Luis bought some milk for his bakery. He used 2.4 gallons in one recipe, and 1/4 of the remaining miolk in another recipe. He had 3/8 of the milk left. How much milk did Luis buy?

The equation that represents the line of Paul's grade downfall is y = -20x + 130.

To find the equation of the line that represents Paul's grade downfall, we need to use the two points given: (2, 90) and (4, 50).

We can use the slope-intercept form of a linear equation,  y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of the line, we can use the formula: slope (m) = (y2 - y1)/(x2 - x1).

Plugging in the values from the two points we have:

m = (50 - 90)/(4 - 2) = -40/2 = -20.

y = mx+b     [Using  (x= 2, y = 90)]

90 =-20(2) + b

90 = -40

b = 130

Plugging these values into the slope-intercept form, we get:

y = -20x + 130.

Thus, the equation is y = -20x + 130

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The solution for x in the equation ax = bx + c is x = c/(a - b)

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

ax=bx+c

Also, from the question, we have the following variable to solve

Variable = x

Rewrite the given equation as

ax = bx + c

Using the above as a guide, we have the following:

Subtract bx from both sides of the equation

So, we have the following representation

-bx + ax = bx + c - bx

Evaluate the like terms

ax - bx = c

So, we have

x(a - b) = c

Divide by a - b

x = c/(a - b)

Hence, the solution is x = c/(a - b)

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True, The dimension of the eigenspace for each eigenvalue equals the multiplicity.

Eigenvalues are a unique set of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar factor.

When a linear transformation is done to an eigenvector, a set of eigenvectors called an eigenspace is created for each eigenvalue. In many cases, the linear transformation uses a square matrix (a matrix that has the same number of columns as it does rows).

yes, it is true that the dimension of an eigenspace of a symmetric matrix is sometimes less than the multiplicity of the corresponding eigenvalue.

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Answer:

Step-by-step explanation:

To determine the ratio of the note B to middle C, we can divide the frequency of B by the frequency of C. Using the information provided, the frequency of B is 493.9 Hz and the frequency of C is 261.6 Hz. The ratio of B to C is therefore 493.9 / 261.6, which is approximately equal to 1.89. This means that the note B is approximately 1.89 times higher in pitch than the note C.

The length of UT if, The line UV || RS, UV is 12 less than UT, RT = 42, and RS = 21 is,24.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Given:

The line UV || RS,

UV is 12 less than UT,

RT = 42, and RS = 21,

Write the equation for the UV and UT,

UV = UT - 12

Calculate the value of UT as shown below,

UT / RT = UV / RS     (For parallel lines, the ratio should be the same)

UT / 42 = (UT - 12) / 21

21 × UT / 42 = (UT - 12)

UT / 2 = (UT - 12)

UT = 2UT - 24

2UT - UT = 24

UT = 24

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The probability of rolling a sum that is at most 7 = 1/6

What is probability and example?

sample space (S) = 36

The probability of rolling a sum that is at most 7

No of sample space = { (1,6) ,(2,5) ,(3,4), (4,3),(5,2),(6,1)}

n(s)/ total sample space = 6/36

                                        = 1/6

Therefore, he probability of rolling a sum that is at most 7 = 1/6

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The answer is 64

If you need a breakdown I don't know how to help.

The speed from City A to City B is 873.33 mi/h.

What is the speed, distance and time?

That is speed = distance ÷ time. Or to put it another way, distance divided by speed will give you the time. Provided you know two of the inputs you can work out the third.

Let's call the speed from City A to City B x. The speed on the return trip was 1.2x. The total distance traveled was 2400 + 2400 = 4800 mi. The total time taken was 330 minutes, which is 330/60 = 5.5 hours. The average speed is the total distance traveled divided by the total time taken, so:

4800 mi / 5.5 h = 873.33 mi/h

The total speed for both legs of the trip is 873.33 + 873.33 = 1746.66 mi/h

The speed for just one leg of the trip is half of the total speed, so the speed from City A to City B is 1746.66/2 = 873.33 mi/h.

Hence, the speed from City A to City B is 873.33 mi/h.

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The gross pay for Riddler for working 47 hours will be $783.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the Riddler earns $18 per hour at the Gotham Police Station. He regularly works 40 hours per week. He is paid time-and-a-half for each hour of overtime work. Last week he worked 47 hours.

The overtime cost = 1/2 x 18

The overtime cost = $9

The gross pay will be calculated as,

Gross pay = ( 40 x 18 ) + ( 7 x 9 )

Gross pay = 720 + 63

Gross pay = $783

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Answer: Given the log function ln(100), this can therefore be written as loge(100)

Step-by-step explanation: Logarithmic functions

Logarithmic functions are inverse of exponential functions. There are different ways to write log function;

Some are written as a exponent base

Some to the base of 10

Loga is also written as log10(a)

lna is written as loge(a)

Given the log function ln(100), this can therefore be written as loge(100)

Answer: C log(10).

Step-by-step explanation: When you calculate In (10), you would be finding the value of log(10).

In mathematics, the logarithm function is used to express the exponent to which a base must be raised in order to produce a given number. The base of the logarithm is usually denoted by "b" and the number whose logarithm is being taken is denoted by "x". The logarithm of x to base b is denoted as logb(x).

For example, the logarithm of 10 to base 10 is denoted as log10(10), which is equal to 1. The logarithm of 100 to base 10 is denoted as log10(100), which is equal to 2.

In general, the logarithm of x to base b can be calculated as follows:

logb(x) = y

This equation states that b raised to the power of y is equal to x.

The natural logarithm, denoted as In, is a special case of the logarithm function where the base is the mathematical constant e (approximately 2.718). The natural logarithm of x, denoted as In(x), is equal to the logarithm of x to base e.

Therefore, when you calculate In (10), you are finding the value of the natural logarithm of 10, which is the logarithm of 10 to base e.

Option A log (10) is incorrect because it is missing the base of the logarithm (e).

Option B log₁0(e) is incorrect because it is the logarithm of e to base 10, which is not the same as the natural logarithm of 10.

Option D 10 In(e) is incorrect because it is the value of 10 raised to the power of the natural logarithm of e, which is not the same as the natural logarithm of 10.

Option C log(10) is correct because it is the natural logarithm of 10, which is the value we are trying to find. Therefore, the correct answer is C log(10).

To solve this problem, we can use the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c and the angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2abcos(C)

In this problem, we are given the measure of angle C and the lengths of sides b and c. We can use this information to find the length of side a and the measures of angles A and B.

First, we can use the Law of Cosines to find the length of side a. Plugging in the given values, we get:

a^2 = c^2 - b^2 + 2bc cos(C)

Substituting in the given values, we get:

a^2 = 151^2 - 181^2 + 2 * 151 * 181 * cos(60.0°)

Solving this equation gives us a = 143 m.

Now that we have the length of side a, we can use the Law of Sines to find the measures of angles A and B. The Law of Sines states that for a triangle with sides a, b, and c and angles A, B, and C opposite these sides, the following equation holds:

a/sin(A) = b/sin(B) = c/sin(C)

We are given the lengths of sides a and b and the measure of angle C. We can use this information to find the measures of angles A and B.

First, we can use the Law of Sines to find the measure of angle A. Plugging in the given values, we get:

a/sin(A) = b/sin(B)

Solving for sin(A), we get:

sin(A) = a * sin(B) / b

Substituting in the given values, we get:

sin(A) = 143 m * sin(B) / 181 m

To find the measure of angle A, we can use the inverse sine function (sin^-1). This gives us:

A = sin^-1(sin(A))

= sin^-1(143 m * sin(B) / 181 m)

Similarly, we can use the Law of Sines to find the measure of angle B:

B = sin^-1(143 m * sin(A) / 181 m)

Since we have two unknowns (A and B) and two equations, there is a unique solution for this triangle.

Therefore, the number of solutions is 1, and the measures of angles A and B are A = 38.5° and B = 101.5°. The length of side a is 143 m.

option c)   4x⁴ -2x³ -2x² +3x -10

On subtracting we will get

(3x²₋ 2x + 4x⁴) - (5x²+2x³-5x+10)

= 3x²- 5x²- 2x -2x³+ 4x⁴+ 5x -10

= -2x² + 3x  -2x³ + 4x⁴- 10

= 4x⁴ -2x³- 2x² + 3x - 10

The given sum belongs to quadratic equation

Quadratic equation definition:

When a, b, and c are real-world coefficients, a second-order equation is said to be quadratic if it is represented as ax²+ bx + c = 0.

The Characteristics of Quadratic Equations' Roots

The discriminant of the quadratic equation ax2+bx+c=0 is (b2-4ac), which determines whether or not the equation has real roots.

The quadratic equation ax2+ bx + c= 0 hence

If b2-4ac >0, two different real roots

If b2-4ac= 0, there are two equal real roots.

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The exponential growth function is P = 6.51 (1.0275)^t. The population of the city in 2018 will be 7.66 million. The population of the city will be 10 ​million in 15.82258467 years and the doubling time is 25.55035862 years

The exponential growth function is of the form P = P₀(1+r)^t

where P₀ is the current population, r is the growth rate and t is the time

Given: P₀ =  6.51 million, r = 2.75​% per year

a) The exponential growth function

P = 6.51 (1+0.0275)^t

P = 6.51 (1.0275)^t

​b) The population of the city in 2018

t = 2018-2012 = 6 years

P = 6.51 (1.0275)^t

P = 6.51 (1.0275)⁶ = 7.66 million

​c) When the population of the city will be 10 ​million

P = 6.51 (1.0275)^t

10 =  6.51 (1.0275)^t        (Solve for t)

(1.0275)^t =10/6.51

log (1.0275)^t = log(10/6.51)

t × log (1.0275) = log(10/6.51)

t = [log(10/6.51)] / [log (1.0275)]

t = 15.82258467 years

d) The doubling time

P =  6.51 (1.0275)^t will become:

2 = 1 (1.0275)^t

1.0275^t = 2

log(1.0275)^t = log 2

t log(1.0275) = log 2

t = log 2 / log 1.0275

t = 25.55035862 years

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The numbers as they appear from left to right on a horizontal number line is Horizontal number line.

This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a horizontal number line, the numbers increase; as we move towards the left, the numbers decrease.

What's the equation of a horizontal line?

Horizontal lines have a slope of 0. Thus, in the slope-intercept equation y = mx + b, m = 0. The equation becomes y = b, where b is the y-coordinate of the y-intercept.

-2.76

-2.57

-2.5

-1.85

-1.58

2.5

2.85

On a number line, we have this horizontal line, meaning it moves left and right, and zero is placed in the middle.

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Answer: x = 10.57 and y = 15 degree

Step-by-step explanation:

Answer: x= 10 degrees

y= 15 degrees

Step-by-step explanation:

There is no enough evidence to assert that the standard deviation of the process (in general) is over 2 mg

To determine whether the standard deviation of the process (in general) is over 2 mg to a 1% level of significance, you can perform a hypothesis test.

In this case, the null hypothesis is that the standard deviation of the process is equal to or less than 2 mg, and the alternative hypothesis is that the standard deviation of the process is greater than 2 mg.

To perform the hypothesis test, you can first calculate the test statistic. That is:

test statistic = (sample mean - hypothesized mean) / (standard error of the mean)

test statistic = (20.2 - 20) / (2.4 / √(13))

                    = 0.2 / 0.67

                    = 0.3

Next, you can look up the critical value for the test statistic in a table of critical values for a one-tailed test with a 1% level of significance and 12 degrees of freedom (df = 13 - 1).

The critical value for the test statistic is 2.6. Since the test statistic (0.3) is less than the critical value (2.6), you cannot reject the null hypothesis.

This means that you do not have enough evidence to assert that the standard deviation of the process (in general) is over 2 mg to a 1% level of significance.

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The graphs of the equations are drawn ad attached here.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

The given equations are (i) y = x-4, (ii) y = 2x-4, (iii) y = 3x-4.

The equations are given in the slope-intercept form.

(i) The given equation is y = x-4.

   the y-intercept of the equation is (0,-4).

Now, substitute y = 0 into the given equation:
0 = x - 4

x = 4

Hence, the line y = x-4 passes through points (0,-4) and (4,0).

Now, draw a line passing through the points (0,-4) and (4,0).

Using the same procedure, the graphs of the other two equations are also drawn.

Hence, the graphs of the equations are drawn ad attached here.

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Answer:

Step-by-step explanation:

It is likely that Sharon's calculated mean time is the better estimate of the actual mean time for the whole class. This is because she collected data from a larger sample of the class (10 students) than Gerald (4 students). A larger sample size generally results in a more accurate estimate of the population mean.

It is more likely for the mean time calculated by Sharon to be better estimate than that of Gerald.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Given,

Mean time to complete the assignment taken from 4 students by Gerald = 38 minutes.

Mean time to complete the assignment taken from 10 students by Sharon = 32 minutes

Population size = 30 students

When the sample size is more closer to the population size, the sample mean would be more closer to the actual mean.

So Sharon's estimate is a better option.

Hence the estimate value of mean calculated by Sharon is more likely to be closer to the actual mean.

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The correct option  4 and 25; the degrees of freedom for the critical value of f.

The essential value F's degrees of freedom are (k-1,n-k).

Four sample groups are provided to us, so,

k = 5.

Additionally, we know that each of the five groups has six observations, therefore

n = 5*6

n = 30

The crucial factor F can vary in freedom.

(k-1,n-k)

(5-1, 30 - 5)

(4,25).

Its degrees of freedom again for critical F value are as a result (4,25).

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Answer:

377 is answer

Step-by-step explanation:

12.33-25 +6

396-25+6

377

Answer:

QR = 49

Step-by-step explanation:

QR = QP

3x + 22 = 10x - 41

x = 9

10(9) - 41

= 49

The completed table and the graph of the proportional relationship are given by the image shown at the end of the answer.

The proportional relationship in this problem is defined as follows:

s=2 b.

The variables are defined as follows:

Then the graph of the proportional relationship is that of a linear function with these following features:

Then the numeric values that complete the table are calculated as follows:

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The term that is the −20,155,392 in the sequence is a₁₀.

A sequence is defined as an arrangement of numbers in a particular order.

The given sequence is 2, -12, 72, -432

a = first term

n = number of terms

r = common ratio

r = -12 / 2 = 72 / -12 = -432 / 72 = -6

a = 2

Therefore, nth term = arⁿ⁻¹

−20,155,392 = 2 × -6ⁿ⁻¹

−20,155,392 / 2 = -6ⁿ⁻¹

- 10077696 =  -6ⁿ⁻¹

6ⁿ⁻¹ = 10077696

6ⁿ⁻¹  = 6⁹

n - 1 = 9

n = 9 + 1

n = 10

Hence, it's the 10th term.

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Answer:

52

Step-by-step explanation:

Substitute the value -4 into the expression and simplify:

3(-4)^2 - (-4)

3(16) + 4

48 + 4

52

Step-by-step explanation:

the domain is the interval or set of all valid x- (or input-)values. in our case here t-values.

the graph shows us

0 <= t <= 35

For the given condition on the graph, the domain of the function is

0 ≤ t ≤ 36.

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical connections in the sciences. A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output.

Here,

The correct answer is option B. 0 ≤ t ≤ 36

To do this question, the main thing is to look at picture.

We know from the graph that this is a quadratic function, So t has to be less than some positive number.

{ if t → -∞, H(t) → -∞, not in the line with the actual situation}

and look at the graph, the point where H(t) equals zero, one is 0 and one is 36.

The domain for the function is 0 ≤ t ≤ 36 for given condition in the graph.

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a. The probability of defective shells from the given samples are:

a. Probability of zero defective shells of samples is equal to 0.9510.

b. Probability of one defective shells of samples is equal to 0.04803

c. Probability of more than 1 defective shells of samples is equal to 0.00107.

As given in the question,

Total number of batches = 350

Sample size used to test for each batch 'n' = 5

Actual defective shells (success) 'p' = 1%

                                                           = 0.01

Actual non-defective shells ' 1 - p ' = 1 - 0.01

                                                         = 0.99

a. Probability of zero defective shells from the given samples is

=  ⁵C₀ × ( 0.01 )⁰ × (0.99)⁵⁻⁰

= [ (5!)/(5-0)!0! ] × 1 × ( 0.99)⁵

= 0.9510

b. Probability of 1 defective shells from the given samples is

= ⁵C₁ × ( 0.01 )¹ × (0.99)⁵⁻¹

= [ (5!)/(5-1)!1! ] × 0.01 × ( 0.99)⁴

= 5 × 0.01 × 0.9606

=0.04803

c. Probability of more than 1 defective shells from the given samples is

= P(2) + P(3) + P(4) + P(5)

= ⁵C₂ × ( 0.01 )²× (0.99)⁵⁻² + ⁵C₃ × ( 0.01 )³ × (0.99)⁵⁻³ + ⁵C₄× ( 0.01 )⁴ × (0.99)⁵⁻⁴+ ⁵C₅× ( 0.01 )⁵× (0.99)⁵⁻⁵

= 0.00097 + 0.000098 +0.000000044 +0.0000000001

=0.00107

Therefore, the probability of following conditions are as follow:

a. Probability of zero defective shells of samples is equal to 0.9510.

b. Probability of one defective shells of samples is equal to 0.04803

c. Probability of more than 1 defective shells of samples is equal to 0.00107.

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The inverse of the rational function h(x) = (2 · x + 3) / (4 · x - 5) is the rational function h⁻¹(x) = (5 · x + 3) / (4 · x - 2).

In this problem we have the definition of a rational function:

h(x) = (2 · x + 3) / (4 · x - 5)

Of which we must determine the inverse of the rational function by using algebraic properties:

h⁻¹(x) = f(x)

First, use the following substitution on h(x):

x = h(x)

h⁻¹(x) = x

Second, substitute in the rational equation:

x = [2 · h⁻¹(x) + 3] / [4 · h⁻¹(x) - 5]

Third, clear h⁻¹(x) in the expression by algebraic properties:

x · [4 · h⁻¹(x) - 5] = 2 · h⁻¹(x) + 3

(4 · x - 2) · h⁻¹(x) = 5 · x + 3

h⁻¹(x) = (5 · x + 3) / (4 · x - 2)

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Given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.

The general equation of a straight line is -

Other possible equations of lines are -

We have the equation of line as -

y = 3x - 8

The given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.

Therefore, given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.

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The graph in the problem is interpreted as follows

What interpretation can be made from the y-intercept?

the y-intercept shows start the timing started when the cheetah is not running

How can the point (3.0, 12) on the graph above be interpreted? At 3.0 s the cheetah was running at 12 m/s

What is the output value of this graph when the input value is 5.0?

the output is 30

Does the graph above have a constant rate of change?

No, the rate of change varies

The term "rate of change" describes the rate at which something changes over time.

Thus, it is not the amount of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate).

When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant.

The slope is another name for the constant rate of change. The rate of change for linear functions will be constant.

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Answer: 48

Step-by-step explanation:

Using isosceles triangle [tex]XWZ[/tex], we know that [tex]WZ=11[/tex].

Using equilateral triangle [tex]XYZ[/tex], we know that [tex]YZ=XY=11[/tex].

So, the perimeter is [tex]WX+WZ+ZY+XY=11+11+11+15=48[/tex].