A prism has a pentagonal base. The area of the pentagon is 45 cm up 2, the height of the prism is 13 cm. Find the volume of the prism.

The Inequality which ensure triangle exists is 22 > 4x > 7.

Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."

Theorem used In ΔABC,

AB + BC >AC

AC+ BC >AB

AC + AB > BC

According to the question,

In triangle ABC.

AC = 18units

BC = 6x units,

AB = 2x + 4 units

.

Substitute the value in the inequality to ensure triangle exists we get 4x > 7 and 22 > 4x.

From (1) and (2) inequality of triangle we get 22 > 4x > 7.

Hence, Inequality which ensure triangle exists is 22 > 4x > 7.

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Which inequality represents the values of that ensure triangle exists? a triangle with these side lengths: AC = 18 units, BC = 6x units, and AB = 2x + 4 units

The equation of the line parallel to PQ that passes through the point (6, -1) is y = (-5/6)x + 4.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that: the coordinates of P are (-3, 8) and the coordinates of Q are (9, -2).

We can find the slope of line PQ.

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of points P and Q, respectively.

m = (-2 - 8) / (9 - (-3))

m = -10 / 12

m = -5/6

Since we want the equation of a line parallel to PQ, it will have the same slope.

Hence, the equation of the line can be written as:

y - y1 = m(x - x1)

where (x1, y1) is the point (6, -1) and m is the slope we found earlier.

Plugging in the values, we get:

y - (-1) = (-5/6)(x - 6)

y + 1 = (-5/6)x + 5

y = (-5/6)x + 5 - 1

y = (-5/6)x + 4

Therefore, the equation of the parallel line to PQ is y = (-5/6)x + 4.

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The volume of the sphere with a diameter of 28 millimeters is 4398.23 cubic millimeters.

To find the volume of a sphere with a diameter of 28 millimeters, we can use the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.

Step 1: Calculate the radius.

Since the diameter is 28 millimeters, the radius is half of that, which is 14 millimeters (28/2).

Step 2: Use the volume formula.

V = (4/3)πr³

V = (4/3)π(14³)

Step 3: Calculate the volume.

V = (4/3)π(2744)

V ≈ 4398.23 cubic millimeters

So, the volume of the sphere with a diameter of 28 millimeters is approximately 4398.23 cubic millimeters.

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The measure of the angles formed by the lines are 30°, 30°,  150° and  150° by definition of vertically opposite angles.

When two straight lines intersect each other at some angle, say line AB intersect line CD, then the opposite angles formed by the two lines are called vertically opposite angles. A pair of vertically opposite angles are equal to each other.

There are two pairs of opposite angles formed by intersection of two straight lines.

The total sum of all the angles formed by intersection of two straight lines is 360°.

Let angle X = x° and angle Y= y° be a pair of opposite angles.

Let the other pair of opposite angles be of angle M = m° and angle N = n°.

Thus, by definition of opposite angles and sum of all angles on intersection of two lines we get,

angle X + angle Y + angle M + angle N = 360°

⇒ x° + y° + m° + n° = 360°

⇒ x° + x° + m° + m° = 360°

⇒ 2( x° + m°) = 360°

⇒ x° + m° = 180° ___ (1)

Also, the measure of one of the angles is five times the measure of another of the angles formed by the lines.

This relation can be written as,

angle X = 5 times of angle M

⇒ x° = 5m° ___(2)

Since angle X and angle M are not a pair of opposite angles but are supplementary angles as observed in equation (1).

Putting equation (2) in equation (1) we get,

5m° + m° = 180°

⇒ 6m° = 180°

⇒ m° = 30°

Thus, x° = 5(30°) = 150°

Hence the angles are 30°, 30°,  150° and  150°.

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The values of a, h, and k are 5, -6 and -2, respectively

In the given function:

y = 5/(x+6) - 2

The function is in the form of a rational function, f(x) = a/(x-h) + k, where a = 5, h = -6, and k = -2.

Therefore, the values of a, h, and k are:

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The number of feet per second that the remote control car travels is: 5 ft/s

The formula to find the speed from distance and time is:

Speed = Distance/time

Now, we are given:

Time: t = 3/40 seconds

Distance = 3/8 ft

Thus:

Speed = (3/8)/(3/40)

Speed = (3/8) * (40/3)

Speed = 5 ft/s

Thus, that is the speed that the remote control car travels

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The value of ZC is 16 units for the given circle and its identities.

A straight line that touches the circle at a single point—the point of tangency—is the tangent of a circle. The digression is opposite to the span of the circle at the place of juncture, and it broadens outward from the circle in the two bearings.

In the circle two external secant segments are LE and ZE, according to the external secant theorem;

⇒ LE × DE =  ZE × CE               (Here, ZE = ZC + 2)

⇒ 9 × 4      =  (ZC + 2) × 2

⇒ ZC + 2 = 18

⇒ ZC = 18 - 2

⇒ ZC = 16

Therefore, the value of ZC is 16 units.

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To calculate a derivative using implicit differentiation, follow these steps:
1. Write down the equation:

2. Differentiate both sides with respect to x:

3. Solve for dy/dx or y':

4. Simplify the result:

Write down the equation:

Start by writing down the equation involving both variables x and y, where y is an implicit function of x.
Differentiate both sides with respect to x: Apply the chain rule, product rule, or quotient rule, as needed, while differentiating both sides of the equation with respect to x.

Remember that when differentiating any term involving y, you'll also need to multiply by the derivative of y with respect to x, denoted as dy/dx or y'.
Solve for dy/dx or y': After differentiating both sides, you will have an equation involving dy/dx or y'.

Solve for this term to find the derivative.
Simplify the result: Simplify your answer as much as possible, if needed.
Remember to use implicit differentiation when the equation is not easily solved for y in terms of x.

It's a powerful technique that helps find derivatives in situations where explicit differentiation isn't feasible.

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Answer:

• f(x) is stretched away from the x-axis by a factor of 2 and is reflected over the x-axis.

Step-by-step explanation:

The function f(x) = 2sin(2x) has an amplitude of 2 and a period of π/2. When we apply the rule g(w) = - f(x), we are reflecting the graph of f(x) over the x-axis and then taking its opposite. This means that the amplitude of g(w) will still be 2, but the graph will be reflected and stretched away from the x-axis by a factor of 2.

I hope it helps you

Identify the predictor and response variables, then create a scatterplot in Minitab. Characterize the association between the variables as linear or nonlinear and negative, none, or positive.

In exploratory data analysis, the first step is to identify the research question and the two variables of interest. The predictor variable (also known as the explanatory variable or independent variable) is the one that is used to explain or predict the outcome of the response variable (also known as the dependent variable).

After identifying the two variables, one can use software such as Minitab to create a scatterplot of the data. The scatterplot helps to visualize the relationship between the two variables.

To characterize the association between the two variables, we would first determine if the relationship appears to be linear or nonlinear. If the relationship is roughly linear, we would then determine if it is negative (meaning that as one variable increases, the other tends to decrease), positive (meaning that as one variable increases, the other tends to increase), or none (meaning that there is no clear trend).

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Answer: True

9/4 = 2 1/4

Step-by-step explanation:

:) See the images below to know more.

Answer:

Set your calculator to degree mode.

[tex] \tan( \beta ) = \frac{7}{12} [/tex]

[tex] \beta = {tan}^{ - 1} \frac{7}{12} = 30.26 \: degrees[/tex]

The Wigwam Motel in Holbrook, Arizona is famous for its large tepees shaped like cones. the floor space inside each tepee is approximately 153.94 square feet.

(a) To find the slant height of the tepee, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle with the height and the radius of the base as the legs.

The radius of the base is half of the diameter, so r = 14/2 = 7 feet. The height of the tepee is 32 feet. Let's call the slant height "s".

Using the Pythagorean theorem, we have:

s² = r² + h²

s² = 7² + 32²

s² = 49 + 1024

s² = 1073

s = sqrt(1073)

s ≈ 32.77 feet

Therefore, the slant height of the tepee is approximately 32.77 feet.

(b) To find the floor space inside the tepee, we need to calculate the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(7)²

A = 49π

A ≈ 153.94 square feet

Therefore, the floor space inside each tepee is approximately 153.94 square feet.

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The only congruence theorem that cannot be used to prove these triangles to be congruent is option B, AAS (Angle-Angle-Side).

The SAS (Side-Angle-Side), SSS (Side-Side-Side), and ASA (Angle-Side-Angle) congruence theorems all involve matching corresponding sides and angles of two triangles. However, AAS only matches two angles and a non-included side, which is not enough to guarantee congruence in all cases.

In fact, the AAS congruence theorem only works if the given non-included side is between the two given angles, forming a "triangle sandwich" with the two given angles as the bread and the non-included side as the filling.

If the non-included side is not between the two given angles, then it is possible to have two non-congruent triangles with the same angle measures, but different side lengths.

Therefore, the AAS congruence theorem cannot be used to prove all cases of triangle congruence, making it the only option that cannot be used to prove these triangles to be congruent

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Answer:

The words "per" and "each" are associated with quantity and division. They are used to express the ratio or rate of one thing in relation to another. For example, "The cost is $10 per pound" or "Each student receives one book."

Answer:

The words per and each are associated with Division.

Step-by-step explanation:

Think of the words "percent". We can divide the word into two easier terms, "per" and "cent". Per means for each. Dividing also means for each.

I'm trying my best without an answer key to help me see what you want to be answered, let me know if there is something specific you would like to know. :)

-a friendly 8th grader :D

The requreid Miriam's test does not provide significant evidence that the true population mean is less than 18.

Since the sample size is small (n = 7) and the population standard deviation is unknown, we should use a t-test for this hypothesis test.

The test statistic is calculated as follows:

t = (x - μ) / (s / √n)

Given that Miriam's test statistic is t = -1.9, we can estimate the p-value associated with this test statistic. This denotes the probability of observing a test statistic as extreme as -1.9 or more extreme, assuming the null hypothesis is true.

Using a t-distribution table with 6 degrees of freedom (n-1), we find that the p-value for a one-tailed test at the 5% significance level is approximately 0.051.

Since the p-value (0.051) is greater than the significance level (0.05), we fail to reject the null hypothesis. We do not have sufficient evidence to conclude that the population mean is less than 18 at a 5% level of significance.

Thus, Miriam's test does not provide significant evidence that the true population mean is less than 18.

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Hence, 186 physics textbooks and 114 biology textbooks were sold as it states that 300 textbooks were sold in total.

The formulas 2x + 3 and 7, for instance, are identical when written as 2x + 3 = 7, where x has been the variable. The x-value that fulfils the equality can be found by solving this equation. In this instance, we can take 3 out of both sides to get 2x = 4, and thereafter divide each sides by 2 to get x = 2. To describe relationships amongst quantities and to solve issues, equations are used widely in mathematics as well as in chemistry, chemistry, economics, and other sciences. They are also utilised in daily life, such as in financial computations and the solution of time, distance, and speed-related issues.

given

Assume that x biology textbooks were sold in total.

The issue states that there were 72 more physics textbooks sold than there were biology textbooks. Hence, x + 72 is the total number of physics textbooks sold.

It states that 300 textbooks were sold in total. Thus, we can create the following equation:

[tex]x + (x + 72) = 300[/tex]

When we simplify and find x, we obtain:

[tex]2x + 72 = 300\\2x = 300 - 72[/tex]

2x = 228

x = 114

Hence, 114 biology textbooks were sold.

The quantity of sold physics textbooks is given by x + 72, or 114 + 72 = 186.

Hence, 186 physics textbooks and 114 biology textbooks were sold as it states that 300 textbooks were sold in total.

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Answer:

Step-by-step explanation:

$10,008.61

Answer:

3.6

Step-by-step explanation:

a^3+b^2=c^2

3^2+2^2=c^2

9+4=c^2

13=c^2

square root to get c alone

3.6055512754639=c

rounded= 3.6

Answer: 3.6

Step-by-step explanation: pythagorean theorem

A^2 + B^2 = C^2

3^2=9

2^2=4

13

Square root of 13 rounded to nearest 10th

3.6

Raw answer: 3.60555127546

Does this table represent a function: C. No, because one x-value corresponds to two different y-values.

In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, all functions are used in mathematics to uniquely map an input variable (domain or independent values) to an output variable (range or dependent values).

Based on the table shown above, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);

3  → 4

4 → 4

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The total number of ways to climb n stairs is the sum of the number of ways to climb n-1 stairs and the number of ways to climb n-2 stairs.

An equation that represents a sequence based on a rule is called a recurrence relation. Finding the following term (next term) based on the prior term (previous term) is made easier.

The recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one stair or two stairs at a time is:

an = an-1 + an-2

This is because to climb n stairs, the person can either take one stair from n-1 stairs and climb the remaining n-1 stairs, or take two stairs from n-2 stairs and climb the remaining n-2 stairs.

Therefore, the total number of ways to climb n stairs is the sum of the number of ways to climb n-1 stairs and the number of ways to climb n-2 stairs.

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Answer:

$78

Step-by-step explanation:

60+30% = 78

...................

There are 6 ways to get two heads and two tails (in any order) when flipping a coin 4 times.

When flipping a coin 4 times, there are 2 possible outcomes (heads or tails) for each flip.

Therefore, there are a total of 2^4 = 16 possible outcomes for 4 coin flips.

To find the number of favorable outcomes for getting two heads and two tails (in any order), we can use combinations.

We need to choose 2 coin flips out of 4 to be heads, which can be done in C(4,2) = 6 ways.

Once we have chosen the positions for the heads, the remaining positions must be tails.

So there are 6 ways to get two heads and two tails (in any order) when flipping a coin 4 times.

These outcomes are:

HH-TT

HT-HT

TH-HT

TT-HH

HT-TH

TH-HT

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In normal distribution the area above 66 for a n(60, 10) is 0.726

What is normal distribution?

In probability theory and statistics, the Normal Distribution, which is also called the Gaussian Distribution, is the most significant continuous probability distribution.  It is also called a bell curve. In this distribution a large number of random variables are either nearly or exactly represented. Moreover, it can be used to approximate other probability distributions,

From the given data n(60, 10) so mean = 60 and standard deviation= 10

Now x≥ 66

so the z-score will be (66-60)/10

                                   = 6/10

                                   = 0.6

Now P(z>0.6)= 1- P(z< 0.6)

                     = 0.726

So, in normal distribution the area above 66 for a n(60, 10) is 0.726.

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If "cow" means that number is correct in value but in the wrong position, then the three-digit secret number is 714.

A "cow" means a digit is "correct in value" but in the "wrong position".

A "bull" means a digit is both "correct in value" and in the "correct position".

⇒ For the first guess (751),

There is 1 cow and 1 bull, which means that one digit is "correct in value" and in the "correct position" (1 bull), and another digit is "correct in value" but in the "wrong position" (1 cow).

⇒ For the second-guess (574),

There is 1 cow and 1 bull, which indicates that "one-digit" is "correct in value" and in the "correct position", and "another-digit" is "correct in value" but in the "wrong-position".

⇒ For the third guess (317),

There is 1 cow and 1 bull, which means that "one digit" is "correct in value" and in the "correct position", and "another digit" is "correct in value" but in the "wrong position".

So, Based on these clues, we can say that the correct secret number has 1 cow and 1 bull.

This means that two digits in the secret number are correct in value, with one digit in the correct position (1 bull), and another digit in the wrong position (1 cow). So, the secret number is likely 714, because it satisfies these conditions.

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The given question is incomplete, the complete question is

Deduce the 3-digit secret number.

[A cow means a number is correct in value but in the wrong position. A bull indicates that a number is both correct in value and in the correct position. i.e. 2 cows and 1 bull would indicate that all three numbers were correct but two were in the wrong positions. ]

Guess     Secret Number   Cows    Bulls

 1st                   751                  1            1

 2nd                 574                 1            1

 3rd                  317                  1            1

The area of the given circle is  1.76625 square feet.

Remember that the area of a circle of radius R is given by the formula:

A = pi*R²

Where pi = 3.14

Here we know the diameter (2 times the radius) of the circle, which is 1.5ft, then the radius is:

R = 1.5ft/2 = 0.75ft

Then the area of the circle is:

A = 3.14*(0.75ft)²

A = 1.76625 ft²

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Answer:

Abiola stayed at work for 8 hours and 40 minutes.

Step-by-step explanation:

Abiola wasted 20 minutes waiting for her friend, so she actually left for work at 7:50 am (7:30 am + 20 minutes).

She arrived at work at 8:20 am, so she spent 30 minutes (8:20 am - 7:50 am) traveling to work.

Abiola worked from 8:20 am to 4:00 pm, which is a total of 7 hours and 40 minutes (4:00 pm - 8:20 am).

She then stayed at work for an additional 1 hour to watch African Magic, so in total, she was at work for 8 hours and 40 minutes (7 hours and 40 minutes of work + 1 hour of watching African Magic).

Therefore, Abiola stayed at work for 8 hours and 40 minutes.

As a result, choice B adequately justifies why a graph that fails the vertical line test cannot be used to represent a function.

A function in mathematics is a rule or association that gives each input value a distinct output value. A function, then, is a collection of ordered pairs, each pair consisting of an input value (also known as an argument or predictor variable) and the control signal value (also known as the value or dependent variable). The output value for each given input value can be found using the formula or graph of a function.

Option B provides the justification for why a graph that fails the vertical line test cannot be used to represent a function: One x-value is coupled with numerous y-values on a vertical line.

A vertical line is not a function since a function cannot have one x-value associated with multiple separate y-values.

To ascertain whether a graph accurately depicts a function, use the vertical line test.

Each vertical line that crosses the graph more than once has an x value and several y values, which is against the definition of a function.

As a result, choice B adequately justifies why a graph that fails the vertical line test cannot be used to represent a function.

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There are 720 ways the Grandview high school band can manage the order of their performance of six pieces of music

To determine the number of ways the Grandview high school band can manage the order of their performance of six pieces of music, we need to find the number of permutations of six objects taken six at a time.

The following is the formula for the number of permutations of n objects taken r at a time:

P(n, r) = n! / (n - r)!

In this case, we need to find P(6, 6), which is:

P(6, 6) = 6! / (6 - 6)!

= 6! / 0!

= 6 x 5 x 4 x 3 x 2 x 1

= 720

Therefore, there are 720 ways the Grandview high school band can manage the order of their performance of six pieces of music.

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