

5x = 180 - 15

x = 165/5 = 33

the measure of angle 5 is the same one of angle 1 then:

∠5 = (3*33 + 5)° = 104°

And angle 4 is supplementary of angle 1, then:

∠4 + 104° = 180°

∠4 = 180 - 104= 76°

These are the measures

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If these conditions/assumptions are met, then the two-sample test for means with independent samples can be used to determine if there is a statistically significant difference between the means of two independent groups.

In order for the two-sample test for means with independent samples to be appropriate, the following conditions/assumptions must be met:

Independent samples: The samples for each group should be selected independently of each other.

Normality: The population distributions should be approximately normal, or the sample sizes should be large enough (n > 30) for the central limit theorem to apply.

Equal variances: The variances of the two populations should be approximately equal. This assumption is important for calculating the pooled variance estimate, which is used in the t-test formula.

Random sampling: The samples should be randomly selected from the populations of interest.

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Answer:

x = 15

Step-by-step explanation:

Since the triangles are similar, then the ratios of corresponding sides are equal, that is

\(\frac{9}{3}\) = \(\frac{x}{5}\) ( cross- multiply )

3x = 45 ( divide both sides by 3 )

x = 15

a) The total number of four-card sequences without any restrictions, allowing replacement, is 6,497,416. b) The number of four-card sequences in which none of the cards can be spades, allowing replacement, is 231,344,376. c) The number of four-card sequences in which all four cards are from the same suit, allowing replacement, is 43,264. d) The number of four-card sequences where the first card is an ace and the second card is not a king, allowing replacement, is 665,856.

a) If there are no restrictions, each card can be chosen independently from the deck. Since there are 52 cards in the deck and replacement is allowed, there are 52 choices for each of the four cards. Therefore, the total number of four-card sequences is 52⁴ = 6,497,416.

b) If none of the cards can be spades, there are 39 non-spade cards in the deck (since there are 13 spades). For each card in the sequence, there are 39 choices. Therefore, the total number of four-card sequences without any spades is 39⁴ = 231,344,376.

c) If all four cards are from the same suit, there are four suits to choose from. For each card in the sequence, there are 13 choices (since there are 13 cards of each suit). Therefore, the total number of four-card sequences with all cards from the same suit is 4 * 13⁴ = 43,264.

d) If the first card is an ace and the second card is not a king, there are 4 choices for the first card (since there are 4 aces in the deck) and 48 choices for the second card (since there are 52 cards in the deck, minus the 4 kings). For the remaining two cards, there are 52 choices each. Therefore, the total number of four-card sequences satisfying this condition is 4 * 48 * 52² = 665,856.

e) To calculate the number of four-card sequences with at least one ace, we can subtract the number of sequences with no aces from the total number of sequences. The number of sequences with no aces is (48/52)⁴ * 52⁴ = 138,411. Therefore, the number of sequences with at least one ace is 52⁴ - 138,411 = 6,358,005.

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