Strontium 90 (Sr-90), a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. Its half-life is 27 years. If the amount of Sr-90 in a certain area is found to be 16 times the "safe" level, find how much time (in years) must elapse before the safe level is reached.

Answer:

$175

Step-by-step explanation:

$60÷3÷4 =5

$5 is the cost of one adult's food for one day.

$5×7×5

=$175

$175 is the cost of food consumed by 7 adults for 5 days.

Answer:

The mathematical name for object that is defined by your selected region is called parabola.

Answer:

44

Step-by-step explanation:

9514 1404 393

Answer:

  27°

Step-by-step explanation:

The inscribed angle is half the measure of the arc it intercepts.

  ∠M = 1/2 arc QR = 1/2(54°)

  ∠M = 27°

Answer:

hope that will help you

Answer:

blue piece is 1/2 because it takes up half of the square, the purple is only 1/4 because it would take 4 purple to fill the big square and the orange is half of the purple so it takes double of pieces so 8 pieces which is 1/8

The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

Recall the compounding formula:

A = P * \(e^{rt}\)

Where:

A = Final amount in the account

P = Initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (as a decimal)

t = Time in years

Given:

Initial principal (P) = $16,000

Annual interest rate (r) = 2%  = 0.02

time (t) = 4 years.

Substitute these values into the formula, we get:

A = $16,000 * \(e^{0.02 * 4}\)

Using a calculator, we can calculate:

A = $16,000 * \(e^{0.08}\)

A = $16,000 * 1.0833

A = $17,332.8

Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

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Answer:

Step-by-step explanation:

It is unclear from the phrasing what dimension 8.2 ft represents.

If 8.2 ft is the direct distance from the edge of the roof to the top of the pitch, then the horizontal distance from the edge to the top is √(8.2²-2.4²) ≅ 7.84 ft, and the slope is 2.4/7.84 ≅ 0.31

If 8.2 ft is the horizontal distance from the edge of the root to the top of the pitch, then the slope is 2.4/8.2 ≅ 0.29

The slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.

The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.

For the given situation,

The diagram below shows the house with the roof.

The vertical height of roof on a house, rise = 2.4 feet

The horizontal length of a roof on a house, run = 8.2 feet

The slope of a roof can be found as

\(Slope = \frac{rise}{run}\)

⇒ \(slope = (\frac{2.4}{8.2} )\)

⇒ \(slope = 0.2926\)

The angle of the slope of a roof can be found as

\(tan \alpha =\frac{vertical height}{horizontal length}\)

⇒ \(\alpha =tan^{-1} (\frac{2.4}{8.2} )\)

⇒ \(\alpha =tan^{-1} (0.2926)\)

⇒ \(\alpha =16.31\)

Hence we can conclude that the slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.

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Answer:

A. The shirt at Store "A".

Step-by-step explanation:

How to find 10% of 28.

First, we need to convert 10% into a decimal.

To do that, we just divide the number by 100.

\(\frac{10}{100}\) \(= 0.1\)

Now, we take the original number (28) and multiply it by the decimal

\(28 x 0.1 = 2.8\)

Finally, we subtract.

\(28.00 - 2.80 = 25.20\)

\(25.20\) > \(25.00\)

Therefore, Store "A" Has the cheapest shirt

The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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Answer:

Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)

Step-by-step explanation:

As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.

11^2 + 5^2 = AC^2

121 + 25 = AC^2

146 = AC^2

sqrt(146) = AC^2

Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)

The answer choice which belongs in the green box and is the longest side of the triangle as required is; 11.06.

It follows from the task content that since the sum of angles in a triangle is; 180°, the missing angle measure is; 180 - 51 - 109° = 20°.

Consequently, it follows from the sine law that;

4 / sin 20° = x / sin 109°

x = 4 sin 109° / sin 20°

x = 11.06.

Ultimately, the number that belongs in the green box is; 11.06.

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Answer:

$22.36

Step-by-step explanation:

The shirt that costs her $26 had the seller take 14 percent off the price.

So instead of paying 100% of the $26, payed 100-14 = 86% of the $26.

How much did she end up paying?

    % to $

100% is $26

 86% is $ x

Cross multiply to find x:

x= (86*26) /100 = $22.36

Answer:

X = -7

Step-by-step explanation:

-6x + 5 = 47

-6x +5 -5 = 47 - 5

-6x = 42

-6x/-6 = 42/-6

X = -7

Answer:

Hello There!!

Step-by-step explanation:

Write the equation: -6x+5=47

Takeaway 5 from both sides: -6x=42

Divide by -6 from both sides: x=-7

Therefore, x=-7.

hope this helps,have a great day!!

~Pinky~

Answer:

162

Step-by-step explanation:

432/24*9

162

Answer:

1/6

Step-by-step explanation:

If you graph your points on a coordinate grid, you will see the rise/run. From the point -4, -3 to the point 14,0 ; there is a rise of 3 and a run of 18. The rise goes over the run and creates a fraction of 3/18 and 3/18 simplified is 1/6! Hope this helps!

Answer:

450 Ribbons

Step-by-step explanation:

multiply the length of 1 ribbon by how many she needs to make. we get, 0.45m x 1000bows

that's 450m ribbon.

plz mark this as brainliest and I hope I helped :)

Step-by-step explanation: I had that q and got it right

Answer:

3%

Step-by-step explanation:

They made 97+3 total jars, 3 out of 100 is 3 percent.

The gradient of the line joining the points (1,-1) and (4,9) is 10/3, while the gradient of the line joining (5,1) and (2,-2) is 1. The x-intercept of the equation 3y = 2x - 2 is 1, and the y-intercept is -2/3. These calculations follow the formula for gradient and the methods for finding intercepts in linear equations.

1) To find the gradient of a line joining two points, you can use the formula: gradient = (change in y)/(change in x).
Given the points (1,-1) and (4,9), the change in y is 9 - (-1) = 10 and the change in x is 4 - 1 = 3.
Therefore, the gradient of the line joining these points is 10/3.
2) Similarly, to find the gradient of a line joining two points (5,1) and (2,-2), we can use the same formula. The change in y is -2 - 1 = -3 and the change in x is 2 - 5 = -3.
Therefore, the gradient of the line joining these points is -3/-3 = 1.
3) To find the x-intercept, we set y to 0 and solve for x.
Given the equation 3y = 2x - 2, if we substitute y with 0, we have 3(0) = 2x - 2, which simplifies to 0 = 2x - 2.
To solve for x, we can add 2 to both sides: 0 + 2 = 2x - 2 + 2, which gives us 2 = 2x.
Dividing both sides by 2, we get x = 1.
Therefore, the x-intercept of the equation 3y = 2x - 2 is 1.
To find the y-intercept, we set x to 0 and solve for y.
Using the same equation, if we substitute x with 0, we have 3y = 2(0) - 2, which simplifies to 3y = -2.
To solve for y, we can divide both sides by 3: (3y)/3 = (-2)/3, which gives us y = -2/3.
Therefore, the y-intercept of the equation 3y = 2x - 2 is -2/3.
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Given:-

8 years with an APR of 4% and monthly payments of $473.

To find:-

Savings plan balance.

So now we use the formula,

So now we substite the values. so we get,

The amount of money in the account after 8 years is $20419.41.

Annual percentage rate (APR) refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or income earned on an investment.

Given that, principal = $473, rate of interest =4% and time period = 8 years.

Here, 8 years = 8×12 =96 months

Amount = 473(1+4/100)⁹⁶

= 473(1.04)⁹⁶

= 473×43.17

= $20419.41

Therefore, amount of money in the account after 8 years is $20419.41.

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Answer:

10.05

Step-by-step explanation:

Each strike is 1 so if you keep counting to L you will get 10.05.

Answer:

x = 5/3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

3x + 1 = 6x - 4

Step 2: Solve for x

Answer:

Exact form

x=5/3

Decimal form

x=1.6

Mixed number form

x= 1 2/3

Step-by-step explanation:

The rental cost in dollars per square foot is $11,00

Cost of renting 1.250 square feet = $13, 750 per month

Rental cost per square foot = Total renting cost / total renting area

= $13, 750 per month / 1.250 square feet

= $11,000

Hence, $11,000 is the rental cost in dollars per square foot.

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The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

The question asks the value of f(x) when x = 4 in the equation

x = 4 is less than or equal to 4, so we use the first equation in the piecewise functions => {4x when x≤4}

Solving for f(x):

4(4)=16

16 is the answer!

Hope it helps!

Answer:

The answer is below

Step-by-step explanation:

A function show the relationship between an independent variable and a dependent variable. An independent variable (input) is a variable that does not depend on other variable while a dependent variable (output) is a variable that depends on other variables.

The number of pages read is the dependent variable. Let it be represented as y while the time is the independent variable, let it be represented as x.

Since the  student reads 3 pages of a book every  5 minutes, therefore the function is:

\(y=\frac{3x}{5}\)

Domain is the set of all input (independent variable) while range is the set of all output (dependent variable)

The domain is from 5 minutes to 1 hour, that is 5 minutes to 60 minutes.

Domain = [5, 60]

When x = 60, y = 3(60)/5 = 36

The range = [3, 36]

Using the z-distribution to test the hypothesis, it is found that:

a) The conclusion is that there is not enough evidence to conclude that the percentage has changed from 2016.

b) A Type II error would mean finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.

At the null hypothesis, it is tested if the proportion is the same as in 2016, that is:

\(H_0: p = 0.581\)

At the alternative hypothesis, it is tested if the proportion is different, hence:

\(H_1: p \neq 0.581\)

A Type II error is the non-rejection of a false null hypothesis, that is, finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.

The equation calculating the test statistic is:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which the variables are listed as follows:

For this problem, the value for these variables is given as follows:

\(\overline{p} = \frac{586}{1048} = 0.559, n = 1048, p = 0.581\)

Hence the test statistic is:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.559 - 0.581}{\sqrt{\frac{0.581(0.419)}{1048}}}\)

z = -1.44.

The critical value for a two-tailed test is with a significance level of 0.05 is:

|z| = 1.96.

The absolute value of the test statistic is of |z| = 1.44 < 1.96, meaning that there is not enough evidence to conclude that the percentage has changed from 2016.

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1) 3:00 to 4:00

2) 103

The required solution is 4:00 to 5:00 and  87  customers.

It is required to fill in the blanks.

The arithmetic refers to working with numbers by doing addition, subtraction, multiplication, and division. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.

Given:

According to question , Initially, there were 75 customers.

From 1:00 to 2:00, a total of 30 more people entered, meaning there were

 75 + 30 - 12

= 93 people.

From 2:00 to 3:00, a total of 14 more people entered, meaning there were

93 + 14 - 8  

= 99 people.

From 3:00 to 4:00, a total of 18 people entered, meaning there were

 99 + 18 - 30

= 87 people.

4:00 to 5:00   :  If the store does not accept any more customers except those who are already inside then, all 87 must leave between 4:00 to 5:00 in order to left from the store by 5:00.

Therefore, the required solution is 4:00 to 5:00 and  87  customers.

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