A cell phone is plugged in to be charged. The table shows the percent of battery power at some times after it was plugged in.

The value of the equations are a = 10 , b = -5.1 and c = 1

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

a + ( -7 ) = 3   be equation (1)

On simplifying the equation , we get

a - 7 = 3

Adding 7 on both sides of the equation , we get

a = 3 + 7

a = 10

Substituting the values in the equation , we get

1.9 + b = -3.2   be equation (2)

Subtracting 1.9 on both sides of the equation , we get

b = -3.2 - 1.9

b = -5.1

Substituting the values in the equation , we get

-1/6 + ( 7/6 ) = c   be equation (3)

c = ( 7 - 1 ) / 6

c = 6/6

c = 1

Hence , the equations are solved

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The probability of getting both a dog and a cat image is 0.25.

The probability of getting two dog images with replacement is 0.25. This is because when selecting with replacement, each draw is independent of the previous draw. Thus, the probability of getting one dog image is 0.50 and the probability of getting a second dog image is 0.50. Thus, the probability of getting two dog images is 0.50 x 0.50 = 0.25. Similarly, the probability of getting two cat images with replacement is 0.25.

The probability of getting one dog image and one cat image with replacement is 0.50 x 0.50 = 0.25. Thus the probability of getting both a dog and a cat image is 0.25.

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The area of the shaded shape WXZY is approximately 29.05 cm² to 1 decimal place.

The sector's area in a circle is the whole area that is included inside the sector's boundary. The middle of the circle is where a sector always begins. The sector of a circle is the region of a circle that is contained between its two radii and the arc next to them. A semicircle is the area of a circle that most frequently represents half of a circle.

The area of the sector OWX can be calculated as:

[tex]A = (75/360) \times \pi \times 35^{2} = 63.62 cm^2[/tex]

And the area of the sector OYZ can be calculated as:

[tex]A = (75/360) \times \pi \times 24^{2} = 34.57 cm^2[/tex]

The shaded area WXZY is the difference between the area of the two sectors, which is:

A = 63.62 - 34.57 = 29.05 cm²

Therefore, the area of the shaded shape WXZY is approximately 29.05 cm² to 1 decimal place.

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Complete question -

Answer:

60b + 12b

Step-by-step explanation:

Khai has a higher ratio of American stamps than Zachariah because 9 over 15 is less than 13 over 20.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Zachariah has 9 American stamps out of 15 stamps

Zachariah's ratio is 9 / 15 = 3 / 5=0.6

Khai has 13 American stamps out of 20 stamps.

Khai's ratio is 13 / 20 = 0.65.

0.65>0.6

Khai has a higher ratio of American stamps than Zachariah because 9 over 15 is less than 13 over 20.

Hence, Khai has a higher ratio of American stamps than Zachariah because 9 over 15 is less than 13 over 20.

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The eigenfunctions of the momentum operator px are wave functions which, when acted upon by px, result in a scalar multiple of the wave function itself, with the scalar being the eigenvalue.

To determine which wave functions are eigenfunctions of the momentum operator px, one can start by solving the eigenvalue equation, px ψ = ħkψ, where ψ is the wave function and ħk is the eigenvalue. In this equation, ħ is Planck's constant divided by 2π and k is the wave number.

To find the eigenvalue, one can multiply both sides of the equation by the complex conjugate of the wave function and integrate over all space. The result is ħk times the normalization constant, which can be used to find the eigenvalue.

The wave functions that satisfy this equation are the eigenfunctions of the momentum operator px, and their corresponding eigenvalues are proportional to their wave numbers.

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"the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, the sum of two numbers is twenty-six the difference between five is more than the larger number and twice the smaller number' into a variable expression.

Since x represents the smaller of the two numbers,

Thus the larger number will be 26 - x

The expression asked above will be:

=> 5 + larger number - 2 * smaller number

=> 5 + 26 - x - 2 * x

=> 31 -3x

therefore,  "the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

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The expression 9/4 is a real number, whereas the expression 9i is a non-real complex number.

Real Numbers:

9/4

The expression 9/4 is a real number. This can be seen by dividing the numerator (9) by the denominator (4) to get the answer 2.25. This is a real number as it can be written with a decimal.

Non-Real Complex Numbers:

9i

The expression 9i is a non-real complex number. This can be seen by taking the coefficient (9) and multiplying it by the imaginary number i. The result is 9i, which is a non-real complex number because it cannot be written with a decimal. The imaginary number i is defined as the square root of -1, which is not a real number.

The expression 9/4 is a real number, whereas the expression 9i is a non-real complex number.

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Answer:

6155.84

Step-by-step explanation:

23000

6% annual

5 years

23000*(1+6%)^5= 30799.19

so 6155.84 per year

April must pay back her auto loan at a rate of $5980 per year. This is calculated by first determining the total repayment sum (principal + interest), and then dividing this total by the number of repayment years.

In this problem about loan repayment, we are asked to find the rate at which April must pay back her loan of $23000 with an interest rate of 6%, which is to be paid off in 5 years. First, we need to determine the total amount to be paid back which is the principal plus the interest. The interest April will pay is given by the formula: Interest = Principal x Rate x Time. So, Interest = $23000 x 0.06 x 5 = $6900. Thus, the total amount to be repaid is $23000 (the principal) + $6900 (the interest) = $29900.

To find out how much she must pay per year, we divide the total payment by the number of years. Therefore, Annual Payment = $29900 / 5 = $5980 per year. So, April must pay back the loan at a rate of $5980 per year.

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The condition probability of a given b must be smaller than the intersection of the same two events a and b:

This statement is False.

The condition probability of event "b" given event "a" (P(b|a)) must be less than or equal to the probability of event "b" (P(b)). This is because the occurrence of event "a" restricts the sample space to only those outcomes that belong to event "a", and thus the probability of event "b" given event "a" cannot be greater than the unconditional probability of event "b".

The concept of conditional probability is used to describe the probability of an event given that another event has already occurred.

The formula for conditional probability is

where P(b|a) represents the probability of event "b" given that event "a" has already occurred.

In order for this to be meaningful, it is required that P(b|a) <= P(b). This means that the probability of event "b" given that event "a" has already occurred cannot be greater than the unconditional probability of event "b".

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The best estimate for 38/6 is option C that is equals to  4.

What is division ?

Division is a mathematical operation that involves splitting a number or quantity into equal parts or groups. It is the opposite of multiplication, where we find how many groups of a certain size can fit into a larger number or quantity.

When we divide one number by another, we are finding out how many times one number can be evenly divided by another number. For example, when we divide 12 by 3, we are asking "how many groups of 3 are in 12?" The answer is 4, because we can divide 12 into 4 equal groups of 3.

The best estimate for 38/6 is option C, 4.

We can see that 6 goes into 38 about 6 times (6 x 6 = 36), and there is a remainder of 2. Therefore, the answer is between 6 and 7. Since the options are all whole numbers, the best estimate is 4.

Therefore, The best estimate for 38/6 is option C that is  4.

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The notations (a) f(t) dt dx, (b) f(x) dx dt, and (c) f(t) dt dx represent functions of x and t, and a number, respectively.

The notation (a) f(t) dt dx can be interpreted as the integral of a function f(t) with respect to t from a to b multiplied by the differential of x with respect to t. By applying the Fundamental Theorem of Calculus, we can calculate this expression by evaluating the antiderivative of f(t) from a to b, which is given by F(b) - F(a), and multiplying it by the derivative of x with respect to t, which is denoted by dx/dt.

Therefore, the expression (a) f(t) dt dx can be written as F(b) - F(a) * dx/dt.

The notation (b) f(x) dx dt can also be interpreted as the integral of a function f(x) with respect to x from a to b multiplied by the differential of t with respect to x. Again, we can calculate this expression by evaluating the antiderivative of f(x) from a to b, which is given by F(b) - F(a), and multiplying it by the derivative of t with respect to x, which is denoted by dt/dx.

Therefore, the expression (b) f(x) dx dt can be written as F(b) - F(a) * dt/dx.

Finally, the notation (c) f(t) dt dx can be interpreted as the integral of a function f(t) with respect to t from a to b multiplied by the differential of x with respect to t. Therefore, this expression can be written as F(b) - F(a) * dx/dt.

It is important to note that this expression is the same as (a) f(t) dt dx, and so it can be seen that it is a number, since F(b) - F(a) * dx/dt is a constant.

The notations (a) f(t) dt dx, (b) f(x) dx dt, and (c) f(t) dt dx represent functions of x and t, and a number, respectively.

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It will take Mills approximately 1 month and 5 days to save the required amount.

Here's how you can calculate the number of months it will take Mills to save the required amount:

Calculate Mills' gross annual income:

Gross income = $20/h × 40 hours/week × 50 weeks/year = $40000/year

Subtract taxes and deductions:

Net income = Gross income - (Gross income × 10%) = $40000 - ($40000 × 10%) = $36000/year

Subtract monthly expenses:

Total monthly expenses = $1200 + $400 + $250 + $350 + $100 + $50 = $2,150/month

Monthly savings = Net income/year ÷ 12 months/year - Total monthly expenses = $36000/year ÷ 12 months/year - $2,150/month = $1,850/month

Divide the cost of the home theater by the monthly savings to find the number of months it will take Mills to save the required amount:

Months = $2150 ÷ $1,850/month = approximately 1.1667 months (or approximately 1 month and 5 days)

Therefore, Mills will need around 1 month and 5 days to save the requisite cash.

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To obtain the other factor is to take the idea  x² - 6x - 7 /x+ 1. Option A

Algebraic expressions are described as expressions comprising of terms, variables, factors, coefficients, and constants.

They are also made up of arithmetic operations, such as;

Given the expression;

x² - 6x - 7

Factorize the terms

x² - 7x + x - 7

Then, we get

(x+1) (x - 7)

The factors are (x + 1) (x -7)

Hence, the step x² - 6x - 7 divided by x - 1

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The value of y when x = 3 is 36.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

y varies directly as x².

This means,

y = kx²

Now,

When x = -1, y = 4

So,

4 = k(-1)²

k = 4/1

k = 4

Now,

y = 4x²

For x = 3,

y = 4 x 3²

y = 4 x 9

y = 36

Thus,

The value of y is 36.

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Given that cos (0) = 0, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to find the value of sin (0).

sin^2(0) + cos^2(0) = 1

sin^2(0) = 1 - cos^2(0)

sin^2(0) = 1 - 0^2

sin^2(0) = 1

So, sin (0) = sqrt(sin^2(0)) = sqrt (1) = 1.

However, the given value is sin (0) = v3/6. This means that sin (0) = sqrt (3)/2, which is the value of sin (60). Therefore, the correct value of sin (0) is sqrt (3)/2, not 1.

trigonometry, the branch of mathematics deal with specific functions of angles and their application to calculations. There is total six functions of an angle commonly used in trigonometry.

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The slope of the linear equation F = 9/5 C + 32 is 9/5. This means that for every increase of 1 degree Celsius, the Fahrenheit temperature increases by 9/5 degrees.

Therefore, the slope can be interpreted as "F increases 9/5 degrees for each increase of 1°C."

The conversion formulae we employ are the same ones found in most textbooks. Subtract 32 from the temperature in degrees Fahrenheit and multiply by.5556 (or 5/9). To convert Celsius temperatures to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.

The greater the number assigned to the temperature in fahrenheit, the hotter it is, and the lower, the colder it is.

As the originator of the thermometer as we know it, Fahrenheit had to put something on them to distinguish between different temperatures. The scale he chose became known as the Fahrenheit scale. Fahrenheit set zero to the lowest temperature he could get using a water and salt combination.

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After solving the Algebraic Expression 2(x + 8)= 2x + 8, we will get x∈∅. Variable x is dissolved in itself, making it impossible to find its value.

Before moving to solve the equation , let's learn how to solve any algebraic expression:

Step 1: Determine whether the Distributive is necessary.

Property. If so, spread the word!

Step #2: Group similar terms together on either side of the equals symbol.

(meaning: combine all of the similar factors AND

Add up each and every integer (number).

Step #3: Align the variables so that they are all to one side of the equals symbol.

utilizing the inverse process. REMEMBER: No matter what you do

You MUST do to the other side of the equals sign what you did to the one side.

equals (symbol).

Fourth Step: When all of your variables are situated on the same side of the

You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:

fourth Step: When all of your variables are situated on the same side of the

You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:

You MUST do anything you do to one side of the equals sign.

the reverse of the equals symbol).

Step #5: Using the variable's ALONE state, isolate it

the opposite process. DO NOT FORGET: No matter what you do to one

You MUST change the other side of the equals symbol to the equals symbol

Given:

2(x + 8)= 2x + 8

2 × x + 2 × 8= 2x + 8

2x+16= 2x+ 8

16= 8

So, x∈∅.

In this equation , the value of x could not be find because variable x is dissolved in itself.

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The value of y = 3 and x' = -1, y' = -3/7.

Given the equation y² = xy + 6 and knowing that y = 3 and x' = -1, we can use implicit differentiation to find the derivative of y with respect to t, y'.

       d/dt (y²) = d/dt (xy + 6)

       2y * y' = x' * y + x * y' + 0

       2 * 3 * y' = -1 * 3 + x * y'

       6 * y' = -3 + x * y'

        6 * y' - x * y' = -3

        (6 - x) * y' = -3

       y' = -3 / (6 - x)

        y' = -3 / (6 - -1)

        y' = -3 / 7

So, when y = 3 and x' = -1, y' = -3/7.

The specific case we were discussing is finding the derivative of y with respect to t, given the equation y² = xy + 6, and the values of y and x' at a certain time t. This is a problem in calculus, which is a branch of mathematics that deals with the rate of change and slopes of curves. By differentiating both sides of the equation and substituting in known values, we were able to find the value of y' at a specific time t. This method of finding derivatives is called implicit differentiation and it is used to find the derivative of an implicit equation, where one variable is expressed in terms of another.

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Answer:

Step-by-step explanation:

D

A system of linear equations has a unique solution if and only if the determinant of the matrix of coefficients is non-zero and the rank of the coefficient matrix is equal to the rank of the augmented matrix.

For the system to have a unique solution, the number of equations and the number of variables must be equal. If the determinant of the matrix of coefficients is non-zero, the system will have a unique solution if and only if the number of linearly independent rows in the coefficient matrix is equal to the number of variables. If the rank of the coefficient matrix is less than the number of variables, then the system will have either no solution or infinitely many solutions.

In conclusion, for a system of linear equations to have a unique solution, the number of equations must equal the number of unknowns and the determinant of the coefficient matrix must be non-zero. The values of a and b do not affect the existence of a unique solution.

The system of linear equations,

ax + by = c

dx + ey = f

will have a unique solution if and only if the determinant of the matrix of coefficients is non-zero, i.e., ae - bd ≠ 0. The values of a and b that satisfy this condition will result in a unique solution for the system.

If ae - bd = 0, then the system will have either no solution or infinitely many solutions, depending on the values of c and f.

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Consider the system of linear equations where a and b are unspecified constants for which values of a and b will the system have a unique solution?

The continuity equation comes from the conservation of mass.

It can be a mathematical statement of the principle of conservation of mass.

According to this, mass inflow in control volume should be equal to the mass outflow from that region at a particular time and the mass can neither be created nor be destroyed.

A continuity equation is an equation that shows the behavior of a quantity as it moves or is transported from one point or state to another

The general form of the continuity equation:

Where p=density of the fluid,

u,v,w=components of velocity in x,v, and z directions respectively.

The above equation is applicable for steady as well as unsteady, uniform s well as non-uniform, compressible as well as incompressible flow.

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The percent increase in the number of apps Tan has on his phone is 340%

Number of apps downloaded in months 1 = 5 apps

Number of apps downloaded in months 7 = 22 apps

Percentage increase in the number of apps = changes in the number of apps downloaded/ Number of apps downloaded in months × 100

= (22 - 5) / 5 × 100

= 17/5 × 100

= 3.4 × 100

= 340%

In conclusion, Tan downloaded 340% more apps on his phone after 6 months.

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Answer:

48 liters.

Step-by-step explanation:

Going from 3/4ths full to 1/2 full has a difference of 1/4; that makes 12 liters 1/4 of the tank.

12 times 4 is 48.  

Answer:

48

Step-by-step explanation:

assume holds x litres

1/2 x + 12 = 3/4 x

so 1/4 x =12

x =48

Answer:

-3/2

Step-by-step explanation:

Parallel lines have the same slope, but different y-intercepts. We can find the slope by converting to slope-intercept form:

[tex]\displaystyle 3x+2y=8\\\\2y=8-3x\\\\y=4-\frac{3}{2}x\\\\y=-\frac{3}{2}x+4[/tex]

Hence, the slope of the parallel line will also be -3/2

Answer:

3.) x=49    4.) x=29

Step-by-step explanation:

3.)

2x+82=180

2x=98

x=49

4.)

3x+3(91)=360

3x+273=360

3x=87

x=29

The required triangle WYV and XYU are congruent triangles with the SAS postulate.

In congruent geometry, the shapes that are so identical. can be superimposed to themselves.

Here,
Consider triangle WYV and XYU

XY = WY                   [Given ]

VY = UY                   [Given ]
∠WYV = ∠UYX         [Alternate interior angles for two intersecting lines are always equal]

ΔWYV ≅ ΔXYU by SAS congruency postulate.

As triangles, WYV and XYU are congruent triangles then,
VW = UX     [sides of a congruent triangle are always equal]

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Answer:

Step-by-step explanation:

You can use conversion to solve for cm

52 km x 1 cm / 4 km = 13 cm

where km cancels out leaving your answer in cm.

the actual distance on the map would be 13 cm

The -value of -2.576 is less than the critical value of 0.05, we can reject the null hypothesis and conclude that the population mean is not less than .

The -value is the probability of observing a test statistic result as extreme or more extreme than the observed result given that the null hypothesis is true. In this hypothesis test, the null hypothesis is that the population mean is less than , and the alternative hypothesis is that the population mean is not less than . With and , the -value can be calculated using the t-distribution as follows:

The t-distribution has degrees of freedom (df) equal to the sample size minus 1. Therefore, the df for this hypothesis test is .

Using the t-distribution with df = , the -value can be calculated as:

-value = P(t≤-2.576)

The -value is the probability of observing a test statistic result as extreme or more extreme than the observed result given that the null hypothesis is true.

Since the -value of -2.576 is less than the critical value of 0.05, we can reject the null hypothesis and conclude that the population mean is not less than .

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The real solutions of the equation of X² + 12X - 64 = 0 are 4 and (-16)

To find the real solutions for a quadratic equation, we need to understand this concept:

(x - a).(x - b) = x² - (a+b)x +ab

We can also use the ABC formula where:

ax² + bx + c = 0

Then:

x = -b ±√(b² - 4ac)

              2a

Using the given equation, we know that:

a = 1

b = 12

c = -64

Then, we will use the ABC formula to find the real solutions for the equation:

x = -(12) ± √(12² - 4(1)(-64))

                       2(1)

x = -(12) ± √(144 - 256)

               2

x = -12 ± √400

           2

x = -12 ± 20

           2

x1 = (-12 + 20) / 2

x1 = 8/2 = 4

x2 = (-12 - 20)/2

x2 = (-32)/2 = -16

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Complete Question:

find all real solutions of the equation by completing the square. (enter your answers as a comma-separated list. if there is no real solution, enter no real solution.) X² + 12X - 64 = 0