Factor out a negative 1 from each expression

1: 7 + (-6)
2: -4 - (5 + 3)
3: -9 - 1
4: 8 - (-6)
5: 3 + (-4 + 8)


Use the distributive property to show that your answers to Questions one through 5 are
correct.

Lucinda will buy 2 kewpie dolls and 1 beanie baby if she were rational.

According to the question,

Given the table below compares the marginal benefit Lucinda gets from Kewpie dolls and Beanie Babies. The image of the table is attached.

If Lucinda has only $18 to spend and the price of kewpie dolls and the price of beanie babies are both $6,

Lucinda will buy the combination for which the marginal benefit is the same.

Therefore, Lucinda will buy 2 kewpie dolls and 1 beanie baby, if she were rational.

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The complete question is:

If Lucinda has only $18 to spend and the price of kewpie dolls and the price of beanie babies are both $6, how many of each would Lucinda buy if she were rational? 0 kewpie dolls and 3 beanie babies 3 kewpie dolls and 0 beanie babies 2 kewpie dolls and 1 beanie baby 1 kewpie doll and 2 beanie babies

Answer:

a:b:c = 20:15:8

Step-by-step explanation:

a:b=4:3 = 20:15

b:c=5:2= 20:8

so a:b:c = 20:15:8

Answer:

m = 6

Step-by-step explanation:

first combine like terms

so 7m = 42

then isolate the variable by dividing both sides by 7

m = 42/7

m = 6

Answer:

the second one. n + (-8) = 14.

Step-by-step explanation:

There are 26 automobiles and 13 vans available for the field excursion.

An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. A mathematical statement that expresses the connection between two values is simply characterized as an equation. In an equation, the two values are usually equated by an equal sign. Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable). A linear equation can include several variables.

Here,

If c represents the number of cars and v represents the number of vans,

5c+8v=234

c=2v

10v+8v=234

v=234/18

v=13 vans

c=26 cars

The number of cars for field trip is 26 and number of vans is 13.

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The dilation is am enlargement or a reduction then the scale factor be 2.

The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).

To scale shapes in various dimensions, utilize the scale factor. Different geometrical shapes, both in two- and three-dimensions, are covered in geometry classes. The scale factor is a way to compare figures that appear to be similar but actually have distinct scales or measurements.

A scale factor is the amount by which a thing is multiplied to produce a separate object that has the same appearance but is a different size. It creates a precise copy that is just bigger or smaller than the original. Scale Factor multiplies the image or object in the same way as a copy machine would enlarge or reduce it.

Taking two points and dividing them would yield the factor.

For instance, if the point was between x = 2 and x = 4, their division would be 4/2 = 2, as shown on the right side.

Now, if we split the points x = -1 and x = -2 on the left side, we get -2/-1 = 2.

Therefore, the scale factor be 2.

The complete question is;

22. the blue figure is a dilation image of the black figure. The center of the dilation is O. Tell whether the dilation is am enlargement or a reduction. Then find the scale factor

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The unit digit of the product of 91, 92, 93, ... 99 is 0.

The digit that goes in the place of one in a number is known as the unit digit. i.e. It is the number's rightmost digit. As an illustration, the unit digit for 243 is 3, whereas the unit digit for 39 is 9.

It is easy to identify the unit place digit of the smaller number but when it comes to the numbers raised to the larger power it becomes difficult to identify the same by simple observation. It is when the concept of cyclicity comes into the picture.

The cyclicity concept is based on the fact that every digit in the number has its own repetitive pattern when raised to any specific power. This particular concept makes it easy for the students to find the unit place digit of the larger numbers and that too at much less time. So, let's learn about the cyclicity concept.

For example: - 2² = 4. Here, the unit digit is 4

2³ = 8. Here, the unit digit is 8.

Given:

91 × 92 × 93......×98 × 99

We want to find unit digit of the product of the numbers.

Here two digit is 92 and 95.

If we multiply 92 and 95, we will get zero as unit digit and if we multiply any digit by zero, unit digit always be zero.

So, the product of 92× 95 has zero in unit place.

So, in product of all numbers 91 × 92 × 93......×98 × 99 the unit will be zero. Because when we multiply any number by zero it become zero.

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The number of each type of books purchased is, 6 mystery and 8 sci-fi

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given  that,

$5 clearance mystery books

And $12 regular-priced science fiction book

Total spent amount = $126

The number of each type of books purchased  = ?

Suppose, the number of clearance mystery books = x

the number of regular-priced science fiction book = y

So it can be written as,

5x + 12y = 126

Here, in question Second condition is missing

So we can took values of x & y from the options,

Let, x = 6 and y = 8

5x6 + 12x8 = 126

It is satisfied the condition

Let, x = 7 and y = 7

5x7 + 12x7  ≠ 126

Similarly, rest options not satisfy the condition

Hence, the number of books 6 mystery and 8 sci-fi

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Answer:

This is actually quite simple

Step-by-step explanation:

Divide them both by 20

then add

Your final answer either should be D or A

Answer:

there's nothing there. If you put the question there, I could help.

The patient should receive 50 gtt/min of heparin using a 60 gtt/ml set.

The unitary method is a useful tool in determining the amount of medication to be administered in a given time period.

The physician has ordered a medication called heparin, which is used to prevent blood clots.

The physician has ordered the patient to receive 1250 units of heparin per hour.

You have a solution of 50,000 units of heparin in 1000 ml.

To calculate the number of drops of heparin that the patient should receive per minute, we will use a method called the unitary method.

First, we need to determine the flow rate in ml/hr.

=> 50,000 units / 1000 ml = 50 ml/hr.

Now, we need to convert this to drops per minute.

=> 50 ml/hr x 60 gtt/ml = 3000 gtt/hr.

Finally, we divide the total number of drops per hour by 60 to get the number of drops per minute. So,

=> 3000 gtt/hr / 60 minutes = 50 gtt/min.

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the point of intersection of equation and the x value of that would be the solution. then You get the coordinate (2.3, 4.1). So x = 2.3, y = 4.1

Put both of those equations into slope intercept form (in order to be typed into the graphing calculator).

2x + 3y = 16.9

3y = -2x + 16.9

y = (-2/3)x + 16.9/3

5x = y + 7.4

5x - 7.4 = y

So in the graphing calculator,

Y1 = (-2/3)x + 16.9/3

Y2 = 5x - 7.4

Then find the point of intersection and the x value of that would be the solution.

You get the coordinate (2.3, 4.1). So x = 2.3, y = 4.1

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complete question is

Solve the system of linear equations by graphing.

2x + 3y = 16.9

5x = y + 7.4

What is the solution to the system of linear equations? Round to the nearest tenth as needed.

Answer:

345 free throws

Step-by-step explanation:

To find the total number of free throws Caroline attempted, we can set up the equation: (total free throws) x 0.20 = 69 (missed free throws)

Solving for the total free throws:

(total free throws) = 69 / 0.20

(total free throws) = 345

So Caroline attempted 345 free throws in the season.

Answer:

2x-3

Step-by-step explanation:

3/x-4=x-5/x=

first what you need to do  is

3/x-4 so its both a fraction 3/x and 5x and subtraction on both sides makes it easer for us so

3/x-5/x=2/x

4-x=3

if wondering why 4x-x = 3 because x basicly means 1 so then you answer will be

2/x-3

am not really sure if you wanted simplifyed but it might be this

The time take for the object to cool down is 5 minutes.

The temperature of a substance is a measure of its thermal energy and it is important to know how it changes over time.

Heat transfer occurs from hot to cold, meaning that the coffee will transfer heat to the room until both reach thermal equilibrium. The temperature difference between the coffee and the room is

=> 80°C - 25°C = 55°C.

We will use this value to calculate the rate of heat transfer. We know that the final temperature of the coffee will be 45°C, so the temperature difference will become

=> 45°C - 25°C = 20°C.

The time it takes to cool from 80°C to 45°C will depend on the heat transfer rate, which is affected by factors such as the mass of the coffee, the material of the container, and the surrounding environment.

Let us consider that the average heat rate is 60 seconds that is one minute.

Then the time taken for it is calculated as,

=>20 x 60 = 300

So, in minutes 5 minutes.

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It is true that if v in r3 and v·v = 0, then v is the zero vector.

If v is a vector in R3 (three-dimensional real space) and v·v = 0, then v is the zero vector.

The dot product of a vector with itself, v·v, is equal to the square of the magnitude of the vector, ||v||^2. If v·v = 0, it follows that ||v||^2 = 0, which means that the magnitude of v is 0. In other words, v has a length of 0.

The only vector in R3 with a length of 0 is the zero vector, which is represented by the vector (0, 0, 0). Thus, if v·v = 0, v must be the zero vector.

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In the given trapezium/trapezoid ABCD, the value for the measure of ∠ADC is obtained as 157.4°.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

A trapezoid is also known as a trapezium.

A trapezium ABCD is given.

BE represents the height of the trapezium.

In Δ ABE use the trigonometric ratio since it is a right-angled triangle, to find the unknown ∠A.

cos θ = base / hypotenuse

Substitute the values in the equation -

cos θ = AE / AB

cos θ = 12 / 13

θ = 22.62°

The value of ∠A or ∠BAC is 22.62°.

Now ∠BAC and ∠ADC lie on the sample plane.

So according to the properties of a trapezium, the angles that lie on the plane have a sum of 180°.

The equation for the statement is -

∠BAC + ∠ADC = 180°

Substitute the values in the equation -

22.62° + ∠ADC = 180°

∠ADC = 180° - 22.62°

∠ADC = 157.38° ≈ 157.4°

Therefore, the measure of ∠ADC is 157.4°.

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Answer:

y = -3/4x - 1/4.

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Given the slope : -3/4 and y-intercept : -1/4, the equation of the line is y = -3/4x - 1/4.

when interpreting a histogram with a normal curve, it is important to look at the shape of the histogram and compare it to the shape of the normal curve. This can help us determine if the data is normally distributed, identify outliers, and determine the goodness of fit of the data to a normal distribution.

Histograms and normal curves are two commonly used graphical representations of data. A histogram is a bar graph that represents the frequency distribution of a set of continuous data. A normal curve, also known as a Gaussian distribution or Bell curve, is a symmetrical and bell-shaped curve that represents the probability density function of a normally distributed set of data.

When a histogram is superimposed with a normal curve, it allows us to visually compare the distribution of the data with a normal distribution. In this article, we will discuss how to interpret a histogram with a normal curve.

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Total time taken to fill the 960 cubic feet pool is  1440 minutes. = 24 hrs = 1 day.

A cuboid is a six-sided solid known as a hexahedron. Quadrilaterals make up its faces. Cuboid is short for "like a cube." A cuboid is similar to a cube in that a cuboid may become a cube by varying the lengths of the edges or the angles between the faces.

Features of a Cuboid :

A cube is a specific instance of a cuboid in which the length, width, and height are all equal. Accordingly, a cuboid is a cube.

The total volume of the cubic pool

with length = 20 feet

breadth = 12 feet

Depth = 4 ft

Volume (V) = 20 * 12*4 = 960 cubic feet.

1 cubic foot of volume = 7.5 gallon of water.

Total water required to fill the tank = 7.5 * 960 = 7200 gallon

The pool is filled at a 5 gallons of water per minutes so the

total time taken to fill the 960 cubic feet pool is = 7200/5 = 1440 minutes. = 24 hrs = 1 day.

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Persons over the age of 40, African-Americans, people with hypertension or pre-hypertension, and people with diabetes are among these populations. Anyone in these groups should restrict their daily salt consumption to 1,500 mg.

Blood sodium levels should be between 135 and 145 mEq/L (3.10 mg/ml to 3.34 mg/ml). Higher sodium levels are often connected with hypertension. Hypernatremia is defined as a sodium level of 150 mEq/L (3.45 mg/ml) or higher, which is frequently caused by dehydration or ingesting too much salt. On some food labels, the salt amount is the sole information provided. To convert sodium to salt, increase the quantity by 2.5. Then double the salt content per 100g by 100 and multiply by the serving size. For most individuals, the American Heart Association advises no more than 2,300 milligrams (mg) per day, with an optimal limit of no more than 1,500 mg per day.

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The maximum number of points on the convex hull of a set of 100 points inside a square is 4.

A Convex Hull is defined as  the smallest convex polygon which contains all the points in a set.

Since the points are inside a square, which means : the convex hull must be a subset of the square's boundary. The boundary of the square has 4 sides, so the maximum number of points on the convex hull is 4.

In Square , the number of points on the convex hull is a function of the distribution of the points and the shape of the region in which they are located.

Therefore , the maximum number of points on the convex hull of a set of 100 points inside a square is 4.

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The mean will increase because the new score of 100 is higher than the previous score of 95.

This dataset is from an exam and has several different statistics, such as the number of students, the mean, standard deviation, median, maximum score, range, and mode.

After a grading mistake was corrected, the student who originally got a 95 now has a 100. This will affect the mean, median, maximum score, and range of the dataset.

The maximum score will change from 95 to 100. The range will also increase, as the difference between the minimum and maximum scores will be larger.

The standard deviation may or may not change, as it depends on the distribution of the scores in the dataset.

If the new score of 100 is significantly different from the other scores, it could increase the standard deviation.

In conclusion, correcting a grading mistake can greatly affect the statistics of a dataset and it is important to understand the impact it may have on the results.

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Answer: 0.25 seconds.

Step-by-step explanation:

To find the time of flight of the bullet, we need to divide the distance the bullet travels by its velocity.

Average speed is distance over time. so

time = distance/speed

time = 500m / (2000 m/s)

time = 0.25 seconds

So, the bullet's flight time is 0.25 seconds.

Answer:

then he'll get a bagel 2 pieced sanwich with a side of E

Step-by-step explanation:

In third table constant rate is not changed.

Hence the correct data table is option C.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here in given question, the constant rate is of motion detector is determined by difference between the distance by time. Now,

In option A)  first table ,

=> constant rate = 10-10 =0

=> constant rate = 10-10=0

=> constant rate = 10-8 = 2

Here 0≠ 2. Then given table is not refer motion detector.

In option B) second table,

=> constant rate = 3-3=0

=> constant rate = 3-5 =-2

Here 0≠-2 then the given table is not refer motion detector.

In option C) third table,

=> constant rate = 9-7 =2

=> constant rate = 7-5 =2

=> constant rate = 5-3 =2

In this given table constant rate is not changed.

Hence the correct data table is option C.

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To show the work:

68 ÷ 0.4 = 170

Explanation:

You can think of dividing by a fraction as multiplying by its reciprocal. The reciprocal of 0.4 is 1/0.4.

So instead of dividing 68 by 0.4, you can multiply it by 1/0.4, which is the same as multiplying by 2.5.

68 * 2.5 = 170

Answer: TRUE

Step-by-step explanation:

For the sake of typing this easier, I'm going to omit using theta however the final answer will have it.

RH:

Knowing that csc = 1/sin, csc² = 1/sin²

LH:

Knowing that cot = cos/sin, cot² = cos²/sin²

Another important trig identity is sin² + cos ² = 1

So therefore you now have:

cos²/sin² + sin² + cos²

Put everything under the same denominator:

cos² + sin²*sin² + cos²*sin² / sin²

= cos² + sin²(sin² + cos²) / sin²

= cos² + sin² (1) / sin²

= 1 * 1 / sin²

= 1 / sin²

Therefore this trig identity is true

Karen that has a piece of fabric that is 1 187/240 yards long needs to trim 227/240 yards

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

To solve this problem we must perform the corresponding algebraic operations with mixed fraction.

Data of the problem:

A mixed operation is solved as follows:

For the denominator: the same denominator is placed.

For the numerator:

The value of the denominator is multiplied by the integer component.

The result is added to the numerator of the fraction.

We transform the mixed fractions into improper fractions and we have:

1 187/240 =

[(240*1) + 187)] /240=

[240+ 187] /240=

427/240

Calculating how many yards should she trim:

Yards to trim: 427/240 - 5/6

Yards to trim: (427 - 200) / 240

Yards to trim: 227/240

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