A piece of cheese is shaped like a triangle. It has a height of 2.5 inches and a base that is 4.75 inches long. If 1 inch = 2.54 centimeters, find the area of the cheese in square centimeters. Round the answer to the nearest square centimeter. Please answer this thank you!

The amount of margarine needed in Kg for making biscuits is  0.6kg

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.

The amount of margarine needed in Kg is calculated using proportions

If 225 ml or soup requires 150 g of margarine then 0.9 liters of soup will require

0.225 l  = 0.15 kg

0.9 l = ?

cross multiplying

0.225 * ? = 0.9 * 0.15

? = 0.135 / 0.225

? = 0.6

Angela will require 0.6 kg of margarine

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The equation of the line, in slope-intercept form,  that passes through the given points, (6,-4) and (6,5) is: x = 6.

An vertical line can be written in slope-intercept form as x = a, because the line has no y-intercept and the change in x values in the slope formula is equal to zero.

The value of a in the equation is the point on the x-axis where the vertical line intercept, irrespective of the change in y-values up the line.

Given the line goes through the points, (6, -4) and (6, 5), it means the line is a horizontal line because they both have the same x-value, 6.

Therefore, the value of a is 6. The equation of the line would be x = 6.

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The formula for the cumulative probability of a Poisson distribution can be used to calculate the likelihood that there will be at most 2 reported car accidents over the course of a month:

Cumulative probability is equal to (number of events * e)/(average number of events per time period).

(Number of events / (-average number of events per time period)!)

In this instance, there are typically 0.05 events per time period (the likelihood that a car accident is reported at the intersection on any given day), and there are typically between 0 and 2 events per time period (at most 2 car accidents). With these values entered into the formula, we obtain:

Cumulative probability is equal to (0.05 * e(-0.05)) / 0, (0.05 * e(-0.05)) / 1, and (0.05 * e(-0.05)) / 2, respectively.

That amounts to:

Probability total = 1 + 0.05 + 0.0025

which translates to 1.0525 percent, or 105.25%. It's crucial to keep in mind that this probability exceeds 1, which is impossible. This is because the formula for cumulative probability makes the assumption that each event is independent, which means that the occurrence of one event has no bearing on the probability of the occurrence of another. The cumulative probability calculated using this formula may not accurately reflect the probability of at most 2 car accidents occurring throughout a month because in reality, the probability of a car accident occurring on a given day may be influenced by the number of car accidents that have already occurred. You would need to account for the dependencies between the events in order to calculate this probability precisely.

Dependent variable: t (total cost of the pizza)

Independent variable: x (number of extra toppings)

Equation: t = 10.50 + 1.50x

To determine the total cost of the pizza with 3 extra toppings, plug in x = 3 into the equation:

t = 10.50 + 1.50(3)

t = 10.50 + 4.50

t = 15.00

So the total cost of the pizza with 3 extra toppings is $15.00.

What is Dependent Variables?

The dependent variable is the variable that is being measured or studied in a statistical or scientific research study. It is called the dependent variable because it is believed to depend on the value of one or more other variables, known as the independent variables.

What is Independent Variables?

Independent variables are variables that are manipulated or controlled by the researcher in a scientific or statistical study. They are called independent variables because they are believed to have an effect on the dependent variable, which is the variable being measured or studied.

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A product is designed to function for 10,000 hours with a 3% chance of failure , then Average number of failures per hour = 0.03/10000 = 0.000003 and MTTF = 1/0.000003 = 333,333 hours

Given,

Chance Product is designed to function for 10,000 hours

of failure is 3%

To find,

Average number of failures per hour

MTTF

Solution,

Average number of failures per hour = Chance of failure/Total hours of function

= 3%/10000

= 0.03/10000

= 0.000003

MTTF = 1/Average number of failures per hour

= 1/0.000003

= 333,333 hours

The product is designed to function for 10,000 hours with a 3% chance of failure. This means that the average number of failures per hour is 0.000003 and the Mean Time To Failure (MTTF) is 333,333 hours. This means that, on average, the product should last 333,333 hours before it fails.

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The force on the object is 40N

Force can be described as the influence that can change the motion of an object.

It is seen as an external agent having the capability of changing a body's state of motion or rest.

It causes b in velocity of an object with mass , that is,  to accelerate. Force can also be described as either a push or a pull.

It is described as a vector quantity, that is, it has both magnitude and direction.

The formula for determining force is given as;

F = ma

Where;

Substitute the values

F = 10(4)

F = 40N

Hence, the value is 40N

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First:

Quotient: [tex]2x^{2} -11x+58[/tex]

Remainder: [tex]-294[/tex]

Second:

Quotient: [tex]x^{3} -5x^{2} +17x-83[/tex]

Remainder: [tex]422[/tex]

Third:

Quotient: [tex]2x-3[/tex]

Remainder: [tex]12[/tex]

Answer:

(A) 19 times, 16 people.

Step-by-step explanation:

There are 374 people in line and 16 people leave the line without riding, so there are 374 - 16 = <<374-16=358>>358 people who want to ride the Caterpillar.

The Caterpillar seats 18 people, so it must run 358/18 = <<358/18=19.89>>19.89 times to accommodate all the riders.

Since the Caterpillar cannot run a fraction of a time, it must run 19 times.

There are 358 people who want to ride and the Caterpillar can accommodate 19 x 18 = <<19*18=342>>342 of them, so there are 358 - 342 = <<358-342=16>>16 people on the last ride.

Therefore, the Caterpillar runs 19 times and there are 16 people on the last ride, so the answer is (A) 19 times, 16 people.

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Answer:
You sold 15 vegetarian sandwiches and 10 turkey sandwiches.

Step-by-step explanation:

First, let's call the number of vegetarian sandwiches sold "V" and the number of turkey sandwiches sold "T".

We can set up the following equation: 3V + 4T = 85

Next, we need to find the values of V and T that satisfy this equation. To do this, we can use the fact that V and T must be whole numbers since we cannot sell a fraction of a sandwich.

We can start by trying V = 1 and T = 6. Plugging these values into the equation, we get: 3(1) + 4(6) = 18 + 24 = 42

Since 42 is not equal to 85, this means that V and T cannot both be 1 and 6.

We can try other values of V and T that are whole numbers until we find a combination that satisfies the equation. One way to do this is to use trial and error.

For example, we can try V = 2 and T = 5, which gives us: 3(2) + 4(5) = 6 + 20 = 26 This is still not equal to 85, so we can try other values. We can also use the fact that V + T = 25 (since we sold a total of 25 sandwiches) to help us solve the equation.

If we set V + T = 25, then we can rewrite the original equation as: 3V + 4(25 - V) = 85 Solving for V, we get: 3V + 100 - 4V = 85 Combining like terms, we get: -V = 15 Dividing both sides by -1, we get: V = 15

Since V + T = 25, this means that T = 25 - 15 = 10

Therefore, we sold 15 vegetarian sandwiches and 10 turkey sandwiches.

The solution to the first inequality is x ≥ -2. Option 1 is correct. The solution to the second inequality is x ≤ -7. Option 1 is correct.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

The inequalities are,

2( x +6 ) > -6( x +1) +2

2x + 12 > -6x - 6 + 2

2x + 6x > -12 - 6 +2

8x > -16

x > -2

-3x - 1 ≥ 20

-3x ≥ 21

x ≥ -7

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The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).

Here given the inequality.

x + 5y ≤ 30

To find the x-intercepts.

We have to substitute 0 for y and solve x to determine the x-intercepts.

x + 5 × 0 = 30

By solving the equation.

x = 30

( 30, 0 ) is the x-intercepts.

To find the y-intercepts.

By substituting 0 for x and solving y will get the y-intercept(s).

0 + 5y = 30

5y =30

y = 30/5

y = 6

In the point form, y-intercept.

Y-intercept(s): ( 0, 6 )

(30, 0) is the x-intercept.

Y-intercepts at : ( 0, 6 ).

The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).

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Answer:The Flemish giant rabbit weighs 32 pounds.

Step-by-step explanation:

Answer: Y=mx+b

Step-by-step explanation:

A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.

A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.

The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.

Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.

Therefore,

A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

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Answer:

10 years old

Step-by-step explanation:

Answer: The answer is $s$ > 7, which represents the number of seconds that can pass for the temperature in the cryotherapy chamber to drop below -20°F.

Step-by-step explanation: The temperature in the chamber will drop below -20°F when it reaches -20°F + 2.5°F = -17.5°F.

The temperature in the chamber is currently 0°F, so we can represent this situation with the inequality 0 - (2.5 * $s$) < -17.5, where $s$ is the number of seconds that can pass.

We can simplify this inequality by multiplying both sides by -1 to get the following: 2.5 * $s$ > 17.5.

Dividing both sides by 2.5, we get the final inequality: $s$ > 7.

Therefore, the number of seconds $s$ that can pass for the temperature in the cryotherapy chamber to drop below -20°F is greater than 7 seconds.

The function g(x) = (x - 5)² has a translation of 5 units to the right.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over x-axis, (-x, y).

-f(x) = Reflection over y-axis, (x, -y).

The parent function is a quadratic f(x) = x².

Now, The transformed function g(x) = (x - 5)² is a horizontal transformation of 5 units to the right.

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The word problem 4 and one tenth times negative 4 times 5 over 12 have a product of negative 8 and one fifth

Multiplication is one of the basic mathematical operator which is used to solve the given problem. It is the inverse of division. the result of multiplication is called the product

Rewriting the word problem 4 and one tenth times negative 4 times 5 over 12 to figures

4 1/10 * -4 * 5/10

solving the equation

= 4 1/10 * -4 * 5/10

= 41/10 * -4 * 5/10

= -41/5

= -8 1/5

The product of the multiplication is negative 8 and one fifth

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The proof for the Base Angles Theorem is explained below:

A triangle's opposite angles are congruent if its two sides are congruent. We shall build the angle bisector through the vertex angle of an isosceles triangle in order to demonstrate the Base Angles Theorem. We created two congruent triangles by building the angle bisector, and then we utilized CPCTC to prove that the base angles are congruent. Base angles: The angles that include the base of an isosceles triangle are known as the "base angles."

Any triangle with at least two congruent sides is said to be isosceles. Legs are the isosceles triangle's congruent sides. The base is the other side. Base angles are the angles formed between the base and the legs.

Given: [tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

Prove: ∠M≅∠N

According to the figure,

Given,

[tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

By the definition of mid-point,

O is the mid-point of [tex]\bar{MN}[/tex]

Now, by joining the two points determine and draw a line of [tex]\bar{LO}[/tex]

Now, Again by the definition of mid-point

[tex]\bar{MO}[/tex]≅[tex]\bar{NO}[/tex]

Now, by using reflexive property,

[tex]\bar{LO}[/tex]≅ [tex]\bar{LO}[/tex]

By SSS rule,

ΔLMO≅ΔLNO

By CPCTC rule,

∠M≅∠N

Hence proved.

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We may calculate our answer using fractions and the fact that the base is 18.3 feet.

The components of a whole or group of items are represented by fractions. A fraction consists of two components.

The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.

The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.

There are three different methods to express a fraction: as a fraction, as a percentage, or as a decimal. Let's examine each of the three representational styles.

According to our question-

The patio is 280 square feet in size. locate the base.

Height = 5x Area = 280 feet square

Base = 6x

The parallelogram A's area can be expressed mathematically as;

Base + height equals area.

A = b×h

the values of area, base, and height are substituted.

280 = 5x × 6x = 30x^2 \sx^2 = 280/30 \sx = √(280/30)

Given that the base is 6x,

swapping out x's value.

Base = 6x = 6(√(280/30))

Base=18.3 feet

18.3 ft tall is the base

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Answer:

At short 18.7 ft is the answer

The median or the middle value of 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80 is 64.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

42 48 52 54 59 61 61 64 65 67 68 70 72 75 80

The given set of numbers is in ascending order.

There are 15 numbers.

The middle number will be the 8th number.

8th number = 64

Thus,

The median is 64.

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The value of y= 5.49≈ 5.5cm

What is 30-60-90 traingle?

The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.

By 30-60-90 triangle rule,

Side across 60° angle = x

Hypotenuse side = 2x= 15

Side across 30° angle = x√3

By solving,

2x= 15

x= 7.5cm

So side across 60° angle= 7.5 cm

Side across 30° angle = 7.5×√3

                                     = 7.5× 1.732= 12.99≈ 13cm

As the figure given us square so,

13= 7.5+y

y= 13-7.5

y= 5.5 cm

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Answer:

22

Step-by-step explanation:

Y is midpoint of WR.

Hence,

YR = 1÷2 of WR ( Half of WR )

So,

WR = 2YR

= 2×11

= 22

yes, z can lie between x and y but z can also lie on another side of x in Number lines.

With an example, define number line?

Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.

                  A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.

What does the math number line mean?

A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.

                               How a number is used—for example, to plot a point—depends on the question that goes with it.

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This mean there are infinite solutions.

Each side is equally satisfied in an endless solution. Infinite is a symbol for boundlessness or limitlessness. Typically, the sign "" is used to denote it.

Solving an equation, Henry gets to the last line of his work and is left with “3 = 3”.

Any value for the Variable would make the equation true, according to infinite solutions.

We can tell which instance it is by examining our findings. If both sides of the equal sign end up having the same word,

such as

3=3 or 3x=3x, then. Finite solutions exist.

This mean there are infinite solutions.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G i.e m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

What is perpendicular bisector?

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

What is the perpendicular of two points?

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G)  i.e  m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f)  i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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Answer:

Step-by-step explanation:

Answer:

-3.5(x-14)+9x=5.5x + 49 is a TRUE statement that equals 0. It has infinite solutions.

Step-by-step explanation: