The value of x is a third of the value of 45–10x.

Answer:

65 years old.

Step-by-step explanation:

If her age is 10 t + u (where t is the tens digit and u is the units digit) then reversing the digits gives 10 u + t. and the sum is 11 t + 11 u, which is a multiple of 11. We know this has to be a square number. Ong Xing Cong from Singapore sent in the following solution.

11 t + 11 u = 11 x 11 = 121

t + u = 11

65 - 56 = 3 x 3

She is 65 years old.

The best solutions do not need trial and improvement methods and they show that the answer or answers found are the only possible answers. Knowing the digits add up to 11 ( t + u = 11), you can also use (10 t + u ) - (10 u + t ) = 9 t - 9 u = 9( t - u ) As this is also a square number you know ( t - u ) is either 1, 4, or 9. The solutions for 4 and 9 don't give whole number values for t in 0  t  9.

The math teacher age is 65 years old.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

My age in years is not a prime, but is odd.

That means, the number is 10m+ n.

Where m is the digits having the place value 10 and n is the unit digit.

Also, when the digits in my age are reversed and the new number added to my age, the result is a perfect square.

That means,

10n + m + 10m + n,

= 11m + 11n

= 11(m+n)

= multiple of 11.

= 11 x 11

= 121

= 65 + 56

Of course, if you prefer, you can take my age and reverse the digits and subtract that from my age and still get a perfect square.

That means,

10n +m - 10m - n,

= 9n - 9m

= 9(n-m)

= 9

= 65 - 56

Therefore, the age is 65.

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Answer:

48

Step-by-step explanation:

24x2=48

16x3=48

Answer:

48

Step-by-step explanation:

multiples of 16: 16, 32, 48, 64....

multiples of 24:24, 48, 72, 96....

in both situations, it is just multiplying the number by 2 to get the next number

as you can see the only number that appears in both sets and is the smallest is 48.

Hope that helps :)

The following a probability model? what do we call the outcome No, the provided information is not sufficient to determine if it is a probability model. The outcome "red" is typically referred to as an event.

A probability model is a mathematical representation of a random experiment, where the sample space is defined, and probabilities are assigned to all possible outcomes. To determine if the given information is a probability model, we would need to know the complete list of possible outcomes, their corresponding probabilities, and ensure that the probabilities meet the necessary conditions (sum up to 1 and are non-negative).

Based on the limited information provided, we cannot determine if it is a probability model. The outcome "red" is called an event in the context of probability.

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With sides that are 4 cm, 3 cm, and 7 cm long, a triangle cannot be built. Because the sum of the other two sides does not exceed that of the third side.

A triangle is referred to as a three-sided polygon that has three vertices. The connection of the three sides ends to end at a single point forms the angle of the triangle. The sum of these angles adds up to 180 degrees.

The triangle's three sides are specified as being 4 cm, 3 cm, and 7 cm. Add the two sides together and see if the result exceeds the third side to determine whether these sides constitute a triangle.

Here, the sum of two sides 4 cm and 3 cm is calculated as,

A+B = 4+3

=7 cm

This sum is equal to the third side C = 7 cm.

Therefore,  \(A+B\ngtr C\). So, the given sides don't form a triangle.

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Answer: 1840 pounds

Step-by-step explanation:4x4=16

460 x 4 = 1840

The greatest common factor for the given expression is 5z.

What is GCF?
The greatest common factor, which is the product of two or more numbers, is the largest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's factors have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF). The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers.

Given, the first expression is: y₁ = 70x³z = 5z.14x³ -(i)
Also, the second expression is: y₂ = 45y4z² = 5z.36yz -(ii)
Comparing (i) and (ii), the greatest common factor for y₁ and y₂ is 5z.
Thus, the greatest common factor for the given expression is 5z.

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The total number of ways an ice-cream can be selected is 27.

A combination is "an arrangement of objects where the order of the constituents is immaterial," according to the definition. In situations where the order of the elements is immaterial, combining these two terms means "Selection of things." Combinations are a subset of permutations in which the order of the choices is ignored.

As per the given data:

A table is given, in which information regarding the ice cream menu is shown.

We have to find the total number of different choices of ice cream that can be made.

Number of sizes = 3

Number of flavors = 3

Number of toppings = 3

ways for selecting one ice cream = \(^3C_{1} \times ^3C_{1} \times ^3C_{1}\) = 3 × 3 × 3 = 27

The total number of ways an ice-cream can be selected is 27.

Hence, The total number of ways an ice-cream can be selected is 27.

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The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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The equation of the function f(x) is h(x) = 1/2(4x - 6) - 3

From the question, we have the following equation that can be used in our computation:

f(x) = 1/2x -3

Also, we have the following steps used to create the function h(x)

When these steps are represented as  an equation, we have the following representations

In the above computations, we have

h(x) = 1/2(x * 4- 6) - 3

Evaluate the product

h(x) = 1/2(4x- 6) - 3

Hence, the equation is h(x) = 1/2(3x- 6) - 3

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Answer:

The coefficient of determination or R-squared is a metric used to evaluate how well the regression line fits the data. It quantifies the percentage of variation in the dependent variable that can be accounted for by the independent variable(s). R-squared values lie between 0 and 1, with higher values indicating a better fit of the regression line to the data. For example, an R-squared value of 0.8 indicates that 80% of the variability in the dependent variable can be explained by the independent variable(s).

The probability of picking blue ball by Liz and Mike are equal =1/3

Probability is a branch of mathematics that deals with the study of random events or experiments. It is concerned with quantifying the likelihood or chance of a particular event occurring, given certain assumptions or conditions.

The probability of an event is typically represented as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain. For example, if you flip a fair coin, the probability of getting heads is 0.5, and the probability of getting tails is also 0.5.

There are different methods for calculating probabilities, depending on the nature of the event or experiment being considered. Some of the most commonly used methods include the classical probability method, the empirical probability method, and the subjective probability method.

Probability has many applications in various fields, including statistics, finance, engineering, and science. It is used to model and analyze complex systems and to make predictions and decisions based on uncertain information.

Given : X contains 9 blue balls and 18 red balls.

Y contains 7 blue balls and 14 red balls.

Probability of picking blue ball is 9/9+18

=9/27=1/3

Now Mike pick ball from bag Y one ball not affect these pick ball

so, 7/7+14=7/21=1/3

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\((f+g)(f)=f(x)+g(x)\\\\\\f(x)=\dfrac{x}{2}-2\\g(x)=2x^2+x-3\\\\(f+g)(x)=\dfrac{x}{2}-2+2x^2+x-3\\(f+g)(x)=2x^2+\dfrac{x}{2}+\dfrac{2x}{2}-5\\(f+g)(x)=2x^2+\dfrac{3x}{2}-5\\(f+g)(x)=2x^2+\dfrac{3}{2}x-5\)

Answer:

4-9y^2

Step-by-step explanation:

(2+3y)(2-3y)

2*2

2*-3y

3y*2

3y*-3y

4-6y+6y-9y^2

4-9y^2

Answer:

\(4−9 {y}^{2} \)

Step-by-step explanation:

\((2+3y)(2−3y)\)

\(2(2−3y)+3y(2−3y)\)

\(2 \times 2+2(−3y)+3y(2−3y)\)

\(2 \times 2+2(−3y)+3y \times 2+3y(−3y)\)

\(4−6y+6y−9 {y}^{2} \)

\(4+0−9 {y}^{2} \)

\(4−9 {y}^{2} \)

Answer:

92

Step-by-step explanation:

12 + [20(5 - k)]

Substitute the value.

12 + [20(5 - 1)]

Evaluate inside the parenthesis.

12 + [20(4)]

Multiply.

12 + 80

Add.

92

Answer:

Speed = 9.6km/s

Distance Traveled in 5 seconds= 48km

Step-by-step explanation:

(6 )(1.6)= 9.6km/s

(9.6)(5)=48km

The vertex is at (-2, -9).

From the equation:

y = x² + 4x - 5

Transpose the c-value to the left side of the equation:

y + 5 = x² + 4x

Complete the square of the expression on the right side of the equation to get a perfect square trinomial:

y + 5 = x² + 4x + 4 - 4

by adding and subtracting 4 to the right side of the equation to maintain its balance.

Add the numbers on the left and factor the trinomial on the right:

y + 9 = (x + 2)²

Transpose the number across to the right side to get the equation into the vertex form, y = a(z-h)² + k:

y = (x + 2)² - 9

Make sure the addition and subtraction signs are correct to give the proper vertex form.

Here, the vertex is at (-2, -9).

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Given:-

To find:-

Answer:-

1) Firstly we are told to transpose the c value to LHS .

With respect to standard form of a quadratic equation, \( ax^2+bx + c \) ,the value of c here will be -5 . So on transposing c to LHS , we have;

\(\implies y + 5 = x^2 + 4x\\\)

w) Next we are told to complete the square on the RHS of the equation. For that add and subtract 4 .

\(\implies y + 5 = x^2 + 4x + 4 - 4 \\\)

\(\implies y + 5 =\{ (x)^2 + 2.2.x + 2^2 \}- 4\\\)

The terms inside the curly brackets are in the form of \( a^2+2ab + b^2\) , which is the whole square of \( (a + b )\) . That is \( ( a + b)^2\) . So , we can rewrite it as ,

\(\implies y + 5 = (x +2)^2 - 4 \\\)

\(\implies y + 5 + 4 = (x+2)^2 \\\)

3) Next we have to add the number on the left and factor the trinomial on right as ,

\(\implies y + 9 = (x+2)^2 \\\)

4) Now we are told to transpose the number on the LHS to RHS and get the equation into vertex form which is \( y = a(z-h)^2+ k \) .

\(\implies\underline{\underline{ y = (x+2)^2 - 9}} \\\)

This is our required answer in vertex form. Also on comparing to the standard equation of vertex form, we have;

\(\implies vertex = ( -2,-9) \\\)

and we are done!

The matrix A of T

a. \(A = [ 0 -1 ]\)

b. \(A = [ 0 -1 ]\)

c. \(A = [ 1/sqrt(2) 1/sqrt(2) ]\)

d. \(A = [ -1/sqrt(2) 1/sqrt(2) ]\)

To find the matrix A of the reflection transformation T in the line \(y = -x\), we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [-1 0]\) and \(T(e2) = [0 -1]\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ -1 0 ]\)

\([ 0 -1 ]\)

To find the matrix A of the transformation \(T(x) = -x\) for each x in R2, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [-1 0]\) and \(T(e2) = [0 -1]\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ -1 0 ]\)

\([ 0 -1 ]\)

To find the matrix A, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [1 1] / sqrt(2)\)  and \(T(e2) = [-1 1] / sqrt(2)\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ 1/sqrt(2) -1/sqrt(2) ]\)

\([ 1/sqrt(2) 1/sqrt(2) ]\)

d. To find the matrix A, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [1 -1] / sqrt(2)\) and \(T(e2) = [1 1] / sqrt(2)\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ 1/sqrt(2) 1/sqrt(2) ]\)

\([ -1/sqrt(2) 1/sqrt(2) ]\)

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Answer:

What would you like me to help you with? ╰_╯

Answer: 7.1

Step-by-step explanation:

Use pythagorean again.

c²=b²+a²      

c=distance

a= distance in x direction = 7

b= distance in y direction =1

plug it in

d²=7²+1²

d²=49+1

d²=50

d=√50    put in calculator

d=7.1

Answer:

math is the worst

Step-by-step explanation:

This results in a probability of approximately 0.044, or 4.4%.  the probability of any number of eagles surviving their first year can be calculated using the binomial probability formula.

The probability of a bald eagle surviving its first year of life is 62%. If 45 bald eagles are randomly selected, we can use the binomial probability formula to calculate the probability of a certain number of eagles surviving their first year.

P(x=k) = (n choose k) * p^k * (1-p)^(n-k)

Where n is the total number of trials (45), k is the number of successes (surviving eagles), p is the probability of success (0.62), and (n choose k) is the binomial coefficient.

To find the probability that exactly 20 eagles survive their first year, we plug in the values:

P(x=20) = (45 choose 20) * 0.62^20 * 0.38^25

This results in a probability of approximately 0.044, or 4.4%.

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Hi, I'm glad to help you with this question. To determine if the normal distribution gives a reasonable approximation using the given data, we need to calculate the mean and standard deviation. Here are the steps:

1. Calculate the mean (average): Add all the data points together and divide by the number of data points.
(71+42+77+84+46+93+94+63+82+88+57+32+79+67+68+83+60+65+58+70) / 20 = 1380 / 20 = 69

Mean = 69

2. Calculate the standard deviation: First, find the difference between each data point and the mean, square the differences, and then find the average of those squared differences. Finally, take the square root of that average.
a. Differences from the mean: (-2, 27, 8, 15, -23, 24, 25, -6, 13, 19, -12, -37, 10, -2, -1, 14, -9, -4, -11, 1)
b. Squared differences: (4, 729, 64, 225, 529, 576, 625, 36, 169, 361, 144, 1369, 100, 4, 1, 196, 81, 16, 121, 1)
c. Average of squared differences: (4520) / 20 = 226
d. Square root of the average: √226 ≈ 15.03

Standard Deviation ≈ 15.03

Now that we have the mean (69) and the standard deviation (15.03), you can compare these values to the distribution line that you draw through the data by eye. If the distribution line follows a bell-shaped curve with the mean at the center and the data points spread around it following the standard deviation, then the normal distribution provides a reasonable approximation for this data set.

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The equation allows us to chart the tree's development over time and forecast its ultimate height.

A function is a mathematical formula that allots each input from one set, known as the domain, to precisely one output from another set, known as the range. A function can be used to model relationships between variables, answer issues, and make predictions. It can be represented by an equation, a graph, a table, or a verbal description. Numerous branches of mathematics, as well as disciplines like physics, engineering, finance, and computer science, make extensive use of functions. Typical instances of functions include: When a function is graphed, it always changes at the same rate and forms a straight line. They are frequently used to simulate relationships between two variables that are related linearly, such as time and location.

given

After d days, Alani created the following algorithm to measure the height of the banana tree:

h = d + 8

Since this function is linear, the banana tree's development will remain constant over time. According to the calculation, the tree starts out at a height of 8 units, and it increases by 1 unit per day after that.

We can enter a figure for d (the number of days) and solve for h using this equation (the height of the tree after d days). For instance, we can enter d = 10 into the calculation to get the height of the tree after 10 days:

h = 10 + 8

h = 18

Therefore, the altitude of the banana plant after 10 days would just be 18 units. This equation allows us to chart the tree's development over time and forecast its ultimate height.

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Answer:

There is one solution  x = 15/19

Step-by-step explanation:

−12x+1=7x−14

Add 12x to each side

−12x+12x+1=7x+12x−14

1 = 19x-14

Add 14 to each side

1+14 = 19x-14+14

15 = 19x

Divide by 19

15/19 = 19x/19

15/19 =x

There is one solution  x = 15/19

Using the properties of parallelograms and the given information, we proved that BAEC is equal to FABC. We utilized angle-angle similarity and the proportional relationships of corresponding sides in similar triangles to establish the equality.

To prove that BAEC = FABC, we will use the properties of parallelograms and the given information.

Given:

ABCD is a parallelogram.

BE is parallel to CD.

BF is parallel to AD.

To prove:

BAEC = FABC

Proof:

Since ABCD is a parallelogram, we know that opposite sides are parallel and equal in length. Let's denote the length of AB as a, BC as b, AD as c, and CD as d.

Since BE is parallel to CD and AD is parallel to BF, we have angle ABE = angle CDF and angle ADB = angle BFD.

By alternate interior angles, angle CDF = angle FAB.

Now, we have two pairs of congruent angles: angle ABE = angle CDF and angle ADB = angle BFD.

Using angle-angle similarity, we can conclude that triangle ABE is similar to triangle CDF and triangle ADB is similar to triangle BFD.

As the corresponding sides of similar triangles are proportional, we have the following ratios:

AB/CD = AE/CF (from triangle ABE and triangle CDF similarity)

AD/BC = BD/CF (from triangle ADB and triangle BFD similarity)

Cross-multiplying the ratios, we get:

AB * CF = CD * AE (equation 1)

AD * CF = BC * BD (equation 2)

Adding equation 1 and equation 2, we have:

AB * CF + AD * CF = CD * AE + BC * BD

Factoring out CF, we get:

CF * (AB + AD) = CD * AE + BC * BD

Since AB + AD = CD (opposite sides of a parallelogram are equal), we have:

CF * CD = CD * AE + BC * BD

Simplifying, we get:

CF = AE + BC

Therefore, we have shown that BAEC = FABC.

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Answer:

Then find the product of the common prime factors. 42 = 2 ⋅3 ⋅7. 70 = 2 ⋅5 ⋅7 ... 6d2 − 21d. 27. 3y3 − 9y2. 28. 20x3 + 30x2. 29.

According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)

Quadrilateral

Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.

If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.

Here we need to find the coordinate of D'.

In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.

While we looking into the graph, we have identify the point of

A (0,0), B(-4, 3), C(1,5) and D(2,3)

Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).

According to this rule, the new coordinates are written as,

A(0,0) = A'(0,0)

B'(-4,3) = B'(-3,-4)

C(1,5) = C'(5, -1)

D(2,3) = D' (3, -2)

Therefore, the new coordinate of D' is (3, -2).

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Answer:

7.632169 units

Step-by-step explanation:

7.6 is radius Step-by-step explanation:

Answer:

1/3

Step-by-step explanation: