help it is due to today help with others please ?????????????????

0.3406 (approx)

Given that 60% of all Americans live in cities with population greater than 100,000 people. If 47 Americans are randomly selected, we need to find the probability thata. Exactly 25 of them live in cities with population greater than 100,000 people.b. At most 26 of them live in cities with population greater than 100,000 people.c. At least 30 of them live in cities with population greater than 100,000 people.d. Between 23 and 28 (including 23 and 28) of them live in cities with population greater than 100,000 people.Probability is defined as the ratio of the favorable outcomes to the total outcomes of an event. The formula to calculate probability is given by;Probability = Number of favorable outcomes / Total number of outcomesa. Exactly 25 of them live in cities with a population greater than 100,000 people.Probability of exactly 25 Americans living in cities with population > 100,000 people is given by the probability mass function of the binomial distribution.P( X = 25) = 47 C 25 * (0.6)25 * (0.4)22= 0.1213 (approx)b. At most 26 of them live in cities with population greater than 100,000 people.We need to find the probability of at most 26 Americans living in cities with population greater than 100,000 people. This means the number of Americans living in cities with population greater than 100,000 is 0, 1, 2, ..., 26.P(X ≤ 26) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 26)P(X ≤ 26) = ΣP(X = r)Where r varies from 0 to 26P(X ≤ 26) = Σ (47 C r * (0.6)r * (0.4)47-r )r = 0 to 26= 0.6413 (approx)c. At least 30 of them live in cities with population greater than 100,000 people.We need to find the probability of at least 30 Americans living in cities with population greater than 100,000 people. This means the number of Americans living in cities with population greater than 100,000 is 30, 31, 32, ..., 47.P(X ≥ 30) = P(X = 30) + P(X = 31) + P(X = 32) + ... + P(X = 47)P(X ≥ 30) = ΣP(X = r)Where r varies from 30 to 47P(X ≥ 30) = Σ (47 C r * (0.6)r * (0.4)47-r )r = 30 to 47= 0.0031 (approx)d. Between 23 and 28 (including 23 and 28) of them live in cities with population greater than 100,000 people.We need to find the probability of the number of Americans living in cities with population greater than 100,000 is between 23 and 28 (both inclusive).P(23 ≤ X ≤ 28) = P(X = 23) + P(X = 24) + ... + P(X = 28)P(23 ≤ X ≤ 28) = ΣP(X = r)Where r varies from 23 to 28= Σ (47 C r * (0.6)r * (0.4)47-r )r = 23 to 28= 0.3406 (approx)Hence, the required probabilities are,a. P(X = 25) = 0.1213 (approx)b. P(X ≤ 26) = 0.6413 (approx)c. P(X ≥ 30) = 0.0031 (approx)d. P(23 ≤ X ≤ 28) = 0.3406 (approx)

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Answer:

13

Step-by-step explanation:

To find the distance between two points in a coordinate plane, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can find the distance between the points (-3, 6) and (-8, -6) as follows:

d = sqrt((-8 - (-3))^2 + (-6 - 6)^2)

= sqrt((-5)^2 + (-12)^2)

= sqrt(25 + 144)

= sqrt(169)

= 13

Therefore, the distance between the two points in simplest radical form is 13.

around 13 jars of paint will the farmer need to buy in order to paint the entire exterior of the silo.

To find the number of jars the rancher required to get, you really want to know the surface area of both the cone and cylinder.

The method for finding the SA of the cone would be area =[tex]3.14 x r^2 + 3.14 x r x sqrt(r^2 + h^2)[/tex].

SA= 1976.0617791 [tex]m^2[/tex].

The method for finding the SA of the cylinder under the cone would be 3.14 x d x (d/2 + h).

A = 3097.6103564 [tex]m^2[/tex]

Then, at that point, you need to add 1976.0617791+3097.6103564 which gives you 5,073.8. (5,073 is the total surface area of the storehouse)

Then, the partition that by 400.

5,073.8/400 = 12.7

He would have to purchase around 13 jars of paint to have the option to paint the whole storehouse.

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The correct statement regarding the translation of the functions f(x) and h(x) is given as follows:

The graph of h is a translation of 4 units left and 7 units down of f(x).

A translation happens when either a figure or a function are moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The meaning of each translation from function f(x) to function h(x) is given as follows:

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Answer:

To determine the best value between chocolate bar A and B, we need to calculate the cost per gram of each chocolate bar.

For chocolate bar A, the cost per gram is:

$1.00 ÷ 80 grams = $0.0125 per gram

For chocolate bar B, the cost per gram is:

$1.20 ÷ 85 grams = $0.0141 per gram

Therefore, chocolate bar A is the better value as it costs less per gram compared to chocolate bar B. While chocolate bar B may weigh slightly more, its higher cost per gram means that you are paying more for each gram of chocolate compared to chocolate bar A.

Z = X/Y is normally distributed because  the ratio of two independent normal variables is itself normally distributed and the same has been proved below:

To prove this, we can use the Central Limit Theorem. This theorem states that if X and Y are independently and identically distributed random variables, then the ratio of the two, Z = X/Y, will be normally distributed regardless of the distribution of X and Y. This is due to the fact that the ratio of two independent normal variables is itself normally distributed.

For example, let X and Y be two independent normal variables. Then their ratio Z = X/Y will follow a normal distribution. This means that the probability density function (pdf) of Z is given by:

f_Z(z) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{z^2}{2\sigma^2}}

where \sigma^2 = \frac{\sigma_x^2}{\sigma_y^2} is the variance of Z.

Therefore, we can conclude that Z = X/Y is normally distributed when X and Y are independent normal distributions.

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Answer: -7.6n + 11.1

Step-by-step explanation:

We will simplify the given expression by combining like-terms.

   Given:

3.1 - 4.6n - 3n + 8

  Subtract like-terms:

3.1 - 7.6n + 8

   Add like-terms:

11.1 - 7.6n

Answer:

[tex] \sf \: -7.6n + 11.1 [/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 3.1 - 4.6n - 3n + 8

Let's simplify the expression,

→ 3.1 - 4.6n - 3n + 8

→ -4.6n - 3n + 3.1 + 8

→ (-4.6n - 3n) + (3.1 + 8)

→ (-7.6n) + (11.1)

→ -7.6n + 11.1

Hence, the answer is -7.6n + 11.1.

1. The upper bound for the perimeter of the regular hexagon is 21.9 cm.

2. All figures on the calculator display for the calculation of Kelly's average speed is: 99.5 / 10.51 = 9.46717412

3. the lower bound for the area of the rectangle is 2.55 × 10⁵ mm²

4. Upper bound for area = 937.6525 cm²

1. The upper bound for the perimeter of the regular hexagon can be calculated by multiplying the length of one side by 6 (the number of sides in a hexagon):

Upper bound for perimeter = 6 × (3.6 + 0.05) = 21.9 cm (rounded to one decimal place)

2. Kelly's average speed can be calculated by dividing the distance she ran by the time she took:

Average speed = distance / time

The lower bound for the distance is 99.5 m (since 100 m was measured to the nearest meter, the actual distance could be as low as 99.5 m).

The lower bound for the time is 10.51 s (since 10.52 s was measured to the nearest hundredth of a second, the actual time could be as low as 10.51 s).

Therefore, the lower bound for Kelly's average speed is:

Average speed = 99.5 / 10.51 = 9.4617 m/s (rounded to 4 decimal places)

3. The length of the rectangle is 645 mm correct to the nearest 5 mm, which means it could be as small as 642.5 mm or as large as 647.5 mm. We can express this as:

645 mm ± 2.5 mm, similarly

400 mm ± 2.5 mm

Lower bound for length = 645 - 2.5 = 642.5 mm

Lower bound for width = 400 - 2.5 = 397.5 mm

Lower bound for area = 642.5 × 397.5 = 255393.75 mm²

Rounded to 3 significant figures, the lower bound for the area of the rectangle is 2.55 × 10⁵ mm².

4. To calculate the upper bound for the area of the rectangle, we need to multiply the upper bounds for the length and width of the rectangle:

Upper bound for length = 35 + 0.45 = 35.45 cm

Upper bound for width = 26 + 0.45 = 26.45 cm

Upper bound for area = 35.45 × 26.45 = 937.6525 cm²

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If Aaron is 8 years older than Judi, then Aaron's age is 22 years , Judi's age is 14 years and Maree's age is 7 years .

Let Maree's age be = M;

Judi is twice as old as Maree, which means ⇒ Judi's age is 2M;

And Aaron is 8 years older than Judi, which means

⇒ Aaron's age is (2M+8);

We know that the sum of their ages is 43, so we can write an equation:

⇒ M + 2M + (2M + 8) = 43

Simplifying and solving for M:

We get,

⇒ 5M + 8 = 43

⇒ 5M = 35

⇒ M = 7

So, Maree's age is 7 years.

Now, we use this to find Judi's and Aaron's ages:

⇒ Judi = 2M = 2 × 7 = 14

⇒ Aaron = 2M + 8 = 2 × 7 + 8 = 22

Therefore, Judi is 14 years old and Aaron is 22 years old.

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For instance, f(x) is equal to 0.5 when x = 1 and equal to 1 when x = 2, function indicating that the amount of water collected rises by 0.5 for each unit increase in time.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

A. It appears that the function f(x) = 2x is exponential.

b. The function may be expressed as f(x) = a * bx, where a denotes the starting value, b the growth factor, and x the input value. As can be seen from the table, the values of f(x) = 2x are exponentially growing by a factor of 2 for each input.

d. A linear function may be used to simulate a tub that collects water from a leaking faucet since the amount of water collected grows steadily over time.

For instance, f(x) is equal to 0.5 when x = 1 and equal to 1 when x = 2, indicating that the amount of water collected rises by 0.5 for each unit increase in time.

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Answer:

  m∠2 = 35°

Step-by-step explanation:

You want to know the measure of angle 2 when angle 1 is 35° and both angles 1 and 2 intercept arc PQ.

Inscribed angles 1 and 2 both intercept the same arc: PQ. The problem statement tells you that such angles are equal.

  ∠2 = ∠1 = 35°

The measure of ∠2 is 35°.

__

Additional comment

This is a vocabulary and reading comprehension test.

In order to understand the comment and the question, you need to know the meaning of "inscribed angle", "intercept [an] arc", "equal" (as applied to angles). You also need to know the meaning of the notation m∠1, the measure of angle 1.

You pass the test when you understand the question is telling you that angles 1 and 2 are both 35°.

There are 6 + 9 + 9 + 12 + 9 + 9 + 6 = 60 outcomes where the sum of the three dice is greater than 5.

So, the probability of rolling a sum greater than 5 is given by:

Probability = Number of favorable outcomes / Total number of outcomes
Probability = 60 / 216
Probability = 5 / 18

We know that when a dice is rolled, the numbers that come up on the dice are 1, 2, 3, 4, 5 and 6. Since there are three dice, the total number of possible outcomes when they are tossed is given by 6 * 6 * 6 = 216.

Now we have to find the probability of rolling a sum greater than 5. To find this probability, we need to consider all the cases where the sum of the three dice is greater than 5.

The possible outcomes where the sum of the three dice is greater than 5 are:

Sum of 6: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1) (Total 6)
Sum of 7: (1, 2, 4), (1, 4, 2), (2, 1, 4), (2, 4, 1), (4, 1, 2), (4, 2, 1), (1, 3, 3), (3, 1, 3), (3, 3, 1) (Total 9)
Sum of 8: (1, 2, 5), (1, 5, 2), (2, 1, 5), (2, 5, 1), (5, 1, 2), (5, 2, 1), (3, 3, 2), (3, 2, 3), (2, 3, 3) (Total 9)
Sum of 9: (1, 3, 5), (1, 5, 3), (3, 1, 5), (3, 5, 1), (5, 1, 3), (5, 3, 1), (4, 2, 3), (4, 3, 2), (2, 4, 3), (3, 4, 2), (2, 3, 4), (3, 2, 4) (Total 12)
Sum of 10: (1, 4, 5), (1, 5, 4), (4, 1, 5), (4, 5, 1), (5, 1, 4), (5, 4, 1), (2, 4, 4), (4, 2, 4), (4, 4, 2) (Total 9)
Sum of 11: (1, 5, 5), (5, 1, 5), (5, 5, 1), (2, 5, 4), (2, 4, 5), (4, 5, 2), (4, 2, 5), (5, 4, 2), (5, 2, 4) (Total 9)
Sum of 12: (3, 4, 5), (3, 5, 4), (4, 3, 5), (4, 5, 3), (5, 3, 4), (5, 4, 3) (Total 6)

Therefore, there are 6 + 9 + 9 + 12 + 9 + 9 + 6 = 60 outcomes where the sum of the three dice is greater than 5.

So, the probability of rolling a sum greater than 5 is given by:

Probability = Number of favorable outcomes / Total number of outcomes
Probability = 60 / 216
Probability = 5 / 18

Hence, the probability of rolling a sum greater than 5 is 5 / 18.

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Answer:

Step-by-step explanation: m miles

Answer: x=10/9

Step-by-step explanation:

Step-by-step explanation:

use the function sohcahtoa to solve as all these triangles are right angled

The ratio x:y in its simplest form is 7:4.

The ratio x:y can be found by dividing x by y. In this case, we can start with the equation y = 4x/7 and solve for x in terms of y.

Multiplying both sides by 7, we get:

7y = 4x

Dividing both sides by 4, we get:

x = 7y/4

Now we can substitute this expression for x into the ratio x:y:

x:y = (7y/4):y

Simplifying by canceling out the y, we get:

x:y = 7/4

So the ratio x:y in its simplest form is 7:4.

This means that for every 7 units of x, there are 4 units of y. The ratio cannot be simplified further because 7 and 4 do not have any common factors other than 1.

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The toe of which the triangle is , is called an isosceles triangle and a right angled triangle.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. There are different types of triangle , some of them are ;

Scalene triangle, isosceles triangle , equilateral triangle e.tc.

To know the type of triangle it is, we need to find the length of each sides.

let A = (2,1)

B = (4,7)

C = ( 6,3)

AB = √ (4-2)²+ (7-1)²

AB = √ 2²+ 6²

AB = √2+36

AB = √40

= 2√10

BC = √ (6-4)²+( 3-7)²

BC = √ 2²+4²

BC = √4+16

BC = √20

= 2√5

AC = √ (6-2)²+(3-1)²

AC = √4²+2²

AC =√ 16+2

AC = √20

= 2√5

therefore since AB² = BC² + AC ² ,the triangle is a right angled triangle

And also since two sides of the triangle are equal it is an isosceles triangle.

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Using the given information, we found the angles of the right triangle as:

∠R = 56.30º

∠P = 33.7º

∠Q = 90º

What is a right triangle?

A triangle with a right angle, also known as a right-angled triangle or right-angled triangle, more technically an orthogonal triangle, has two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle. A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilise specific terminology. The side opposite the right angle is always the hypotenuse of a right triangle.

Given one of the angles of the triangles as 90º.

So it is a right triangle.

PQ = 7.5cm
QR = 5cm
∠Q = 90º

The figure is given below.

Now PR is the hypotenuse.

Hypotenuse = [tex]\sqrt{base^2+height^2}[/tex]

base = 5 = QR

height = 7.5 = PQ

PR = [tex]\sqrt{5^2+7.5^2} = \sqrt{81.25}[/tex] = 9.01 cm

We can find the angles using trigonometric relations.

sin R = PQ/PR = 7.5/9.01 = 0.832

∠R = 56.30º

∠P = 180 - (∠Q+∠R) = 180 - (90+56.30) = 33.7º

Therefore using the given information, we found the angles of the right triangle as:

∠R = 56.30º

∠P = 33.7º

∠Q = 90º

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ECDF=1/100

The value of the empirical cumulative distribution function (ECDF) at the smallest observation in a sample of 100 observations is 1/100.What is the empirical cumulative distribution function (ECDF)?The empirical cumulative distribution function (ECDF) is a graph that depicts the distribution of a given data set. It is used to illustrate the proportion or percentage of data points that fall below a particular value in the distribution. The ECDF can be used to construct a distribution function for data that do not have an existing theoretical distribution.The ECDF value at the smallest observation in a sample of 100 observations is 1/100. This is because the ECDF takes on a value of 0 for all values that are smaller than the smallest observation. Since there are 100 observations in the sample, each observation has a weight of 1/100. Thus, the ECDF value at the smallest observation is 1/100.

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The most specific category that this shape can be sorted into is "Triangle."

What is the triangle?

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

The Venn diagram shows the relationships between different types of triangles.

The Scalene circle represents all the triangles that have no equal sides.

The Isosceles circle represents all the triangles that have two equal sides.

The Equilateral circle represents all the triangles that have three equal sides.

The triangle with a tick mark on each side does not provide enough information to determine whether it is a scalene, isosceles, or equilateral triangle.

Therefore, the most specific category that this shape can be sorted into is "Triangle."

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Based on the coordinate plane, the ordered pair for the post office is (9, 9).

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

By critically observing the coordinate plane shown in the image attached below, we can logically deduce that the coordinates of the post office would be located in quadrant I at point (9, 9).

Similarly, the the coordinates of the library is also located in quadrant I and it is represented by the ordered pair (6, 2).

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hypotenuse^2 = 16^2 + 25^2

hypotenuse^2 = 256 + 625

hypotenuse^2 = 881

hypotenuse = sqrt(881)

hypotenuse ≈ 29.67 inches

Now that we know the length of the hypotenuse, we can use the 16-inch side and the hypotenuse as the base and height of the triangle, respectively. Plugging these values into the formula, we get:

Area = (16 x 29.67) / 2

Area ≈ 237.36 square inches

Therefore, the area of the triangle is approximately 237.36 square inches.

Answer:

Population: The population is the total demand (sale) of the product over all days.

Variable of interest: The variable of interest is the daily demand (sale) of the product.

To obtain the confidence interval for the average daily demand at a confidence level of 97%, we can use the following formula:

Confidence interval = sample mean ± (t-value x standard error)

where t-value is the value from the t-distribution for the desired confidence level and degrees of freedom, and the standard error is calculated as:

standard error = sample standard deviation / √n

where n is the sample size.

Using the given data, we can calculate:

Sample mean = (35+44+38+55+33+56+60+45+48+40+45+35+42)/12 = 44.5

Sample standard deviation = 9.92

Degrees of freedom = n-1 = 12-1 = 11

From the t-distribution table with 11 degrees of freedom and a confidence level of 97%, the t-value is approximately 2.718.

Therefore, the confidence interval for the average daily demand is:

Confidence interval = 44.5 ± (2.718 x 9.92/√12) = 44.5 ± 9.14

The lower limit is 44.5 - 9.14 = 35.36 and the upper limit is 44.5 + 9.14 = 53.64.

So, we can say with 97% confidence that the true population average daily demand falls within the range of 35.36 to 53.64 thousand units.

The simplified expression is 8x² + 24x.

The distributive property of multiplication over addition is a fundamental property of arithmetic that relates multiplication and addition. It states that when you multiply a number by the sum of two or more numbers, you can first distribute the multiplication over each addend and then perform the addition.

In other words, if a, b, and c are any numbers, then:

a x (b + c) = (a x b) + (a x c)

To simplify the expression 4x° (2x + 6)°, we can use the distributive property of multiplication over addition.

4x° (2x + 6)°

= 4x° * 2x° + 4x° * 6° (using distributive property)

= 8x² + 24x (simplifying by multiplying)

Therefore, the simplified expression is 8x² + 24x.

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Answer:

It's very difficult

maby

Answer:

14, 7, 0, -7.

Step-by-step explanation:

To find the first four terms of the sequence, we can substitute different values of n into the given expression and simplify.

The expression for the nth term of the sequence is 7(3 - n).

Let's find the value of the first term (n = 1):

T₁ = 7(3 - 1) = 7(2) = 14

The first term of the sequence is 14.

Now, let's find the value of the second term (n = 2):

T₂ = 7(3 - 2) = 7(1) = 7

The second term of the sequence is 7.

Next, let's find the value of the third term (n = 3):

T₃ = 7(3 - 3) = 7(0) = 0

The third term of the sequence is 0.

Finally, let's find the value of the fourth term (n = 4):

T₄ = 7(3 - 4) = 7(-1) = -7

The fourth term of the sequence is -7.

Therefore, the first four terms of the sequence are:

To find the first four terms of the sequence, we can substitute different values of n into the given expression and simplify.

The expression for the nth term of the sequence is 7(3 - n).

Let's find the value of the first term (n = 1):

T₁ = 7(3 - 1) = 7(2) = 14

The first term of the sequence is 14.

Now, let's find the value of the second term (n = 2):

T₂ = 7(3 - 2) = 7(1) = 7

The second term of the sequence is 7.

Next, let's find the value of the third term (n = 3):

T₃ = 7(3 - 3) = 7(0) = 0

The third term of the sequence is 0.

Finally, let's find the value of the fourth term (n = 4):

T₄ = 7(3 - 4) = 7(-1) = -7

The fourth term of the sequence is -7.

Therefore, the first four terms of the sequence are:

14, 7, 0, -7.

The length of line JC is 20 miles.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in geometry that states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of sides of triangle.

To find the length of line JC, which is the hypotenuse of the right triangle JSC, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).

In this case, we have:

JS² + SC² = JC²

Substituting the given values, we get:

12² + 16² = JC²

144 + 256 = JC²

400 = JC²

Taking square root both sides, we get:

JC = √400JC = 20

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Based οn this pattern, we can determine the vοlume οf the next figure in the pattern by using a height οf 4 units: 1 x 1 x 4 = 4 cubic units.

A cube is three-dimensiοnal sοlid οbject that has six square faces οf equal size. It is special type οf rectangular prism in which all six faces are squares οf equal size. A cube has twelve edges οf equal length and eight vertices where three edges meet.

Let's analyze each figure separately and find the vοlume using the fοrmula fοr the vοlume οf a rectangular prism: length x width x height.

First figure: The length, width, and height are all 1 unit, sο the vοlume is 1 x 1 x 1 = 1 cubic unit.

Secοnd figure: The length and width are still 1 unit, but the height is nοw 2 units. Sο, the vοlume is 1 x 1 x 2 = 2 cubic units.

Third figure: The length and width are still 1 unit, but the height is nοw 3 units. Sο, the vοlume is 1 x 1 x 3 = 3 cubic units.

Frοm the analysis, we can see that the pattern is that the length and width οf each figure remain cοnstant at 1 unit, while the height increases by 1 unit fοr each successive figure.

Based οn this pattern, we can determine the vοlume οf the next figure in the pattern by using a height οf 4 units: 1 x 1 x 4 = 4 cubic units.

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Based on the difference between the temperature when Casey went to bed and when he woke up, the temperature when he went to bed was 7 degrees, which was 12 degrees warmer than -5 degrees.

The temperature difference is determined using subtraction.

Subtraction is one of the four basic mathematical operations, involving the minuend, the subtrahend, and the result of the operation called the difference.

The temperature when Casey woke up to prepare for school = -5

The difference between the temperature when Casey went to bed and when he woke up = 12 degrees warmer.

The temperature when Casey went to bed = 7 degrees (12 - 5)

Thus, we can conclude that Casey had a temperature of 7 degrees when he went to bed but woke up when it was -5 degrees.

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