given that 2a+6sqrt7=18-3sqrtb find values of a and b

The product of the values -2/7 and -3/4 is 3/14

The multiplication expression which relates Cassie's fraction with Amy's can be written thus :

Therefore, the multiplication result of the two fractional values is \( \frac{3}{14} \)

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In matrix notation, the system can be represented as:

[d/dt] [x] = [7ty - 5]

[y] [3x - 7y]

The given system of linear differential equations, dx/dt = 7ty - 5 and dy/dt = 3x - 7y, can be written in matrix notation as follows:

[d/dt] [x] = [7ty - 5]

[y] [3x - 7y]

Here, [d/dt] represents the operator for taking the derivative with respect to t, [x] is the column vector representing the variables x and y, and on the right-hand side, we have the column vector of the expressions 7ty - 5 and 3x - 7y.

In matrix notation, the system can be represented as:

[d/dt] [x] = [7ty - 5]

[y] [3x - 7y]

Please note that the matrix notation allows for a compact representation of the system of differential equations, which can be useful for solving the equations and performing various matrix operations.

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Answer:

First find x

70-x=4x

-x-4x=-70

-5x=-70

x=14

Angle BEC = 70°-x

=70-14

=56°

Angle AEB = 180- 56

= 124°

Angle DEA =4x

= 4× 14

= 56°

Angle CED = 180-56

=124°

Answer:

38 cm²

Step-by-step explanation:

Given that,

→ Length (l) = 4 cm

→ Breadth (b) = 3 cm

→ Height (h) = 1 cm

Formula we use,

→ 2(lb + bh + lh)

The surface area of cuboid will be,

→ 2(lb + bh + lh)

→ 2{(4 × 3) + (3 × 1) + (4 × 1)}

→ 2(12 + 3 + 4)

→ 2 × 19

→ [ 38 cm² ]

Hence, the surface area is 38 cm².

The correct option is option (C) .

Cluster Sampling is a type of probability sampling and other options are non- probability sampling examples .

Sampling :

Sampling is defined as a technique that selects individual members or subsets from a population to help determine characteristics of the population as a whole.

Croach and Housden postulate that a sample is a finite number taken from a large group for testing and analysis, and that the sample can be taken as representative of the group as a whole.

There are two main types of sampling:

i) probability sampling

ii) Non-probability sampling

A) probability sampling:

It is defined as the sampling technique which researchers use a related method to draw probability theory samples from a larger population.

The most important requirement for probabilistic sampling is that everyone in the population has a known equal chance of being selected.

Probability Samples:

1. Stratified Sampling: Stratified sampling is a type of sampling technique that divides the total population into smaller groups or strata to complete the sampling process. Hierarchies are formed based on some common characteristics of demographic data.

2. Cluster Sampling: Cluster sampling is a probabilistic sampling technique in which researchers divide a population into multiple groups (clusters) for research purposes. Researchers then select random groups using simple sampling techniques for data collection and data analysis.

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To work out the volume of the cone, we can use the formula V = (1/3) * π * r² * h, where r is the radius of the base of the cone and h is the height of the cone. The volume of the cone is approximately 171.55 cubic units.

The formula for calculating the volume of a cone is given as V = (1/3) * π * r² * h. In this formula, 'r' represents the radius of the base of the cone, and 'h' represents the height of the cone. By substituting the given values, the volume of the cone is calculated to be approximately 171.55 cubic units. This formula is widely used in various fields, such as architecture, engineering, and manufacturing. Calculating the volume of a cone is useful in determining the amount of material required to construct or fill a cone-shaped object, such as a cone-shaped container or a cone-shaped structure. The formula is also used in solving real-life problems related to cones, such as calculating the volume of ice cream in a cone-shaped ice cream cone or the volume of a cone-shaped tank used for storing liquids.

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Answer:

She must score 90 points

Step-by-step explanation:

Find the average of the first 2 tests

76 + 80 = 156

Divide the sum of the first 2 tests by how many tests there were

156 ÷ 2 = 78

Multiply 82 by 3

82 x 3 = 246

Subtract 156 from 246

246 - 156 = 90

Add all the numbers together to get the average

90 + 80 + 76 = 246

246 ÷ 3 = 82

Hope this helps!

Answer:

x=4.8

Step-by-step explanation:

AE.EC=DE.EB

6×8=10×x

48=10x

x=4.8

The length of x in the given circle is 4.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is πr².

We have,

The chords in a circle are line segments that connect two points on the circumference of the circle.

They do not necessarily pass through the center of the circle.

All chords in a circle have the same properties, regardless of their length or position.

So,

DB = AC

DE + EB = CE + EA

10 + x = 8 + 6

10 + x = 14

x = 14 - 10

x = 4

Thus,

The length of x is 4.

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Antonella have a number of coins of quaters and nickels whose total value is 250.

The number of coins of nickel is 10 and the number of coins of quarters is 7.

Nickel and quarters are the coin based form of currency in the United States. The value of one nickel is 5 cents, while that of one quarter is 25 cents. We have given that

Antonella has 3 more quaters than nickles.

Let she has "x" number of quaters and "y" be number of nickels .

According to question,

y = 3+ x ---(1)

Combined value of all is 225 cents .

i.e 25 × x + y× 5 = 225 cents

plug the value of y from equation (1) to equation(2) we get,

25 x + 5(3+x) = 225

solve the equation

=> 25x + 15 + 5x = 225

=> 30x = 210

=> x = 7

put the value of x in equation (1)

y = x + 3 = 10

Hence, the number of nickels coins is 10 and numbers of quaters are 7.

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Answer:

6

Step-by-step explanation:

f(x)=2x^3-5x when x=2. So f(2)=6

Answer: 9/12 equals 0.75 so 75 percent is the answer.

Step-by-step explanation:

This is a regular conditional expression because it is in the form "If P, then Q"

P = Maura is going to the library

Q = she is bringing her favorite binder

A biconditional is of the form "P if and only if Q"

The "if and only if" is the key phrase needed. It allows us to swap the positions of P and Q to say "Q if and only if P".

According to Weber's law, two items must differ in weight by "5 percent"of weight in order to detect a difference.

We are given that Weber's law

For weight discrimination, Weber’s law states that the JND is proportional to the weight of the stimulus.

The JND is defined as the smallest difference between two weights that can be detected by an observer.

The proportionality constant is known as Weber’s fraction and varies depending on the type of stimulus and the sensory modality involved.

For weight discrimination, Weber’s fraction is typically around 2-3%.

This means that two items must differ in weight by approximately 2-3% of their weight in order to detect a difference.

The difference of weight in percent is 5%, the correct option is A.

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On solving the provided question, we can say that the provided expression is = 5a -25  since it is linear expression, so it will have only one factor, a = 5

In mathematics, the integer m serves as the divisor (also known as factor n) of an integer n, which may be multiplied by the integers to get n. We may also state that n in this situation is a multiple of m. A number without a residue that divides another number is said to be a factor. In other words, if you multiply two integers to create a product, the numbers you multiply are factors of the product since the result is divisible by the numbers you multiply. Factors can be found using either division or multiplication.

the provided expression is = 5a -25

since it is linear expression, so it will have only one factor

5a -25

5a = 25

a = 5

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Answer:

Distance traveled is equal to the length of wheel circumference as it “unrolls” along the ground as the wheel turns. One full turn of the wheel will move the robot one circumference's distance. Therefore, students will find the distance traveled by multiplying circumference by the number of rotations.

The dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

Let's assume that the width of the rectangle is x meters. According to the given information, the length of the rectangle is 3 meters less than double the width, which can be expressed as 2x - 3.

The area of a rectangle is given by the formula: Area = Length × Width. In this case, the area is given as 14 m². Therefore, we can write the equation:

(x)(2x - 3) = 14

Expanding the equation:

2x² - 3x = 14

Rearranging the equation to standard form:

2x² - 3x - 14 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 2, b = -3, and c = -14. Plugging in these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(2)(-14))) / (2(2))

x = (3 ± √(9 + 112)) / 4

x = (3 ± √121) / 4

x = (3 ± 11) / 4

Simplifying further:

x = (3 + 11) / 4 or x = (3 - 11) / 4

x = 14 / 4 or x = -8 / 4

x = 7/2 or x = -2

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 7/2 meters.

Now, we can substitute the value of x into the expression for the length:

Length = 2x - 3

Length = 2(7/2) - 3

Length = 7 - 3

Length = 4 meters

Thus, the dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

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The final result for the money is \(172.40\) after you multiply it by a percent.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage.

Rather than being stated as a fraction, a percent is a piece of an entire thing expressed as just a number between zero and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the total by its entirety and multiply the result by 100 to get the percentage.

\(w-[0.15]=146.54\)

so \(w-85p=146.54\)

\(146.54\) divided by \(80=1.724\) so when you make it a percent it turns it into \(172.40\) which is the final answer for the money.

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The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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Answer:

Hey there! So the square root of 38 can be simplified by breaking it down into simpler parts. We can use a technique called prime factorization. We need to find the largest perfect square that is a factor of 38 and extract it from the square root. So, we can express 38 as 219 and that means we have 2^2=4 as the largest perfect square. Therefore, we can simplify the square root of 38 as 2sqrt(19).

It can't be simplified anymore, but it gives us a more manageable form. Let me know if you have any more questions, I'm happy to help!

________________________________________________________

A perfect square is a number that can be written in the form of n^2 (n raised to the power of 2) for some whole number n. For example 4, 9, 16, 25 and 36 are perfect squares. A way to determine if a number is a perfect square is by taking the square root of that number, if the result is a whole number it's a perfect square. Also, you can check it by finding the prime factorization of the number, if each of the prime factors appears in even power, it's a perfect square.

There are a few techniques that can make simplifying square roots quicker and easier:

Recognizing perfect squares (as described above) and extracting them from the square root

Using prime factorization to simplify the square root

Recognizing when the square root can be written as a rational number (a fraction of two integers)

Another way to approach is to factorise the radicand and combine any pairs of identical factors out from the square root.

Please let me know if you have any other questions on this topic or any other topic I could help with.

√38 is the simplest representation of the square root of 38.

The square root of a number is a value that, when multiplied by itself, gives the original number.

In the case of √38, we are looking for a number that, when multiplied by itself, equals 38.

Since 6 multiplied by itself is 36 and 7 multiplied by itself is 49, we can conclude that the square root of 38 lies between 6 and 7.

We cannot find a whole number that satisfies the equation √38 = x, where x is an integer.

Therefore, we express the square root of 38 as an irrational number, meaning it cannot be expressed as a simple fraction or a terminating or repeating decimal.

Hence, √38 is the simplest representation of the square root of 38.

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The median lies in the group "30 < x < 40".

To determine the median, we followed these steps:

Therefore, the median lies in the group "30 < x < 40".

The median is a statistical measure that represents the middle value in a set of numerical data. It is used to describe the central tendency of the data and to determine where the majority of the values lie. To find the median, the data must be arranged in ascending or descending order, and the middle value is taken.

If the number of observations is odd, the median is the middle value. If the number of observations is even, the median is the average of the two middle values. The median is useful for finding the central value of data that may have extreme outliers or skewness, as it is not affected by the presence of such values.

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Answer: y = 2/3x

Step-by-step explanation: A slope of 2/3 means every time you travel up, two units on a graph, you have to travel over three. this means that if the x-value in our equation was equal to 3, we would have traveled over 3 units, and upwards of two units, which can be calculated with the equation y = 2 / 3 * (3) or (x) equals 2. The way to find the equation mathematically would go as follows.

Use your point (3,2), and add our x-value (3) into the equation.

1. y = (2/3) * 3

\(\frac{2}{3}\) * \(\frac{3}{1}\) = \(\frac{6}{3}\)

2. y = 6/3

6 / 3 = 2

3. y = 2

so our x-value is 3, and our y-value is 2, making the point (3,2)

This proves that the point given falls on the slope without any altered y-intercept. However, when the point falls on a different coordinate, lets say we were given the point (3,3) we would follow the same process.

1. y = (2/3) * 3

\(\frac{2}{3}\) * \(\frac{3}{1}\) = \(\frac{6}{3}\)

2. y = 6/3

6 / 3 = 2

3. y = 2

Well, this doesn't match up with our initial point (3,3), so what went wrong?

There can be a few explanations, the graph could travel up a couple of units from 0 on the y-axis, or down a couple of units. The way to figure this out would be to take the y-value from the point we were given the (3,3) and subtract the y-value we found using our equation, so 2

3 - 2 = 1

What the 1 essentially means is that our graph doesn't start out from zero, somebody places it one unit above our x-axis, so the equation would go as follows.

y = slope(2/3x) + y-intercept(1)

the y-intercept is basically the number of units the graph is moved up or down on the y-axis.

Answer:

180- 117 = 63

Step-by-step explanation:

Answer:

ZX = 1.3 in

EG = 3.0 in

M∠X = 48°

M∠G = 25°

Step-by-step explanation:

As we can see in the attached figure that these two triangles are identical i.e their corresponding sides and angles are equal

Therefore if we say that

ZX = EF

So ZX = 1.3 in.  

Now the same is applied for other sides and angles

EG = XY

So, EG = 3.0 in

M∠X = M∠E

hence, M∠X = 48°

For the M∠ G,

The angle is

= 180° - 107° - 48°

= 25°

Hence, the M∠ G is 25°

Step-by-step explanation:

3a+10° 4a-10°

3a+10= 4a-10° (keeping =)

3a-4a=-10°-10°

-a=-20°

a=20°

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Solve the problem?

Given that a card is selected from a 52-card deck that has been thoroughly shuffled without being replaced, the following card is drawn.

A: The top card is a 4, and B: The next card is an ace.

Probability =A∩B

After this first card is pulled, if 10is drawn, we have 51 cards left with 4 aces in them. This is the probability we need to discover for

P(A). =  10/52  

P(B) = number of aces in 51 cards divided by 51, thus = 4/51

Hence A∩B =10/52×10/51

=   100/2652

(From this, we can see that, after changing the card count, A and B are independent.

Additionally, we multiply the probability for both.)

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Answer: 254.34

Step-by-step explanation:

The equation for area is: \(r^{2} * \pi\)

So you find  9 squared which is 81. Then, you multiply it by pi(using 3.14). This equals 254.34

a) 80 sundaes are possible using one flavor of ice cream and three different toppings.

b) 256 sundaes are possible using one flavor of ice cream and any number of toppings from 0 to 6.

c) 4 different combinations of flavors of three scoops of ice cream are possible if all three scoops are the same flavor.

a) To make a sundae with one flavor of ice cream and three different toppings, we need to choose one flavor of ice cream from the four available flavors and choose three toppings from the six available toppings.

The number of ways to choose one flavor of ice cream is 4. The number of ways to choose three toppings from six is the number of combinations of 6 items taken 3 at a time, which is given by the formula:

C(6,3) = 6! / (3! × (6-3)!) = 20

Therefore, the total number of sundaes possible using one flavor of ice cream and three different toppings is:

4 × 20 = 80

b) To make a sundae with one flavor of ice cream and any number of toppings from 0 to 6, we need to choose one flavor of ice cream from the four available flavors and choose any number of toppings from 0 to 6.

The number of ways to choose one flavor of ice cream is 4. The number of ways to choose any number of toppings from 0 to 6 is the sum of the number of combinations of toppings taken 0 at a time, 1 at a time, 2 at a time, up to 6 at a time. This is given by the formula:

∑(k=0 to 6) C(6,k)

Using the formula for the sum of binomial coefficients, we get:

∑(k=0 to 6) C(6,k) = 2^6 = 64

Therefore, the total number of sundaes possible using one flavor of ice cream and any number of toppings from 0 to 6 is:

4 × 64 = 256

c) To make a sundae with three scoops of the same flavor of ice cream, we need to choose one flavor of ice cream from the four available flavors.

The number of ways to choose one flavor of ice cream is 4.

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