The question is.. "The expression 5(3r - 10) means the product of 5 and the difference of three times r minus 10. If r = 4, the value of the expression is [?] This is 6th grade math and im kinda stuck here

Answer:

The length is 5 meters and the width is 3 meters.

Step-by-step explanation:

The dimensions of the rectangle are 5 meters by 3 meters.

Let's say the length of the rectangle is l and the width is w. We are given that w = l - 2 and lw = 15.

We can substitute the first equation into the second equation to get:

l(l - 2) = 15

This simplifies to:

\(l^2\) - 2l - 15 = 0

We can factor this equation to get:

(l + 3)(l - 5) = 0

This means that either l = -3 or l = 5.

Since the length of a rectangle cannot be negative, we know that l = 5.

Substituting this value back into the equation w = l - 2, we get:

w = 5 - 2 = 3

Therefore, the dimensions of the rectangle are 5 meters by 3 meters.

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The schedule for the number of hours worked by employees at Waterloo Park is represented by the functions b(x), t(x), r(x), and s(x) for Bill, Ted, Rufus, and Socrates, respectively, on a given day x.

In the schedule, the function b(x) represents the number of hours worked by Bill on a given day x. Similarly, the function t(x) represents the number of hours worked by Ted, the function r(x) represents the number of hours worked by Rufus, and the function s(x) represents the number of hours worked by Socrates on the same given day x.

By using these functions, you can determine the specific number of hours each employee worked on any given day. For example, if you have a value for x, you can substitute it into the functions to find the corresponding number of hours worked by each employee.

It's important to note that the functions b(x), t(x), r(x), and s(x) are specific to Waterloo Park and the employees mentioned. The given schedule provides a way to track the hours worked by each employee on different days. By utilizing these functions, you can analyze and calculate the hours worked by each employee effectively.

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Answer:

12

Step-by-step explanation:

See attachment for step-by-step instructions

By applying the Triangle Inequality Theorem, the number of non-identical triangles that can be made using the given side lengths is one.

In Mathematics, the Triangle Inequality Theorem can be defined as a type of theorem which states that the sum of any two (2) side lengths of a triangle must be greater than the measure of the third (2) side.

This ultimately implies that, the sum of the lengths of any two (2) sides of a triangle cannot be less than the length of the third (3) side of the triangle in accordance with the Triangle Inequality Theorem, as represented by this mathematical expression:

b - c < a < b + c

Where:

a, b, and c represent the side lengths of this triangle.

By applying the Triangle Inequality Theorem to the side lengths of this triangle, the number of non-identical triangles is given by:

5 + 7 > 10

12 > 10 (True).

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Given the function:

`f(x) = x^2 - 8/x`

and find its inverse

`(f^-1(x))` when `x ≤ 0`

To find the inverse of the function, we first write `y` in place of `f(x)`.i.e.

`y = x^2 - 8/x`

Now, we interchange `x` and `y` to get:

`x = y^2 - 8/y

Next, we solve this equation for `y`.`

\(x = y^2 - 8/y\)

Multiply both sides by

\(`y`.y × x = y × y^2 - 8y\)

Simplify.

y^3 - xy - 8 = 0

Solve for `y` using the formula for a quadratic equation.

`y = [-(-xy) ± √((-xy)^2 - 4(1)(-8))]/(2 × 1)`

Simplify.\(`y = [xy ± √(x^2y^2 + 32)]/2`\)

Therefore,

\(`f^-1(x) = [xy ± √(x^2y^2 + 32)]/2` for `x ≤ 0`. Answer: `f^-1(x) = [xy ± √(x^2y^2 + 32)]/2`.\\\)

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Answer:

dy/dx= 7- 3x^-1/2

when X=1

dy/dx = 4

as it is a tangent M1=M2=4

now,

at gradient 4 and point (1,1)

equation of curve is ,

y-y1= m(x-x1)

or, y-1=4(x-1)

or, y-1=4x-4

or, y-4x= -3

or, 4x-y=3

Answer:

BRAINLEST ANSWER

Step-by-step explanation:

dy/dx=7-3x^-1/2

when x=1

Dy/dx=4

as it is a tangent M1=M2=4 now

at gradient 4 and point(1,1) equation of a curve is y-y1=m(x-x1)

or y-1=4(x-1)

or y-1=4x-4

or y-4x=-3

or 4x-y=3

The area of one side of the rectangular wooden board is (210.92±8.18) cm². The uncertainty in the area is ±8.18 cm². If the thickness of the board is (1.1±0.2) cm, the volume of the board is (230.96±13.08) cm³. The uncertainty in the volume is ±13.08 cm³.

To find the area of one side of the rectangular wooden board, we multiply the length and width of the board. Given the length as (21.4±0.4) cm and the width as (9.8±0.1) cm, we perform the calculation as follows:

Area = Length × Width

= (21.4 cm) × (9.8 cm)

= 209.72 cm²

To determine the uncertainty in the area, we consider the maximum and minimum values of length and width:

Maximum area = (21.4 + 0.4) cm × (9.8 + 0.1) cm = 22.8 cm × 9.9 cm = 225.72 cm²

Minimum area = (21.4 - 0.4) cm × (9.8 - 0.1) cm = 20.8 cm × 9.7 cm = 201.76 cm²

The uncertainty in the area is half the difference between the maximum and minimum values:

Uncertainty in area = (225.72 cm² - 201.76 cm²) / 2 = 8.18 cm²

Therefore, the area of one side of the rectangular wooden board is (210.92±8.18) cm², with an uncertainty of ±8.18 cm².

Moving on to the volume calculation, we multiply the area of one side by the thickness of the board. Given the thickness as (1.1±0.2) cm, the volume can be determined as follows:

Volume = Area × Thickness

= (210.92 cm²) × (1.1 cm)

= 231.01 cm³

To find the uncertainty in the volume, we again consider the maximum and minimum values of the thickness:

Maximum volume = (210.92 cm²) × (1.1 + 0.2) cm = 210.92 cm² × 1.3 cm = 273.20 cm³

Minimum volume = (210.92 cm²) × (1.1 - 0.2) cm = 210.92 cm² × 0.9 cm = 189.83 cm³

The uncertainty in the volume is half the difference between the maximum and minimum values:

Uncertainty in volume = (273.20 cm³ - 189.83 cm³) / 2 = 13.18 cm³

Therefore, the volume of the board is (230.96±13.08) cm³, with an uncertainty of ±13.08 cm³.  

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Answer:

x =-18

Step-by-step explanation:

5(x + 9) = -45

Divide each side by 5

5/5(x + 9) = -45/5

x+9 = -9

Subtract 9 from each side

x+9-9 = -9 -9

x =-18

Answer:

The correct answer is x = -1.

Step-by-step explanation:

Step 1: 5(x + 9) = -45 <----- This is the original problem.

Step 2: 5(9x) = -45 <----- Add the variable.

Step 3: \(\frac{5(9x)}{5} = \frac{-45}{5}\) <----- Divide both sides by 5.

Step 4: 9x = -9 <----- Simplify

Step 5: 9x/9 = -9/9 <----- Divide both sides by 9.

            x = -1

Hope this helps! :D

Answer:

2/3+1/9 =7/9

Step-by-step explanation:

u are looking for the lcm of 3 and 9 and then u divide the denominator and mutiply the numerator to get the answer

Answer:

x = 19 1/3

Step-by-step explanation:

6/14 = 7/(x-3)

Using cross products

6 * (x-3) = 7*14

6x -18 = 98

Add 18 to each side

6x-18+18 =98+18

6x = 116

Divide each side by 6

6x/6 = 116/6

x =58/3

x = 19  1/3

Answer= 58/3

Step by Step

Step 1: Cross-multiply.

6*(x−3)=(7)*(14)

6x−18=98

Step 2: Add 18 to both sides.

6x−18+18=98+18

6x=116

Step 3: Divide both sides by 6.

6x /6 = 116 /6

x= 58 /3

Linear functions are used to represented straight lines.

The linear function is \(y = -\frac 12x + 1\)

The points on the graph are: (2,0) and (0,1)

Start by calculating the slope (m) using:

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

Substitute values for x and y

\(m = \frac{1 - 0}{ 0 -2}\)

\(m = \frac{1 }{ -2}\)

Rewrite as:

\(m = -\frac{1 }{2}\)

The equation is then calculated as:

\(y = m(x - x_1) + y_1\)

This gives

\(y = -\frac 12(x -0) + 1\)

\(y = -\frac 12(x) + 1\)

Open bracket

\(y = -\frac 12x + 1\)

Hence, the linear function is \(y = -\frac 12x + 1\)

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Binomial squared:

\(\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}\)

\(\\ \sf\longmapsto \left(\dfrac{3+4}{2},\dfrac{-9+8}{2}\right)\)

\(\\ \sf\longmapsto \left(\dfrac{7}{2},\dfrac{-1}{2}\right)\)

Answer:

y = 3/2x

Step-by-step explanation:

it seems what they are asking for here is our slope.

To find this, we must figure out the change in  y over the change in x.

This can be viewed as:

Δy/Δx = slope

In this case, we can see that the line crosses at (4,6), and at (0,0)

Since our y changes by 6, and our x changes by 4, our slope is:

6/4 = slope

Or:

3/2 = slope

So your answer is 3/2x.

Hope this helps!

It is instructed that we change 44.0 gallons to liters. One gallon is one unit of volume. A gallon is equivalent to 3.785 liters.

3.785411784 litres make to one US gallon. 4 quarts, 8 pints, or 128 fluid ounces make up a gallon. In American measurements, a gallon is equivalent to 3.785 litres, 128 fluid ounces, 4 quarts, 8 pints, or 16 cups. A gallon's volume is about equivalent to 3.78541 litres. Thus, a gallon is more than three litres. A gallon of one liquid could weigh differently than a gallon of another. As one imperial gallon is equal to 4.54609 litres, it takes up space that is nearly 4,546 cubic centimetres (roughly a 16.5cm cube). An average glass holds eight ounces. So, 16 eight-ounce glasses of water make up a gallon.

44.0 gallons to 3.785 liters.

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The probability that at least one of them lives more than 87 minutes is 0.87.

Probability

In statistics, the possible way of happening a particular event is called probability.

Given,

Suppose that an experimenter studies the lifespan of members of a colony of bacteria. let t be the lifespan of a randomly chosen member of the colony. suppose the lifespan of the bacteria has an exponential distribution with expected value 100 minutes.

Here we need to find if we choose 5 members of the colony, then what is the probability that at least one of them lives more than 87 minutes.

Here we know that,

Total number of members = 5

Life span = 87 minutes

Expected value = 100 minutes

So, the probability is calculated as,

=> 87 /100

=> 0.87

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Answer:

Check your question well

Step-by-step explanation:

U didn't ask to draw angle p so how can we get the angle r

The radius of the spherical part is 3 inches and the length of the tube is 21 cm.

The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.

Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.

The two equations can be formed as below:-

4554 / 7 = πr²l + (2/3)πr³

396 = πr²( l - 9 ) + (2/3)πr³

Subtract the second equation from the first,

( 4554 / 7 ) - 396 = 9πr²

9πr² = 254.5

r² = 9

r = 3 cm

The length will be calculated as:-

4554 / 7 = πr²l + (2/3)πr³

4554 / 7 = π( 3 )²l + (2/3)π(3)³

l = 21 cm

Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.

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Using the graph and function concepts, it is found that:

a) The domain is \([-5,4]\), while the range is \([-2,-5]\)

b) The function is increasing in \([0,1]\) and \([2,3]\), and decreasing \([-5,0], [1,2]\), and \([3,4]\).

--------------------

--------------------

Item a:

--------------------

Item b:

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Answer:

$72 is the retail price

Step-by-step explanation:

100 x (100-28)/100

Answer:

Yes

Step-by-step explanation:

y is the litters of water in the tank

x is the time in minutes

m is the change in litters

b is the initial amount of water

so the formula is y = mx + b

whereas m is -14 and b is 770

y = -14x + 770 or y = 770 - 14x

since the population standard deviations (σ1 and σ2) are not provided, we cannot calculate the exact test statistic Z.

To test the null hypothesis H0: (μ1 - μ2) = 0 versus the alternative hypothesis Ha: (μ1 - μ2) ≠ 0, we can use a two-sample z-test. The test statistic is calculated as:

Z = (x bar1 - x bar2) / sqrt((σ1^2 / n1) + (σ2^2 / n2))

Where:
X bar1 and x bar2 are the sample means of the two groups,
σ1 and σ2 are the population standard deviations of the two groups,
n1 and n2 are the sample sizes of the two groups.

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Answer:

m ∠J = 45°; m ∠K = 135°

Step-by-step explanation:

In a parallelogram the opposite angles are congruent and consecutive angles are supplementary.

m ∠H ≅ m ∠J    in a parallelogram opposite angles are congruent.

 45° = 45°

m ∠H and m ∠K are supplementary

m ∠H + m ∠K = 180°       Definition of supplementary

 45° + m ∠K = 180°

         m ∠K = 180 - 45

         m ∠K = 135°

Answer:

xxxxxxxxxxxxxxxxxxdddddddddddddddddddddddd

Step-by-step explanation:

Answer:

c 14 marbles

Step-by-step explanation:

Answer:

its c 14

Step-by-step explanation:

When both groups are shifted to a situation in which they earn an alternative reward after being trained to navigate a runway for food, the group that received three food pellets will continue to perform the task at a high level while the group that received one food pellet will experience difficulty.

It is known that rats have a natural preference for higher rewards. As a result, the group that received three pellets will be more motivated to complete the task since they have already tasted a higher reward. Therefore, they will continue to perform at a high level in the new environment.

On the other hand, the group that received only one pellet may find it challenging to adapt to the new situation since they are now receiving a lower reward. As a result, they may struggle to complete the task, and their performance may decrease.

In conclusion, the group that received three pellets will perform better than the group that received one pellet when both groups are shifted to a situation in which they earn an alternative reward. This is because the rats have a natural preference for higher rewards.

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The expected value of this gamble is $1.

The expected value of this gamble is the weighted average of all possible outcomes where the weights are the probabilities of each outcome happening.

The formula for expected value (EV) is as follows:

          Expected Value = (Probability of Winning × Amount Won) − (Probability of Losing × Amount Lost)

Hence, substituting the values:

          Expected Value = (0.5 × $10) − (0.5 × $8)

          Expected Value = $5 - $4

          Expected Value = $1

Therefore, the expected value of this gamble is $1.

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The equation of the parabola is y = -5x^2 + 3

The points and the vertex represent the given parameters

From the question, we can see that the equation is a parabola

A parabola function is represented as

y = a(x - h)^2 + k

Where

Vertex = (h, k)

Point = (x, y)

From the question, we have

Vertex = (h, k) = (0, 3)

Point = (x, y) = (1, -2)

So, we have

y = a(x - 0)^2 + 3

Evaluate

y = ax^2 + 3

Using the point, we have

-2 = a(1)^2 + 3

This gives

a = -5

So, we have

y = ax^2 + 3

y = -5x^2 + 3

Hence, the equation is y = -5x^2 + 3

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According to the combination method, the number of elements in the sample space for this experiment is 3060

Combination method:

Basically, the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter

Given,

A person eating at a cafeteria must choose 4 of the 18 vegetables on offer.

Here we have to calculate the number of elements in the sample space for this experiment.

While we looking into the given question, we have identified the following things,

They are

Total number of available vegetables = 18

Number of choices we have made = 4

Therefore, here the value of n = 18 and the value of x = 4,

Therefore, according to the ncx formula, it can be written as,

=> ¹⁸n₄ = 18! / 4! (18 - 4)!

=> ¹⁸n₄ = 18! / 4! (14)!

=> ¹⁸n₄ = 3060.

Therefore, there are 3060 number of elements in the sample space for this experiment.

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The quadratic equation is solved as;

2x² + 5x - 12 = 0

2x² + 8x - 3x - 12 = 0

2x(x + 4) - 3(x + 4) = 0

x: -4 and 3/2

From the information given, we have that the quadratic equation is;

2x² + 5x = 12

Equate the quadratic equation to zero, we have;

2x² + 5x - 12 = 0

Now, find the product of the coefficient of x² and -12. Then, find the pair factors of the value that sum up to 5, we have;

-8 and 3

Substitute the values

2x² + 8x - 3x - 12 = 0

Factorize the expressions in pairs, we get;

2x(x + 4) - 3(x + 4) = 0

Then, we have;

2x - 3 = 0

x = 3/2

and

x + 4 = 0

x = -4

x: -4 and 3/2

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