-
Evaluate the following expression
22 - 53 +3

Answer:

400x45.2=18080

Step-by-step explanation:

The complete compound inequality is 9 <= 1.5x <= 12

From the given figure, we have'

Height = x

Base = 3

The area of a triangle is

Area = 0.5 * Base * Height

So, we have

A = 0.5 * 3 * x

Evaluate

A = 1.5x

The compound inequality is given as

9 <= A <= 12

Substitute A = 1.5x in 9 <= A <= 12

9 <= 1.5x <= 12

Hence, the complete compound inequality is 9 <= 1.5x <= 12

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Answer:24-25a

Step-by-step explanation:

Answer:

a. x = 82 degrees

b. All angles less than 90 degrees are 65 degrees and 33 degrees and 82 degrees in an acute triangle.

Step-by-step explanation:

A triangle has to equal to 180 degrees, add 65 and 33 together to get 98 degrees, subtract 180 from 98 to get 82 degrees.  Part B is self explanatory.

This algebraic expression represents the same mathematical relationship as the original English phrase.

To translate the English phrase "the quotient of the product of 6 and 6r, and the product of 8s and 4" into an algebraic expression, we need to first identify the mathematical operations involved and then convert them into symbols.

The phrase is asking us to divide the product of 6 and 6r by the product of 8s and 4. In mathematical terms, we can represent this as:

(6 × 6r) / (8s ×4)

Here, the symbol "*" represents multiplication, and "/" represents division. We multiply 6 and 6r to get the product of 6 and 6r, and we multiply 8s and 4 to get the product of 8s and 4. Finally, we divide the product of 6 and 6r by the product of 8s and 4 to get the quotient.

We can simplify this expression by dividing both the numerator and denominator by the greatest common factor, which in this case is 4. This gives us the simplified expression:

(3r / 2s)

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The English phrase "the quotient of the product of 6 and 6r, and the product of 8s and 4" can be translated into an algebraic expression as follows: (6 * 6r) / (8s * 4)

Let's break down the expression:

Therefore, the complete expression becomes: 36r / 32s

In this expression, the product of 6 and 6r is calculated first, which is 36r. Then the product of 8s and 4 is calculated, which is 32s. Finally, the quotient of 36r and 32s is calculated by dividing 36r by 32s.

This expression represents the quotient of the product of 6 and 6r and the product of 8s and 4. It signifies that we divide the product of 6 and 6r by the product of 8s and 4.

In algebra, it is important to accurately represent verbal descriptions or phrases using appropriate mathematical symbols and operations. Translating English phrases into algebraic expressions allows us to manipulate and solve mathematical problems more effectively.

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The total amount it costs Jeff and Valerie to fill up their vehicles.

The correct option is D.

bx is most likely the amount it costs Jeff and Valerie to fill up their cars because they both pay x dollars per gallon.

Ay = Megan Bx

= Valerie and Jeff

Ay + Bx = Megan + Valerie and Jeff

Algebra is a field of mathematics that assists in the depiction of problems or situations using mathematical expressions. To produce a meaningful mathematical expression, variables like as x, y, and z are used, as well as mathematical operations such as addition, subtraction, multiplication, and division.

Working from left to right, first complete multiplication and division, then addition and subtraction.

The principles of algebra include numbers, variables, constants, expressions, equations, linear equations, as well as quadratic equations.. It also includes basic mathematical operations such as addition, subtraction, multiplication, and division within algebraic equations.

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Answer:

660000

Step-by-step explanation:

The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

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0.0945 (approx)  is the probability that exactly 12 of them are strikes.

p(x=12)

nC12(p)12 (q) (n-12)

22C12 (0.431)12 (0.569)(22-12)

=646646(0.431)12 (0.569)10

=0.094518

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.

The probability of an event can be calculated by simply dividing the number of favorable outcomes by the total number of possible outcomes using the probability formula.

probability = number of paths to success—a total number of possible outcomes. For example, the probability of flipping a coin and getting heads is ½. This is because there is one way to get heads and the total number of possible outcomes is 2 (heads or tails). We write P(heads) = ½.

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The monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

To calculate the monthly mortgage payment, we can use the formula for calculating the fixed monthly payment for a fully amortizing loan. The formula is: M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly mortgage payment

P = Principal balance

r = Monthly interest rate (annual interest rate divided by 12 and converted to a decimal)

n = Total number of monthly payments (loan term multiplied by 12)

Plugging in the given values into the formula:

P = $100,000

r = 0.05/12 (5% annual interest rate divided by 12 months)

n = 30 years * 12 (loan term converted to months)

M = 100,000 * (0.004166667 * (1 + 0.004166667)^(3012)) / ((1 + 0.004166667)^(3012) - 1)

M ≈ $536.82

Therefore, the monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

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Answer:

Step-by-step explanation:

\(10t^-5 = 10/t^5\)

The value of  10\(t^{-5\) in positive power is 10/ \(t^5\).

The base number is the number that is being multiplied by itself an infinite number of times, and the exponent is the number of times that it is being multiplied. The nth power of the given number is an expression that results from multiplying a given number by itself n times.

We have,

Expression: 10\(t^{-5\)

We know to make the power positive we have to reciprocate the number.

Now, using exponents we get

\(a^{-m}= 1/a^m\)

So,  10\(t^{-5\)

=  10/ \(t^5\)

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Answer:

y+2=1/2(x+3)

Why?

Point slope form is written as (y-y1) = m(x-x1) with y1 being the value of y at a certain point, x1 being the value of x at a certain point, and m being slope. y1 and x1 are given to us by the point (-3, -2) letting us know that y1=-2 and x1=-3. The only thing left to find is slope. Parallel lines have the same slope. If the line we are trying to find is parallel to the one given in the question, we just need to find the slope of the equation given. That equation is given in slope-intercept form which is y = mx + b. m is still slope so we can see that the slope is 1/2. Now we can plug m, x1 and y1 into the point slope form equation to get y + 2 = 1/2(x + 3)

Answer:

8

Step-by-step explanation:

When you add it together, you get 8.

Answer:

pt 1 is 3/5

Step-by-step explanation:

cuz i know

Answer:

Step-by-step explanation:

1. 60%

2.  First one takes 3 hours

second one takes 3 hours

Third one does not take three hours

forth one takes 3 hours

fifth one does not take three hours

3. I'm not sure about this one but i think the trip is 20 miles away.

The probability of getting four consecutive heads in four 2-sided coin tosses is 1/16 or 0.0625 or 6.25%.

The Probability is defined as a measure of the likelihood or chance that an event will occur, expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty.

To calculate the probability of getting four consecutive heads in a row, we multiply the probabilities of each individual toss.

The Probability of heads (H) is = 1/2,

So, The Probability of four consecutive heads (HHHH) is :

= (1/2) × (1/2) × (1/2) × (1/2) = (1/2)⁴ = 1/16,

Therefore, the required probability is 1/16 or 6.25%.

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Answer:        

f(x) ≥ 7

g(x): neither even or odd

Step-by-step explanation:

Answer:

864 square inches

Step-by-step explanation:

To find surface area, you need to find the area of each face of the cube.

Since all faces of a cube are equal in size, we just need to find the area of one face and multiply it by 6, since there are 6 faces.

So, let's find the area of one of the faces

The length is 12 inches, and since it is a square, the other sides are the same length.

To find the area, we multiply length times width

12 x 12 = 144

Since there are 6 faces, we need to multiply 144 by 6

100 x 6 = 600

40 x 6 = 240

6 x 4 = 24

600 + 240 + 24 = 864

864 square inches

Answer:

La porción de la casa que le corresponde pintar a Alan es \(\frac{13}{72}\)

Step-by-step explanation:

Sabes que Alejandro pinta 3/8 de la casa durante el primer día, mientras que Alberto pinta 4/9 de la casa durante el segundo día. Entonces, la porción pintada de la casa durante esos dos días es la suma entre la porción pintada por Alejandro y la porción pintada por Alberto:

\(\frac{3}{8} +\frac{4}{9}\)

Un método para sumar fracciones con distinto denominador consiste en buscar el común denominador de las fracciones que se van a sumar. Para ello se multiplica los denominadores de las fracciones: 8*9= 72. El común denominador se divide entre el denominador de la primera fracción.   El resultado de la división se multiplica por el numerador de la misma fracción. Una vez que se divide y se multiplica, el resultado se coloca en el numerador con el signo correspondiente. Se realiza el mismo procedimiento con la otra fracción y se realiza la suma con los numeradores resultantes.

Entonces, en este caso se obtiene:

\(\frac{3}{8} +\frac{4}{9}=\frac{27+32}{72} =\frac{59}{72}\)

Entonces, para calcular la porción de la casa que le corresponde pintar a Alan, y considerando que 1 representa un entero, la totalidad de la casa que se desea pintar, se realiza la resta entre la totalidad de la fachada a pintar y la porción pintada por Alejandro y Alberto:

\(1-\frac{59}{72}\)

Considerando que el procedimiento de la resta es similar a la suma, se obtiene:

\(1-\frac{59}{72}=\frac{72-59}{72} =\frac{13}{72}\)

La porción de la casa que le corresponde pintar a Alan es \(\frac{13}{72}\)

Answer:

The distributive property

Step-by-step explanation:

You have to distribute the 3 to the parenthesis so it is the distributibe property.

The rate of change of the area of the square when the side length is 7cm is  112 .

In the question ,
it is given that

the decreasing rate of the side length of the square is 8 cm per second ,

let the side length of the square be =  "\(s\)" .

So , ds/dt = -8 cm/s

the formula for area of \(s\)quare is ,

area = side²

A = s²

On differentiating both sides with respect to \(t\) ,

we get

dA/dt = 2s*ds/dt

Since we have to find rate of change of area when the side length is 7 cm ,

we substitute s = 7 , and ds/dt is given as  -8 cm/s

On substitution of values , we get

dA/dt = 2(7)*(-8)

= 14*(-8)

= -112

the negative sign in the answer means that the area is decreasing .

Therefore , The rate of change of the area of the square when the side length is 7cm is 112  .

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The statement is proven true by induction: for any positive integer n, the sum of (2i - 1)³ from i = 1 to n is equal to n²(2n² - 1).

To prove the statement using mathematical induction, we need to establish two conditions: the base case and the inductive step.

Base Case:

Let's start with the base case, where n = 1.

When n = 1, we have p₁ ∑ (2i - 1)³ = 1³ = 1.

On the right-hand side, we have 1 * (2 * 1² - 1) = 1.

Since the statement holds true for n = 1, the base case is satisfied.

Inductive Step:

Next, we assume that the statement holds true for some positive integer k, i.e., pₖ ∑ (2i - 1)³ = k²(2k² - 1).

Now, we need to prove that the statement also holds for n = k + 1, i.e., pₖ₊₁ ∑ (2i - 1)³ = (k + 1)²(2(k + 1)² - 1).

Starting with the left-hand side:

pₖ₊₁ ∑ (2i - 1)³ = (pₖ ∑ (2i - 1)³) + (2(k + 1) - 1)³

                 = k²(2k² - 1) + (2k + 1)³ (using the inductive hypothesis)

                 = 2k⁴ - k² + 8k³ + 12k² + 6k + 1

Simplifying the right-hand side:

(k + 1)²(2(k + 1)² - 1) = (k² + 2k + 1)(2k² + 4k + 2 - 1)

                         = 2k⁴ + 4k³ + 2k² + 4k³ + 8k² + 4k + 2k² + 4k + 2 - k² - 2k - 1

                         = 2k⁴ + 8k³ + 12k² + 6k + 1

Comparing the left-hand side and right-hand side, we can see that they are equal.

Therefore, by the principle of mathematical induction, the statement is proven true for all positive integers n.

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a) No, a single spray of 10 grams of butter would not be enough to entirely cover the area of 4 slices of toast at 2 meters. The area of 4 slices of toast is larger than the area of 1 slice of toast, meaning that it would require more butter than 10 grams to cover the entire area.

b) A single spray of 10 grams of butter would be enough to cover the area of 8 slices of toast at 3 meters.

c) These changes would affect the amount of butter on each piece of toast in that there would be more butter on each piece with a larger rack and further distance from the "butter gun".

d) At 5 meters from the gun, our up-and-coming chef would be able to spray 16 slices of toast with a single burst of 10 grams of butter. Each piece of toast would also have more butter than it would if it was sprayed at a closer distance.

e) To duplicate the original single-slice toast at 5 meters from the gun, the chef would need to reduce the amount of butter being sprayed. He could do this by simply reducing the distance between the gun and the toast rack.

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Complete question :

A harried chef can't keep up with his breakfast orders and decides to automate the process with a "butter gun." The gun provides a 10 gram burst of butter spray with each hit of the trigger. He starts with a rack that holds one piece of toast 1 meter away. The demand again exceeds supply and he realizes he can use the same gun to produce more toast by placing a larger rack at a greater distance. He finds that a four-slice rack works at a distance of 2 meters. Pleased with profits he carries the idea a step further and puts a holder 3 meters away, maintaining a 10 gram spray. See figure below.a) If 1 spray entirely covers the area of a single slice at 1 meter, can it entirely cover the area of 4 slices at 2 meters? Why or why not?b) How many slices can one spray cover with a 3 meter arragnement?c) How do these changes affect the amount of butter on each piece of toastd) Our up-and-coming chef moves the fun back to 5 meters. Predict how much toast he can spray and how much better each piece gets.e) Explain how he could duplicate the original single-slice toast at 5 meters from the gun.

The answer is B part

As the requirement for the student is either a senior or one who studies maths or both.

So, just add the values within the two venn circles divide it by total no of values.

=> 240+40+110/240+40+110+840

=> 360/1200

Answer:

B

Step-by-step explanation:

840 people aren't senior or don't takes math.

210 + 40 = 250 are seniors

110 + 40 = 150 people take math

In this class has 840 + 210 + 40 + 110 = 1200 people => All

210 + 40 + 110 = 360 people are seniors or take math. => P( S U M)

Probabilty that a randomly selected student is a senior or takes math =>\(\frac{P(S U M)}{All}\)

\(\frac{P(S U M)}{All} = \frac{360}{1200}\)

Hope this helps ^-^

Answer: D.

Step-by-step explanation:

The way to know if it is “greater than or equal to” opposed to jsut greater than is to look at the dot. If it is filled in it is “equal to” if not it isn’t.

\(\\ \sf\longmapsto 3y=z-2x\)

\(\\ \sf\longmapsto -2x=3y-z\)

\(\\ \sf\longmapsto 2x=-3y+z\)

\(\\ \sf\longmapsto 2x=z-3y\)

\(\\ \sf\longmapsto x=\dfrac{z-3y}{2}\)

Answer:

\( x = \frac{z - 3y}{2} \)

Step-by-step explanation:

Question :

\(3y = z - 2x\)

First take 2x to the left to make the 2x as a positive number (So, It's easy to solve)

\(3y + 2x = z\)

Then take 3y to the right side

\(2x = z - 3y\)

Now, divide both sides by 2 to make the x as the Subject

\( \frac{2x}{2} = \frac{z - 3y}{2} \\ x = \frac{z - 3y}{2} \)

hope this helps you.

Please let me know if you have another questions :-)

To find the percentage of observations that fall between 16 and 24, we can use the standard normal distribution table to convert these values to standard units and then find the corresponding cumulative probability.

First, we convert the values to standard units by subtracting the mean of 20 and dividing by the standard deviation of 2:

$16 \rightarrow (16-20)/2 = -2$

$24 \rightarrow (24-20)/2 = 2$

Next, we look up the cumulative probability for $-2$ and $2$ in a standard normal distribution table, which gives us 0.0228 and 0.9772, respectively.

The percentage of observations between 16 and 24 is equal to the difference between these two probabilities, which is $0.9772 - 0.0228 = 0.9544$, or 95.44%. So, approximately 95.44% of the observations fall between 16 and 24.

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a)  the magnitude of the static frictional force is approximately 358.17 N.

b)  the maximum force that needs to be applied before the refrigerator starts to move is approximately 358.17 N.

To determine the static frictional force exerted by the floor on the refrigerator, we can use the equation:

Static Frictional Force = Coefficient of Static Friction * Normal Force

(a) Magnitude of Static Frictional Force:

The normal force exerted by the floor on the refrigerator is equal in magnitude and opposite in direction to the weight of the refrigerator. The weight can be calculated using the formula: Weight = mass * gravitational acceleration. In this case, the mass is 58 kg and the gravitational acceleration is approximately 9.8 m/s².

Weight = 58 kg * 9.8 m/s²= 568.4 N

The magnitude of the static frictional force is given by:

Static Frictional Force = Coefficient of Static Friction * Normal Force

                      = 0.63 * 568.4 N

                      ≈ 358.17 N

Therefore, the magnitude of the static frictional force is approximately 358.17 N.

Direction of Static Frictional Force:

The static frictional force acts in the opposite direction to the applied force, which is in the negative x direction (as stated in the problem). Therefore, the static frictional force is in the positive x direction.

(b) Maximum Force Required to Overcome Static Friction:

To overcome static friction and start the motion of the refrigerator, we need to apply a force greater than or equal to the maximum static frictional force. In this case, the maximum static frictional force is 358.17 N. Thus, to move the refrigerator, a force greater than 358.17 N needs to be applied.

Therefore, the maximum force that needs to be applied before the refrigerator starts to move is approximately 358.17 N.

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