5. The half-life of a certain radioactive material is 78 hours. An initial amount of the material has
a mass of 790 kg. Write an exponential function that models the decay of this material. Find
how much radioactive material remains after 18 hours. Round your
answer to the nearest
thousandth.

Answer:      6 × (10 × 40)

Answer:

6 × (10 × 40)

Step-by-step explanation:

6 × 14 = 84

6 × (10 + 4) = 6 × 14 = 84

6 × 7 + 6 × 7 = 42 + 42 = 84

6 × 10 + 6 × 4 = 60 + 24 = 84

6 × (10 × 40) = 6 × 400 = 2400

Answer:

B

Step-by-step explanation:

The rate of change is the slope.  See the picture.  The blue line (Function B) is steeper than the red line (Function A).

Answer: 13x^6+3x^4+9x^3+2x^2+13

Step-by-step explanation:

Answer:

Combine like terms.

Step-by-step explanation:

Subtract 0.02x from 0.05x

Then your equation should look like:

0.03x + 3 = 4

Answer:The mean of combined group is 71.12 kg

Step-by-step explanation:

Mean of 35 students test score=75.3

Total score of 35 students=mean×test score

=35×75.3

=2635.5

Mean of 26 students test score=65=65.6

Total score of 26 students= 26×65.6

=1705.6

Mean of combined group=(Total score of 35 students+Total score of 26 student ÷Number of total students

=(12635.5+1705.6)÷61

=71.16

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The combined group's average is 71.16.

Given;

If the average test score for one class of 35 students is 75.3 while the average test score for another class of 26 students is 65.6

Mean of 35 student's test scores = 75.3

The total score of 35 students is the mean * test score

=35 * 75.3   =2635.5

Mean of 26 student's test scores = 65.6

The total score of 26 students = 26 * 65.6  =1705.6

Mean of combined group = (Total score of 35 students + Total score of 26 students) / Number of total students

                                          = (12635.5 + 1705.6)  / 61

                                           = 71.16

Hence, the mean of the combined group is 71.16

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The algebraic expression for the verbal description:

The amount of acid in x liters of a 45% acid solution is

0.45x

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The amount of acid in x liters of a 45% acid solution.

This can be written as an expression as,

= 0.45x

We know that,

45% = 45/100 = 0.45

Thus,

The algebraic expression for the verbal description:

The amount of acid in x liters of a 45% acid solution is

0.45x

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clinical prediction is not the fairest way to combine assessment information about job applicants, but the other methods (unit weighting, rational weighting, and multiple regression) are more fair

Clinical prediction appears to have a serious shortcoming in terms of overall fairness for applicants because it is a subjective process of bringing information and hence clinical prediction is not the fairest way to combine assessment information about job applicants .

unit weighting is the simple method which add scores of each candidate at each level of assessment in order to arrive at a total score

Thus the other methods (unit weighting, rational weighting, and multiple regression) are more fair

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Answer:

An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).

Step-by-step explanation:

The working of T critical value calculator is explained

What is t test?

t test is the test used  if the sample standard deviation is known and population standard deviation is unknown.

t test is used if the sample standard deviation is known and population standard deviation is unknown.

Here, t value is calculated by the formula

[tex]t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]\bar{x}[/tex] = mean of the sample

[tex]\mu[/tex] = mean of the population

s = standard deviation of sample

n = Number of samples

Now, with the help of degree of freedom (n - 1) and the level of significance, the critical value of t is to be noted from the t table. Let it be [tex]t_{critical}[/tex]

if the value of t lies between [tex]-t_{critical}[/tex] and [tex]+t_{critical}[/tex] then the null hypothesis is accepted, otherwise the null hypothesis is rejected.

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The time taken for the increase in temperature by 4 degrees Celsius is 1/2 minute.

Suraj took a slice of pizza from the freezer and put it in the oven. The pizza's temperature (in degrees Celsius) as a function of time (in minutes) is given in the form of a graph. The coordinates of the points through which the line passes are (2, 10) and (4.5, 30). We can find the slope of the straight line. If the coordinates of two points are (x1, y1) and (x2, y2), then the slope of the passing line is given as below.

m = (y2 - y1)/(x2 - x2)

m = (30 - 10)/(4.5 - 2)

m = 20/2.5

m = 8

This means there is an increase of 8 degrees in temperature in one minute. We need to calculate the time taken for a 4-degree increase in temperature.

m = Δy/Δx

8 = 4/Δx

Δx = 4/8 = 1/2

Hence, the increase in temperature by 4 degrees Celsius took half a minute.

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The number of mini hotdogs in the combination meal is 4.

The number of pizza rolls in the combination meal is 10.

The variables that you use to write the system are x and (x + 6).

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

Example:

2x + 3 = 9 is an equation

We have,

Number of hot dogs = x

Number of pizza = x + 6

Hot dogs calories = 90

Pizza calories = 50

Now,

90x + 50(x + 6) = 860

Solve for x.

90x + 50x + 300 = 860

140x = 860 - 300

140x = 560

x = 560/140

x = 4

We can cross-check.

90 x 4 + 50 x 10 = 860

360 + 500 = 860

860 = 860

Thus,

The number of hot dogs is 4.

The number of pizzas is 10.

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Answer:

B . 72 you have to skip count by 12

C . 18 because 54 divide by 3 is 18 because they frame 3 houses in one week

Sorry I tried to do the rest but got confused I hope this helps u

Step-by-step explanation:

Answer:

Step-by-step explanation:

the question is about 15% tax equaling 19 cents.  So what amount of principle would be needed to make 19 cents worth of tax.

.19/.15=1.26666666

round up to $1.27 since we don't have parts of pennies for money.

8.25-1.27=$6.97 for the watermelon.  

Answer:

a) y=4

b) x=8

Step-by-step explanation:

a) y will always be equal to 4 for this equation, so y=4

b) y will always be equal to 8 for this equation, so x=8

Each board must be within how many inches of 15 is l' actual = (15±0.03) inch, l" actual = (15±0.03) inch.

size is the quantification of attributes of an item or occasion, which can be used to evaluate other objects or occasions. In other words, measurement is a system of figuring out how massive or small a bodily amount is compared to a primary reference quantity of the identical kind.

size is the simple idea inside the have a look at of arithmetic and technology. measurement quantifies the traits of an object or occasion, which we can compare with other things or activities. measurement is the most commonly used word, on every occasion we address the department of an amount. dimension gear makes our lives higher and more secure, and they enhance the best and quantity of lifestyles. measurement is a contrast of an unknown quantity with a known fixed amount of the equal kind. The cost received on measuring a quantity is referred to as its value. The value of a quantity is expressed as numbers in its unit.

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Cesium would remain 10g after 2 years in 9.55 gram.

A process known as exponential decay is when a quantity diminishes over time at a pace that reduces proportionally as the quantity shrinks. The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

Given,

Cesium 134 decays exponentially. the half life of cesium-134 is 2 years.

The half-life of cesium is approximately 30 years.

The formula for half-life decay is A = P(1/2)t/d.

The half life is D. A Equals 9.55 gram when 10 gram and 2 years are entered into the equation.

Cesium would remain 10g after 2 years in 9.55 gram.

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The value of x is 51°

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.

Given a right triangle with hypotenuse = 9 and perpendicular = 7

Using sine of angle, we get,

sinx = perpendicular/hypotenuse

sinx = 7/9

x = [tex]sin^{-1}[/tex]7/9

x = 51°

Hence, The value of x is 51°

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The number which when increased by 12 is two times its opposite. is

N = -4

final equation N + 12 = -2N

Additive inverse is the opposite of a number in terms of addition, this is the number that gives zero when added to the original number.

To get a result equal to 0, add the original number and the additive inverse or by simply changing the sign of the integer. On the basis of negation of the original number.

The problem says

N + 12 = -2N

N + 2N = -12

3N = -12

N = -4

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In the expression 8ab + 3b + 16 - 4a ,

(a) the number of terms are four .

(b) the factors of 8ab are  1 , 8 , a , b , 8a , 8b , ab , 2ab .

(c) the third term "16"is a constant .

In the question ,

the expression is given as 8ab + 3b + 16 - 4a .

Part(a)

the number of terms that are there in the expression is 4 ,

the terms are 8ab , 3b , 16 , 4a .

Part(b)

the first term is 8ab ,

the factors of 8ab is 1 , 8 , a , b , 8a , 8b , ab , 2ab .

Part(c)

the constant term is 16 , because there is no variable .

Therefore , In the expression 8ab + 3b + 16 - 4a ,

(a) the number of terms are four .

(b) the factors of 8ab are  1 , 8 , a , b , 8a , 8b , ab , 2ab .

(c) the third term "16"is a constant .

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Answer:

1898

Step-by-step explanation:

Multiply both numbers together to find the area.

Answer:

4.32 s (if you were asked to use 32.17 for g)

4.33 s (if you were asked to use 32 for g)

4.318 s (if you were asked to use 32.174 for g)

Step-by-step explanation:

This is an example of free fall! The free fall equation in terms of distance is as follows:

[tex]s=\frac{1}{2}gt^2[/tex]

Let's rearrange the equation so it's in terms of time.

[tex]t=\sqrt{\frac{2s}{g} }[/tex]

Plugging in [tex]300ft[/tex] for the distance and [tex]32.17\frac{ft}{s^2}[/tex] for the acceleration due to gravity,

[tex]t=\sqrt{\frac{2(300)}{32.17} }\\t=\sqrt{18.65}\\ t=4.32s[/tex]

The answer will vary based on what value you use for acceleration due to gravity. If you were asked to use 32, the answer will be 4.33s, if you were given a more specific value, like 32.174, the answer will be 4.318.

Step-by-step explanation:

y = 3

Step-by-step explanation:

Calculate the slope between the 2 points using the slope formula, then equate to - 3

m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }

x

2

−x

1

y

2

−y

1

with (x₁, y₁ ) = (12, - 12 ) and (x₂, y₂ ) = (7, y )

m = \frac{y-(-12)}{7-12}

7−12

y−(−12)

= \frac{y+12}{-5}

−5

y+12

= - 3 ( multiply both sides by - 5 )

y + 12 = 15 ( subtract 12 from both sides )

y = 3

Answer:

Step-by-step explanation:

The function is decreasing at the interval (-∞, -3) ∪ (-1, 1) ∪ (3, ∞), and the function is increasing at the interval (-3, -1) ∪ (1, 3), and the minima of the given function at the point (-3, -12), and maxima at point (3,2).

A graph can be defined as a pictorial representation or a diagram of any function that represents data or values.

According to the given graph,

We can see that the function is decreasing at the interval (-∞, -3), then the function is increasing at the interval (-3, -1), then the function is decreasing at the interval (-1, 1), the function is increasing at the interval (1, 3), and the function is decreasing at the interval (3, ∞).

The function is decreasing at the interval (-∞, -3) ∪ (-1, 1) ∪ (3, ∞), and the function is increasing at the interval (-3, -1) ∪ (1, 3).

Thus, the minima of the given function at the point (-3, -12), and maxima at point (3,2).

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Answer:

Step-by-step explanation:

Hope this helps :)

Answer:

1.01 g/cm³

Explanation:

The density of drink is 1.01 g/cm³ when 25 cm³ of apple juice are mixed with 15 cm³ of fruit syrup and 280 cm³ of carbonated water to make a drink with a volume of 320 cm³.

25 cm³ of apple juice are mixed with 15 cm³ of fruit syrup and

280 cm³ of carbonated water to make a drink with a volume of 320 cm³.

Let us find the mass of each drink mixed to make the new drink

mass = density × volume

mass of apple juice =  1.05 × 25

                                = 26.25 g

Mass of fruit syrup = 1.4 × 15

                              = 21 g

Mass of carbonated water = 0.99 × 280

                                           = 277.2 g

Total mass of the drink = 26.25 g + 21 g + 277.2 g

                                      = 324.45 g

Volume of the given drink =  320 cm³

Density of the drink = total mass of liquids/ volume

                                = 324.45g/320cm³

                                 = 1.01 g/cm³

Thus, the density of drink is 1.01 g/cm³ when 25 cm³ of apple juice are mixed with 15 cm³ of fruit syrup and 280 cm³ of carbonated water to make a drink with a volume of 320 cm³.

Answer:

So, she should add 13 trees per acre for maximum harvesting

Step-by-step explanation:

a farmer finds that if she plants 80 trees per acre, each tree will yield 55 bushels of fruit. she estimates that for each additional tree planted per acre, the yield of each tree will decrease by 2 bushels. how many trees should she plant per acre to maximize her harvest? trees

Let x be the number of trees per acre she adds

Total trees per acre = 80+x

Yield per tree = 55-2x

F(x) = 4400−105x−2x2

Applying differentiation,

F1 (x) = -105 – 4x

Putting F1 (x) =0, gives x = -270/4

X= -67.5

F11 (x) = -4 < 0, hence maximum at x =-67.5

Trees

80-67.5 = 13

So, she should add 13 trees per acre for maximum harvesting

Answer:

$1.2

Step-by-step explanation:

If the tax is 3% then we will have to multiply the price($40) by .03

40*.03= 1.2

Answer: 4v so this would be the correct answer.

Cone A Has same height Twice radius of cone b what is ratio of volume of cone A to volume B therefore The ratio is 4:1

We know that,

[tex]volume of cone = \frac{1}{3}\pi (r)^{2}h[/tex]

From the question, we have

Cone A has same height of cone B

Cone A has twice radius of cone B

Ratio,

[tex]\frac{volume of cone A}{volume of cone B} = \frac{\frac{1}{3}\pi (2r)^{2}h }{\frac{1}{3}\pi (r)^{2}h} \\=\frac{4}{1}[/tex]

Divide:

Split is to divide into two or more equal sections, places, groupings, or divisions in its most basic form. To divide something simply means to provide it to a group in equal quantities or to cut it up into equal pieces. Let's imagine a diagonal divides a square into two triangles with equal areas. An integer may or may not be the result of a division operation. Sometimes the result will be expressed as decimal numbers.

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