What is 4325 + 970 step by step explanation pls

Answer:

x>-2

Step-by-step explanation:

3 times five is fifteen, which is larger than 12, so all x needs to be is be bigger negative 2.

We need to know how to read a graph inorder to solve the problem. At the end of 6 weeks, Lorena will have more money, she will have $8 more than Benita.

We know that Lorena started with $40 and she added $8 every week. We need to find out the final amount she has at the end of 6 weeks. For Benita, we can see from the graph that she started with $50, since the graph starts from $50, and if we observe the amount after every week we can see that she adds $5 every week to the savings. We can directly say from the graph that the final amount Benita has after 6 weeks is $80.

amount Lorena has after 6 weeks = 40+ (6x8)=40+48=$88

Therefore we can see that Lorena will have more money after 6 weeks and she has $8 more than Benita.

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Answer:

Step-by-step explanation:

The sampling distribution for is normal (or approximately normal) and give its mean and standard deviation is  the mean is $28520 and its standard deviation is $762.5.

The notion of mean is crucial in both mathematics and statistics. The mean is the average or most frequent value among a set of numbers. It is a statistical measure used to determine the median and mode of a probability distribution's central tendency. It's also known as an expected value. Sum of all observations divided by the total observations equals the mean. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.  

Given information :

Mean annual income = $28540

Standard Deviation = $5000

Given sample size is n = 43

Sample size doesn't affect the mean, hence the mean remains the same

New mean = $28540

New standard Deviation = Standard Deviation / n^1/2 = 5000/ (43)^1/2

New standard Deviation = 5000/6.5574 = $762.5

Hence, The mean is $28520 and its standard deviation is $762.5

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⇒For perpendicular lines when their gradients are multiplied they have to give -1, in this case we are given a line with gradient [tex]\frac{1}{2}[/tex] meaning the gradient of the line perpendicular to it will be -2 since

[tex]-2*\frac{1}{2} =-1[/tex]  this means that the gradient of the new line will be -2

⇒Now we have a point and  gradient.

⇒And we know that the general equation for a straight line is y=mx+c

[tex]3=-2(0)+c\\3=c\\c=3[/tex]

The equation of the line perpendicular to the given one is

y=-2x+3

GOODLUCK!!

Given data:

The given amount of equipment purchased by the Sandra is A=$1,200.

To solve an inequation for x you have to follow the same procedure you follow when solving equations, with exception that when you multiply/divide by a negative number the direction of the inequality gets inverted.

So to solve the given inequelity for x, you have to pass "+49" to the other side of the expression. To do so, subtract it from both sides of the expression:

The result of the inequality is x > -21

Answer:

7/6 feet

Step-by-step explanation:

The board is 3 and 1/2 feet long, so it is 3+(1/2) feet long.

3 + 1/2 = ?

3/1 + 1/2 = ?

6/2 + 1/2 = ?

(6 + 1)/2 = ?

= 7/2

3 + 1/2 = 7/2

In other words, the board is 7/2 feet long.

Now we have to divide by 3 since Andrea is cutting the board in three pieces.

So:

(7/2)/3       or        (7/2) ÷ 3       or        [tex]\frac{\frac{7}{2}}{3}[/tex]        or     (7/2) × (1/3)

= 7/(2×3)

= 7/6

So we found that each piece (after cutting the board into three pieces) is 7/6 feet long.

We have the following expression

This can't be a vertex, since, in geometry, a vertex is a point where two or more elements meet.

A domain is not either, since, in mathematics, the domain of a function is the set of the existence of itself, that is, the values for which the function is defined.

The Standard Form of a Quadratic Equation looks something like this:

Where a, b, and c are known values and a cannot be 0.

In conclusion, the answer is that is a Quadratic

Solve for b

-73 = b/7- 81

b= 56

-511=b-567

b-567=-511

b=-511+567

b=56

Solution 2

Add 81 to both sides.

-73+81= b/7

simplify -73+81 to 8

8=b/7

8*7=b

simplify 8*7 to 56

56=b

switch sides b= 56

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If the equation be -73 = b/7- 81 then the value of b is 56.

Solve for b

-73 = b/7- 81

b= 56

-511=b-567

b-567=-511

Hence,

b=-511+567

b=56

Solution 2

Add 81 to both sides.

-73+81= b/7

simplify -73+81 to 8

8=b/7

8*7=b

simplify 8*7 to 56

56=b

switch sides b= 56

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Total capacity the tower holds 1.034 x 10^5  gallons of water

One tower holds 8.4 x 10^3 gallons of water

Other tower holds 9.5 x 10^4 gallons of water

The combined water capacity of the two towers in scientific notation is,

Total capacity the tower holds = 9.5 x 10^4 + 8.4 x 10^3

    = 9.5 x 10^4 + 0.84 x 10^4

    = 10.34 x 10^4

    = 1.034 x 10^5

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The answer for the equation:

7x+31 = 8x -1/3(27x+3) is x=-4

Answer:Answer: number 2 is correct

The equation of the line is found as y = -x/2 + 9/2.

For the given question;

The equation of the perpendicular line is given as;

y = 2x - 7

Compare the equation with the standard form of slope intercept.

y = mx + c

m = slope and c is the y intercept.

m1 = 2

Now, the line is perpendicular, thus the relation between both slopes is;

m1 × m2 = -1

m2 = -1/2

The passing coordinates of the line is (1. 4).

Find the equation using formula.

y - y1 = m2(x - x1)

y - 4 = (-1/2) (x - 1)

Simplifying,

y = -x/2 + 9/2

Thus, the equation of the line is found as y = -x/2 + 9/2.

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The 80th percentile for the number of hours spent studying each day is 7.07 hours.

A data set with a normal distribution has the majority of its values clustered in the middle of the range, while the remainder taper off symmetrically toward either extreme. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are dispersed when the standard deviation is high.

The percentage of scores below a given value is shown by percentiles. They provide information about how a score compares to other scores.

Given Data :

Mean time (u) = 6.4 hour

Standard Deviation = 0.80 hour

It is given that the probability distribution is normal.

The formula for the z-score is z =( x- mean)/standard deviation

For the 80th percentile,  the z value from the z table is 0.842.

We have,

0.842 = (x - 6.4)/0.8

0.842*0.8 = x - 6.4

0.6736 =x - 6.4

x = 0.6736 + 6.4

x = 7.0736

x = 7.07

Hence, the 80th percentile for the number of hours spent studying each day is 7.07 hours.

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We have the next function

First we need to make h(x)=y

Then we make x=y and y=x

Then we isolate the y

Therefore the inverse function is

Explanation:

Take any two whole numbers you want. Multiplying them together always result in some (other) whole number.

Examples:

In other words,

(whole number)*(whole number) = whole number

This is why we consider the set closed under multiplication.

The percentage of young adults who send fewer than 218 text messages is 99.87%.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 218

μ = mean = 128

σ = standard deviation = 30

z-score = (218 - 128) / 30

z-score = 90 / 30

z-score = 3

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 3

probability = 0.9987

To get the percentage, multiply the probability by 100.

percentage = probability x 100

percentage = 0.9987 x 100

percentage = 99.87%

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The width of the cooling tower at the base of the structure is (D) 40 meters.

Now, calculate the cooling tower's width:

Equation: x2/400 given (y-90)

Calculating the width:

Therefore, the width of the cooling tower at the base of the structure is (D) 40 meters.

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When q = -17, the value of the equation, q - 7 would be: d. -24.

If we are given an equation to evaluate for a given value of a variable, we are to substitute the value of the variable into the equation and solve or simplify.

For example, if an equation is given as 3x + 4, and we are told that the x = 3, to determine the value of the equation, 3x + 4, substitute x = 3 into the equation as:

3(3) + 4

= 9 + 4

= 13

Here, we can now conclude that the value of the equation is 13.

Given the equation, q - 7, to find the value of the equation when q = -17, substitute the value of q into q - 7.

Therefore:

q - 7 = -17 - 7

= -24.

The value of the equation is: d. -24.

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The value of q - 7, when q = - 17 is - 24.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, q = - 17.

∴ q - 7.

To solve our expression we'll substitute the numerical value of q in the given expression.

= (-17) - 7.

= - 17 - 7.

= - 24.

We can also take negative sign common in the second step and distribute them later.

- 17 - 7.

= - (17 + 7).

= - (24).

= -24.

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Compound interest: $8,765.58

The approximate air distance from La Sarre to Lebel-sur-Quevillon is 167.71 km.

To determine the air distance from La Sarre to Lebel-sur-Quevillon, analyze the path she has traveled.

When she drove east and drove another north, the total path she ave traveled is similar to the sides of a right triangle, where the distance from the start and end point is the hypotenuse. (see photo attached)

Using Pythagorean theorem, solve the distance from La Sarre to Lebel-sur-Quevillon.

c² = a² + b²

where a = 150 km and b = 75 km

distance² = 150² + 75²

distance² = 22500 + 5625

distance² = 28125

distance = 167.71 km

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The most appropriate choice for matrices will be given by-

Required Equation

[tex]y = 2x^2 - 3x + 1[/tex]

What are matrices?

If the numbers are arranged in the form of rows and columns, then the arrangement is called matrix.

Here,

The equation is [tex]y =Ax^2 + Bx + C[/tex]

The function contains the points (0, 1), (-2, 15), (3,10).

On putting these coordinates in the equation,

C = 1

[tex]15 = A(-2)^2 + B(-2) + 1\\4A - 2B = 15-1\\2(2A - B ) =14\\2A - B = \frac{14}{2}\\2A -B = 7[/tex]................ (1)

[tex]10 = A(3)^2 + B(3) + 1\\9A + 3B = 10-1\\3(3A + B ) =9\\3A + B =\frac{9}{3}\\3A + B = 3[/tex].................... (2)

Here matrix method will be used

Let

[tex]P = \begin{bmatrix} 2 & -1\\ 3 & 1 \end{bmatrix}[/tex], [tex]Q = \begin{bmatrix} x \\ y\end{bmatrix}[/tex], [tex]R = \begin{bmatrix} 7\\3 \end{bmatrix}[/tex]

PQ = R

[tex]Q = P^{-1}R[/tex]

Adjoint P =

[tex]\begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}^T\\\\\begin{bmatrix} 1 & 1 \\ -3 & 2 \end{bmatrix}[/tex]

Det P = [tex]\begin{vmatrix} 2 & -1\\3&1\end{vmatrix}[/tex]

          = [tex]2\times 1 - 3 \times (-1)\\5[/tex]

[tex]P^{-1} = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}[/tex]

[tex]Q = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}\begin{bmatrix}7\\3\end{bmatrix}[/tex]

[tex]Q = \frac{1}{5}\begin{bmatrix} 10\\-15\end{bmatrix}\\Q= \begin{bmatrix} 2\\-3\end{bmatrix}[/tex]

A = 2, B = -3

Required Equation

[tex]y = 2x^2 - 3x + 1[/tex]

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Complete Question

Use matrices to write the equation of the function in the form [tex]y = Ax^2 + Bx + C[/tex]that contains the points (0, 1), (-2, 15), (3,10).

Answer:

14.7 times bigger is (1.176 x 10¹) than (8 × 10-¹) if the numbers are  (1.176 x 10¹) than (8 × 10-¹).

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

To compare numbers this way, we divide.

(1.76 × 10^1) / (8 × 10^-1) =

= 1.76/8 × 10^1 / 10^-1

= 0.22 × 10^(1 - (-1))

= 0.22 × 10^2

= 22

     The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

  For instance, the equation -2x²-8x = 10 consists of the two equations  is rewritten in the form of 2(x-p)²+ q = 0. , which are separated by the 'equal' sign.

Answer :q = -2

-2x²-8x = 10 (divide both sides by -2)

x² + 4x = -5 (Apply completing the square method)

x² + 4x + (4/2)²= -5 + (4/2)²

x² + 4x + 2²= -5 + 2²    (reduce left hand side using a²+2ab+b² =  (a+b)² )

(x+2)² = -5 +4

(x+2)² = -1

(x+2)² + 1 = 0   (multiply both sides by -2)

(-2)(x+2)² + 1 (-2) = 0

-2[x - (-2)]² + (-2) = 0  ---> compare this with -2(x-p)² + q = 0

We can see that p = 2 and q = -2

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By solving matrices  we get,

[tex]A+B= \left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] , C-B=\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right] \\\\\\\\A+B+C = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]

A matrix is a rectangular array or table that contains numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a characteristic of such an entity. As an illustration, consider a matrix with two rows and three columns.

Adding matrices, subtracting matrices, and multiplying matrices are the three algebraic operations that make up the majority of matrix operations. Array of numbers or expressions arranged in rows and columns is called a matrix. The field of mathematics has several useful uses for matrices.

Here the matrices A, B and C are given in the question, so we use matrix addition and matrix subraction operations to solve the question.  

When solving by using the matrices solving method we get

[tex]A+B=\left[\begin{array}{ccc}5&7\\-1&6\\3&-9\end{array}\right] +\left[\begin{array}{ccc}8&3\\5&1\\4&4\end{array}\right]= \left[\begin{array}{ccc}5+8&7+3\\-1+5&6+1\\3+4&-9+4\end{array}\right]=\left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] \\[/tex]

[tex]C-B = \left[\begin{array}{ccc}0-8&4-3\\-2-5&5-1\\7-4&-1-4\end{array}\right] =\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right][/tex]

[tex]A+B+C= \left[\begin{array}{ccc}5+8+0&7+3+4\\-1+5+-2&6+1+5\\3+4+7&-9+4+-1\end{array}\right] = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]

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Given that;

Line a and b are two straight lines cut by two transversal lines l and m.

The tranversal line l shows that;

But also;

Thus,

Then, if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

Thus, line l is parallel to m