If you buy 3 shirts, you get 10% discount. If you paid $270 for 6 shirts
what is the original price of a T-shirt?

Hey love! <3

Answer:

1. 2100 inches^2

Step-by-step explanation:

Let's solve this together! First you have to find the lateral area.

The lateral area is the product of the perimeter of the base and the height.

The perimeter of the base is 15 in.+20 in.+25 in.=60 in... So the lateral area is 60 in.⋅30 in.=1800 in.2.

Now the base area is 12⋅20 in.⋅15 in.=150 in.2.

There are two bases, so the surface area is 1800 in.2+150 in.2+150 in.2=2100 in.2.

2. A hypotenuse is the longest side of a right-angled triangle.

Step-by-step explanation:

Hypotenuses are the side opposites of the right angle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides in a geometric equation.

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The table layout and relationship structure of a relational database is called its schema.

A schema in a relational database refers to the overall structure and organization of tables, their attributes (columns), and the relationships between them. It defines the blueprint for how the data is organized and stored in the database.

The schema includes information such as the table names, column names, data types, constraints, and the relationships established through keys (such as primary keys and foreign keys). It provides a logical representation of the database structure and helps ensure data integrity and consistency.

The schema serves as a guide for creating, modifying, and querying the database tables. It defines the structure that enforces rules and relationships between tables, facilitating data manipulation and retrieval.

By designing a well-defined schema, database administrators and developers can establish the foundation for efficient data storage, retrieval, and management within a relational database system.

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The ratio by mass of copper to zinc in the alloy is 3:1.

To find the ratio by mass of copper to zinc in the alloy, we need to first calculate the total mass of the alloy. We can do this by adding the mass of copper and zinc:

Total mass of alloy = 13.5 g + 4.5 g = 18 g

Now we can find the ratio of copper to zinc by dividing the mass of copper by the mass of zinc:

Ratio of copper to zinc = 13.5 g / 4.5 g = 3:1

Therefore, the ratio by mass of copper to zinc in the alloy is 3:1.

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A federal study reported that 7.5% of the u.s. workforce has a drug problem

a-1. You would expect 1.5 of the 20 employed workers in the sample to have a drug problem.

a-2. The standard deviation for this problem would be 1.1180.

b. The likelihood that none of the workers sampled has a drug problem is 0.3679.

c. The likelihood that at least one of the workers sampled has a drug problem is 1 - 0.3679 = 0.6321.

Using drugs may result in dependency and addiction, as well as physical and mental health concerns, difficulties sleeping, and other negative outcomes. Your usage of drugs has an effect not just on you but also on the people around you.

a-1. It is reasonable to anticipate that 1.5 of the 20 employed people in the sample will have a problem with drugs.

a-2: The value of 1.1180 would be used to represent the standard deviation for this situation.

a. The probability that any of the employees who were surveyed struggle with substance abuse is 0.3679.

c. The probability that at least one of the employees who have sampled struggles with substance abuse is 1 less than 0.3679, which equals 0.6321.

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There is only one triangle in this situation.

To determine the number of triangles in this situation, we need to use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we can start by finding the measure of angle B:

angle A + angle B + angle C = 180 degrees

48 degrees + angle B + 180 degrees - (48 degrees + angle C) = 180 degrees

angle B - angle C = 0

angle B = angle C

Now we can use the law of cosines to find the length of side c:

\(c^2 = a^2 + b^2 - 2ab*cos(angle C)\\c^2 = 21^2 + 17^2 - 22117*cos(angle B)\\c^2 = 1136 - 714*cos(angle B)\\\)

Next, we can use the triangle inequality theorem to determine the possible combinations of sides that could form triangles. We know that c must be less than the sum of a and b:

c < a + b

Taking the square root of both sides of the equation we derived for c earlier, we have:

c = √(1136 - 714*cos(angle B))

Therefore, we need to find the range of values of cos(angle B) for which c < a + b:

sqrt(1136 - 714*cos(angle B)) < 21 + 17

1136 - 714*cos(angle B) < 784

cos(angle B) > (1136-784)/714

cos(angle B) > 0.676

angle B lies between 48 degrees and 180 degrees, so we take the inverse cosine of 0.676 to find the minimum value of angle B that satisfies the inequality:

angle B > 46.4 degrees

Similarly, we can use the triangle inequality theorem with the other two sides to find the ranges of values for angles A and C:

b < a + c

a < b + c

Using the same approach as before, we find that angle C is greater than 46.4 degrees, and angle A is greater than 85.6 degrees.

Therefore, the only combination of side lengths that could form a triangle is sides a, b, and c. So there is only one triangle in this situation.

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Answer: 5:1

Step-by-step explanation:

25:5

Divide by 5 both sides

5:1

Answer:

$452.56

Step-by-step explanation:

400 * 1.025^(5)

If the null hypothesis is true in a chi-squared test, then we expect the test statistic to be approximately equal to its expected value.

In a chi-squared test, the null hypothesis is the statement that there is no significant association between two variables. If the null hypothesis is true, then we expect the test statistic to be approximately equal to its expected value. The expected value is calculated using the degrees of freedom and the expected frequency of each category in the contingency table.

The chi-squared test statistic is calculated by subtracting the observed frequency from the expected frequency for each category and then squaring the result. These squared differences are then summed across all categories to calculate the chi-squared test statistic.

If the null hypothesis is true, we expect the test statistic to be close to its expected value. This is because when the null hypothesis is true, the observed frequencies should be close to the expected frequencies. Therefore, the squared differences should be small, resulting in a small test statistic.

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The difference in the elevation between the canyon and the bird's nest is 737. 3 feet

From the information given, we have that;

Let's convert the mixed fractions to improper fraction;

= - 263/ 5 = - 52. 6 feet

789 3/ 10 = 7893/ 10 = 789. 3 feet

The difference in the elevation between the canyon and the bird's nest ;

= -52. 6 + 789. 9

= 737. 3 feet

Thus, the difference in the elevation between the canyon and the bird's nest is 737. 3 feet

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The efficiency E (expressed as a percent) of the assembly line worker at time t hours since the worker's shift began is given by E(t) = 50t - 2t^2 + 48.

To find E(t), we need to integrate the rate function E'(t) with respect to time t:

∫E'(t) dt = ∫(50 - 4t) dt

E(t) = 50t - 2t^2 + C

where C is a constant of integration. We can determine the value of C by using the initial condition E(1) = 96:

E(1) = 50(1) - 2(1)^2 + C = 96

Simplifying this equation, we get:

C = 48

Now we can substitute C into our equation for E(t):

E(t) = 50t - 2t^2 + 48

Therefore, the efficiency E (expressed as a percent) of the assembly line worker at time t hours since the worker's shift began is given by E(t) = 50t - 2t^2 + 48.

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Answer:

1 mile a minute

Step-by-step explanation:

There is 60 minutes in an hour, so we divide miles by minutes.

60 divide by 60 = 1

result: the car is driving 1 mile per minute

Answer:

+3,+2+3+4+2

Step-by-step explantion

so nowd it be 14

It is not necessarily true that either [a] = [0] or [b] = [0] when [a],[b] ∈ z6 and [a]·[b] = [0].

This is because in z6, there are other pairs of elements that multiply to [0] besides [0] and any other element. For example, [2]·[3] = [6] = [0] in z6, but neither [2] nor [3] are equal to [0].

However, if [a],[b] ∈ z7 and [a]·[b] = [0], then it is necessarily true that either [a] = [0] or [b] = [0]. This is because z7 is a field, meaning that it has no zero divisors (elements that multiply to [0] besides [0] itself). Therefore, the only way for [a]·[b] = [0] in z7 is if either [a] or [b] are equal to [0].

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Answer:

D. 72.7 + 27.9

Step-by-step explanation:

if minus multiply with -ve number it will become +ve

so, 72.7-(-27.9) will become 72.7 + 27.9

After solving the value of x = 1/2.

From the figure:

AB = 4 ,BD = 3,DE = 4

AD = AB + BD

= 4+3

= 7

ADE is a right angle triangle.

AE^2 = AD^2+DE^2

= 7^2 + 4^2

= 49 + 16

= 65

AE = \(\sqrt{65}\)

AC = AE/2

= \(\sqrt{65}\)/2

ABC is a right angle triangle.

AC^2 = AB^2+BC^2

\((\sqrt{65}/2)^2\)= 4^2+x^2

65/4 = 16 + x^2

65/4 - 16 = x^2

65 - 16*4 / 4 = x^2

1/4 = x^2

x = \(\sqrt{1/4}\)

x = 1/2

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Chemical energy.

Step-by-step explanation:

in food can be converted to another form of chemical energy when it is stored as glucose or fat. It can be converted to thermal energy because our body produces heat when digesting our food.

The expression without using absolute value symbols of |x+5| and x ≤ −7 can be expressed as (-x - 5) for x ≤ -5. Here is the explanation for the same.

When the value of x is less than or equal to -5, then |x+5| becomes negative. So, we can represent this as (-x-5) to remove the absolute value symbols. In this way, we get the correct answer.

The given inequality is x ≤ -7 which means x is less than or equal to -7. So, (-x - 5) is the required expression for this inequality.

Let's check it:If x = -8,-x - 5 = - (-8) - 5= 8 - 5= 3As x ≤ -7, we can use the above expression and check it for the value of x as -8.

As the expression is giving the correct answer, we can say that it is the correct expression.

Hence, the answer is (-x - 5) for x ≤ -5.

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Answer:

i think its $27.00 with a 20% discount

Step-by-step explanation:

$25 with a 10% discount is $22.50, $26 with a 15% discount is $22.10, and $27 with a 20% discount is $21.60. Therefore the cheapest option is $27.00 with a 20% discount.

Answer:

Yes

Step-by-step explanation:

The quantity of more flour that she needs to add would be = 3/4

A fraction is defined as the representation of the part of a whole data in a form of numerator and denominator.

The quantity of flour Ryan needs for baking = 3¼

The quantity of flour she has already added = 2½

The remaining amount that she needs to add;

= 3¼-2½

= 3/4

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Answer:

She used an average of (115/30) gigabytes of data per day

Step-by-step explanation:

To get the average data usage per day, we simply divide the total data used by the number of days

Mathematically, that will be

115 gigabytes/ 30 days = 3.83 gigabytes per day

Exact value of the definite integral is 320. Comparing the results: Exact value of the definite integral = 320, Trapezoidal Rule approximation (n = 4) = 340, Simpson's Rule approximation (n = 4) ≈ 246.6667.

What is trapezoid?

A trapezoid is a quadrilateral (a polygon with four sides) that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs.

To approximate the value of the definite integral ∫[0, 4] 5x * x^2 dx using the Trapezoidal Rule and Simpson's Rule, we need to specify the value of n, which represents the number of subintervals.

Let's calculate the approximations using n = 4 for both methods:

Trapezoidal Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using the Trapezoidal Rule is given by:

\(T_4 = (h/2) * [f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + f(x_4)]\)

Plugging in the values:

\(T_4 = (1/2) * [f(0) + 2f(1) + 2f(2) + 2f(3) + f(4)]\\\\= (1/2) * [5(0)(0^2) + 2(5)(1)(1^2) + 2(5)(2)(2^2) + 2(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/2) * [0 + 10 + 80 + 270 + 320]\\\\= (1/2) * 680\\\\= 340\)

Simpson's Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using Simpson's Rule is given by:

\(S_4 = (h/3) * [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + f(x_4)]\)

Plugging in the values:

\(S_4 = (1/3) * [f(0) + 4f(1) + 2f(2) + 4f(3) + f(4)]\\\\= (1/3) * [5(0)(0^2) + 4(5)(1)(1^2) + 2(5)(2)(2^2) + 4(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/3) * [0 + 20 + 40 + 360 + 320]\\\\= (1/3) * 740\\\\= 246.6667\)

Exact value of the definite integral:

∫[0, 4] 5x * \(x^2\) dx = [(5/4) * \(x^4\)] evaluated from 0 to 4

\(= (5/4) * 4^4 - (5/4) * 0^4\\\\= (5/4) * 256 - (5/4) * 0\\\\= 320 - 0\\\\= 320\)

Comparing the results:

Exact value of the definite integral = 320

Trapezoidal Rule approximation (n = 4) = 340

Simpson's Rule approximation (n = 4) ≈ 246.6667

As we can see, the Trapezoidal Rule approximation is slightly greater than the exact value, while Simpson's Rule approximation is less than the exact value.

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Answer:

-21, -22, -23, & -24

Step-by-step explanation:

on the number line, the to the left, the smaller the value.

The general solution of the y" + 2y + y= 7 +75sin2x is given as:

y =  (c₁+c₂x)\(e^{-x}\) + 7 - 12cos2x - 9sin2x

The Greek terms trigonon (triangle) and metron (measure) are the origin of the word trigonometry. The connections between the lengths and angles of triangles' sides are the subject of this area of mathematics. An equation with one or more trigonometric ratios of unknown angles is said to as trigonometric. The ratios of sine, cosine, tangent, cotangent, secant, and cosecant angles are used to express it.

y" + 2y' + y = 7 + 75sin2x

Auxlliary equation are (m²+2m+1) = 0

CF = (c₁+c₂x)\(e^{-x}\)

PI = \(\frac{1}{D^2+2D+1} (7+75sin2x)\)

Now,

\(\frac{7}{D^2+2D+1} +\frac{75}{D^2+2D+1} (sin2x)\)

7 -3(2D+3)sin2x

7 - 6D.sin2x - 9sin2x

7 - 6 x 2cos2x - 9sin2x

7 - 12cos2x - 9sin2x

PI = 7 - 12cos2x - 9sin2x

Finally,

y = C.F + P.I

y =  (c₁+c₂x)\(e^{-x}\) + 7 - 12cos2x - 9sin2x.

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according to question the linearization of f(x) = x^(2/3) at a = 64 is:

l(x) = 16 + (1/6) * (x - 64)

To find the linearization of a function f(x) at a point a, we need to use the formula:

l(x) = f(a) + f'(a) * (x - a)

where f(a) is the value of the function at the point a, f'(a) is the derivative of the function evaluated at a, and (x - a) is the difference between x and a.

First, we need to find the value of f(a):

f(a) = a^(2/3) = 64^(2/3) = 16

Next, we need to find the derivative of f(x):

f'(x) = (2/3) * x^(-1/3)

Now, we evaluate f'(a):

f'(a) = (2/3) * 64^(-1/3) = (2/3) * (1/4) = 1/6

Finally, we can plug in these values into the formula for the linearization:

l(x) = 16 + (1/6) * (x - 64)

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Answer:

87.3

Step-by-step explanation:

131 ÷ 1.5 = 87.3

The answer will be 87.3 repeat.

131 divided by 1.5 is equal to 8 with a remainder of 11, or 8.7333 (rounded to four decimal places).

We have,

To divide 131 by 1.5, we can perform the division operation as follows:

131 ÷ 1.5

To make the calculation easier, we can convert 1.5 to an equivalent fraction with a denominator of 10.

We can multiply both the numerator and denominator by 10 to get 15.

So, the division becomes:

131 ÷ 15

When we divide 131 by 15, we get a quotient of 8 with a remainder of 11.

Therefore,

131 divided by 1.5 is equal to 8 with a remainder of 11, or 8.7333 (rounded to four decimal places).

131 ÷ 1.5 is approximately equal to 8.7333.

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Answer:

A

Step-by-step explanation:

The rest of the steps are right

The probability of getting the 6 on the first die given that the minimum of two numbers is 4 would be 0.11.

What is the probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Two dice are rolled.

Then the sample space (n) = 36

Possible outcomes = {(6,1), (6, 2), (6, 3), (6, 4)}

Probability = 4/36

                 = 0.11

Hence, the probability of getting the 6 on the first die given that the minimum of two numbers is 4 would be 0.11.

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