what is the slope of the line that passes through (37, -9) and (36, 81)

Answer:

a) The equation has the greatest slope.

Step-by-step explanation:

The table has the values as shown below;

x    y

1    3

2   6

3   9

The gradient of the line can be found as;

m=Δy/Δx

m= 9-3 /3-1

m= 6/2

m₁= 3

The equation of the other line is :   y=4x

The gradient is , m₂ = 4

The presentation with the greatest slope is the equation that has a slope of 4.

The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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Answer:

m=13

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I don´t really understand.

I am so sorry!

Therefore , the solution of the given problem of surface area comes out to be  0.2083 yard square.

A surface is a measurement of how much overall space an object's surface takes up. Surface area of a three-dimensional shape is determined by the total area of its surroundings. Surface area is the term used to describe a triangular shape's entire surface area. The particular area of each face on a cube with six square faces can be added up to determine the cube's surface area. Alternately, you can get the box's dimensions by using the following formula: Surface (SA) equals twice twice twice twice. A three-dimensional shape's surface area is calculated as the sum of all the space it occupies.

Here,

Given : width : 5/6 yard

and length = 1/4 yard

To find the area = length * width

=> area = 5/6 * 1/4

=> area = 5/24

=> 0.2083 yard square.

Therefore , the solution of the given problem of surface area comes out to be  0.2083 yard square.

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Answer:

-1...................

Step-by-step explanation:

x+3-x-4

o-1

-1

Answer :

-1

Explanation:

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Answer:

2/5

Step-by-step explanation:

start by 8*5 then 10 times 10 then simplify

Answer:

2/5

Step-by-step explanation:

A nickel is worth= 5 cents.

A dime is worth= 10 cents.

So ratio=8×5/10×10

=40/100

=2/5

So the ratio is 2/5

The elements of set C that are less than or equal to -11 are -11, -12, -13, -14, and -15.

Set C consists of negative integers greater than -15. In order to determine which elements of set C are less than or equal to -11, we need to identify the negative integers that fall within that range.

Starting with the number -11, we can check if it is included in set C. Since the set C includes negative integers greater than -15, and -11 is greater than -15, we can conclude that -11 is an element of set C.

Therefore, the elements of set C that are less than or equal to -11 are -11, -12, -13, -14, and -15.

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Answer:

irrational

Step-by-step explanation:

every number that times with pi are irrational, only zero gives a rational number

This problem is about equations.

The first car have the next equation for your distance from math city:

where d is the distance and h is our unknown value.

And for the second car the equation for distance is:

So, we want to know the value of h which make d equal value for both cars. That's mean:

Now, we isolate h from the equation above:

The answer is h=4 hours.

Answer:   y=-2x+9

Step-by-step: Subtract 2x from 2x+y=9 and get y=-2x+9

The remaining amount of salt that Tom needed to pour was 67.59 grams.

To subtract in mathematics is to take something away from a group or a number of objects.

In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

The group's total number of items decreases or becomes lower when we subtract from it.

As per the given,

The total amount that Tom needs to pour = 84.99 grams

Amount poured = 17.4 grams

Remaining = 84.99 grams - 17.4 grams = 7.59 grams

Hence "The remaining amount of salt that Tom needed to pour was 67.59 grams".

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Answer:

$44.04

Step-by-step explanation:

let 3 be the number of people and 14.68 the person owes

3*14.68 = 44.04

Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

It is

log 39=2

Explanation:

By definition the logarithmic form

log bx=y is equivalent to the exponential form

by=x

Hence from the given 32=9 you have b=3 , y=2 , x=9

hence the logarithmic form is

log 3 9=2

The independent Variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

The table above illustrates the relationship between the temperature of a substance and its volume. The independent variable is the temperature of the substance and the dependent variable is the volume of the substance.

The symbol or name used to represent the independent variable is "T" for temperature and its units are given as degrees Celsius or °C.The symbol or name used to represent the dependent variable is "V" for volume, and its units are given as milliliters or mL.

The temperature is the independent variable as it is being manipulated in the experiment while the volume is dependent on the temperature as it is changing based on the temperature.

An independent variable is a variable in an experiment that is being manipulated by the experimenter, while the dependent variable is the variable that is being measured in response to changes in the independent variable.

In summary, the independent variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

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Answer:

The quadratic equation is in the standard form: ax^2 + bx + c = 0. To use the quadratic formula to find the solutions, we need to identify the values of a, b, and c in the equation:

a is the coefficient of the x^2 term, which is -3 in this case.

b is the coefficient of the x term, which is -5 in this case.

c is the constant term, which is 9 in this case.

Therefore, the values of a, b, and c in the quadratic equation -3x^2 - 5x + 9 = 0 are:

a = -3

b = -5

c = 9

Check the picture below.

The value of a is 5, b is 4, c is 0, d is 3, e is 6 and R is 6 after following the long division method.

According to the question,

We have to divide 430 by 8 by following the long division method.

Note that when we follow long division method then the number by which we are dividing (divisor) is to be multiplied in such a way that the result remains less than the number in the dividend.

Now, we will solve it step by step.

In dividing 43 by 8, we have to multiply 8 by 5. Then, we get 40.

So, we have a = 5, b = 4 and c = 0.

Now, after this we have 30 and the number that we get after multiplication is 24. So, 3 has to be multiplied in 8 to get 24.

So, we have d = 3.

Now, when we will subtract 24 from 30, we will get 6.

So, we have e = 6.

And e is also the remainder, R. So, we have R = 6.

Hence, the values of a, b, c, d, e, and R are 5, 4, 0, 3, 6, and 6 respectively.

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Answer:

Step-by-step explanation:

a) The formula for the regression function is:

Maintenance Cost = 54.7757 + 120.689 x Age of Car

b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.

c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:

Y = a + bX ± tα/2 * SE

where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.

Plugging in the values, we get:

Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442

Y = 923.167 ± 26.010

Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.

d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.

To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.

The surface area of the cylinder is 948m²

The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;

SA = 2πr(r+h)

Where r is the radius of the base and h is the height of the cylinder.

r =8m

h = 4m

SA = 2 × 3.14 × 8 (8+4)

SA = 78.96 × 12

SA = 947.52 m²

to the nearest whole number

SA = 948 m²

therefore the surface area of the cylinder is 948 m²

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Answer:

Least common multiple (LCM) of 12 and 24 is 24.

Step-by-step explanation:

The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

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

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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Answer:

Step-by-step explanation:

Let T represent table and B represent bench. The garden table costs $62 less than the bench. T = B - 62. plug T = B - 62 into T + B = 788. B - 61 + B = 788. This gives us 425. B = 425.

Answer:

\(y = 56.6208\)

Step-by-step explanation:

Given

The attached triangle

Required

Find y

To find y, we make use of the relationship between sides lengths 44 & y and angle 39

The relationship is:

\(cos(39) = \frac{44}{y}\)

i.e.

\(cos(\theta) = \frac{Adjacent}{Hypotenuse}\)

Make y the subject

\(y = \frac{44}{cos(39)}\)

\(y = \frac{44}{0.7771}\)

\(y = 56.6208\) -- approximated

If the area to the right of a standard normal random variable z is 0.9803, the value of z is approximately -2.05.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. A normal distribution is a continuous probability distribution that is symmetric and bell-shaped, and it is often used to model many real-world phenomena.

A standard normal random variable, denoted by Z, is a random variable that follows a standard normal distribution. This means that the probability density function of Z is given by:

f(z) = (1/√(2*pi)) * e^(-z^2/2)

where pi is the mathematical constant pi (approximately 3.14159), e is the mathematical constant e (approximately 2.71828), and sqrt() represents the square root function.

The cumulative distribution function (CDF) of Z is given by:

F(z) = P(Z <= z) = integral from -infinity to z of f(x) dx

The CDF gives the probability that a standard normal random variable Z is less than or equal to a given value z.

To find the value of z for a given area under the curve, we use the inverse of the CDF. That is, we find the value of z that corresponds to a given probability or area under the curve. In this case, we were given an area to the right of z, so we first found the area to the left of z by subtracting the given area from 1.

Then, we used a standard normal distribution table or calculator to find the z-value that corresponds to this area. This is often denoted as the "z-score" for the given probability or area.

The z-score is a standardized value that tells us how many standard deviations a given value is from the mean of the standard normal distribution. In this case, a z-score of approximately -2.05 means that the value is 2.05 standard deviations below the mean of the standard normal distribution.

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Answer:x<-18

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

-1/2x+3>12

Step 2: Subtract 3 from both sides.

-1/2x+3-3>12-3

-1/2x>9

Step 3: Multiply both sides by 2/(-1).

(2/-1)*(-1/2x)>(2/-1x)*(-1/2x)

X<-18

:D