a variable x is normally distributed with mean 21 and standard deviation 5. round your answers to the nearest hundredth as needed. a) determine the z -score for x

Y = 3x + 210

y = 10x

Set the two equations equal to each other:

10x = 3x +210

Subtract 3x from both sides:

7x = 210

Divide both sides by 7:

x = 30

Answer: 30 shirts

Answer:

30 T-shirts

Step-by-step explanation:

Given system of equations:

a) y = 3x + 210

b) y = 10x

1. Substitute the given value of y into y = 3x + 210:

⇒ 10x = 3x + 210

2. Solve for x:

⇒ 10x = 3x + 210 [subtract 3x from both sides]

⇒ 10x - 3x = 3x - 3x + 210

⇒ 7x = 210 [divide both sides by 7]

⇒ 7x ÷ 7 = 210 ÷ 7

⇒ x = 30 (# of T-shirts)

3. Find the value of y by substituting the given value of x into y = 10x:

⇒ y = 10(30) [multiply]

⇒ y = 300 (total cost of the T-shirts)

4. Check your work:

a) y = 3x + 210

⇒ 300 = 3(30) + 210

⇒ 300 = 90 + 210

⇒ 300 = 300 ✔

b) y = 10x

⇒ 300 = 10(30)

⇒ 300 = 300 ✔

∴ Sam needs to sell 30 T-shirts to break even.

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x ³ = 1

x ³ - 1 = 0

x ³ - 1³ = 0

Factorize the right side as a difference of cubes:

(x - 1) (x ² + x + 1) = 0

Then

x - 1 = 0   or   x ² + x + 1 = 0

The first equation yields x = 1 as a root.

For the other equation, rearrange and complete the square to get the other two roots,

x ² + x + 1/4 = -3/4

(x + 1/2)² = -3/4

x + 1/2 = ±√(-3/4) = ± i √3/2

x = -1/2 ± i √3/2

x = (-1 ± i √3)/2

Since complex roots occurs in conjugate pairs, taking the sum of these two roots eliminates the imaginary part:

(-1 + i √3)/2 + (-1 - i √3)/2 = (-1 - 1)/2 = -2/2 = -1

and adding to 1 indeed shows that the sum of roots is zero.

y changes by approximately 0.807 units as t changes from 1 to 6.

To find how much y changes as t changes from 1 to 6, we need to integrate the given derivative with respect to t:

y(t) = ∫ 6e^(-0.08(t-5)^2) dt

We need to evaluate the above integral between t=1 and t=6 to find the change in y over that interval.

y(6) - y(1) = ∫₁⁶ 6e^(-0.08(t-5)^2) dt

Unfortunately, this integral cannot be solved analytically. However, we can approximate the value using numerical methods. One common method is to use a numerical integration technique such as the trapezoidal rule or Simpson's rule. These methods use discrete approximations to the integral to compute an estimate of its value.

Using the trapezoidal rule with 10 subintervals, we get:

y(6) - y(1) ≈ (5/18) [6e^(-0.08(1-5)^2) + 4(6e^(-0.08(1.5-5)^2) + 2(6e^(-0.08(2-5)^2) + ... + 2(6e^(-0.08(5.5-5)^2) + 4(6e^(-0.08(6-5)^2) + 6e^(-0.08(6-5)^2))]

y(6) - y(1) ≈ 0.807

Therefore, y changes by approximately 0.807 units as t changes from 1 to 6.

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The statement describes the percentage of people in the nation who eat out without making any inferences or assumptions.

The statement made by the person is a descriptive statement. This means that the statement simply describes the percentage of people in the nation who always eat out. It does not make any assumptions or inferences based on the data or evidence given. A descriptive statement is one that simply states facts or information without making any assumptions or interpretations about it. It is important to note that a descriptive statement does not imply any cause and effect relationship between the facts or data given. For example, in this statement, there is no inference being made that the people who eat out are healthier or more likely to be successful than people who don't eat out. It is simply stating the percentage of people in the nation who always eat out.

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(-4,0)

-4 is in the y axis and 0 is in the x axis

Answer:

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer: the answer is false

We need to calculate the z-score and then use a z-table to find the proportion of scores smaller than X = 35 in the normal distribution with a mean (µ) of 40 and a standard deviation (σ) of 10.
The z-score formula is: z = (X - µ) / σ

For X = 35, µ = 40, and σ = 10, the z-score is:
z = (35 - 40) / 10 = -0.5

Now, you need to look up the z-score (-0.5) in a z-table, which gives you the proportion of scores smaller than X = 35. The value associated with a z-score of -0.5 is 0.3085.
So, the correct answer is: a. 0.3085

Now, we can use the standard normal distribution table or a calculator with a normal distribution function. We know that the mean of the distribution is 40 and the standard deviation is 10. We want to find the proportion of scores that are smaller than X = 35.

First, we need to standardize the value of 35 using the formula:

z = (X - µ) / Ï

where X is the value we want to standardize, µ is the mean, and Ï is the standard deviation.

Plugging in the values we have:

z = (35 - 40) / 10 = -0.5

This means that a score of 35 is 0.5 standard deviations below the mean.

Next, we can use the standard normal distribution table or a calculator to find the proportion of scores that are smaller than z = -0.5. Using the table or calculator, we find that this proportion is 0.3085.

Therefore, the answer is (a) 0.3085.

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7 = s²

s = x + 2

7 = (x + 2)²

7 = (x + 2)(x + 2)

7 = x² + 2x + 2x + 4

7 = x² + 4x + 4

x² + 4x = 3

Answer:

Step-by-step explanation:

The point-slope form of the equation of a line: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passing through.

m = -5

(2, -9)    ⇒    x₁ = 2,  y₁ = -9

So:

y - (-9) = -5(x - 2)      ← the point-slope form of the equation

y + 9 = -5x + 10               {subtract 9 from both sides}

y = -5x + 1                  ← the slope-intercept form of the equation

Answer:

-8

Step-by-step explanation:

-8 plus 6 is equivalent to -2

Answer:

\(y \geqslant \frac{2}{3} x - 2\)

\(y + 2 \geqslant \frac{2}{3} x\)

\( \frac{2}{3}x - y \leqslant 2\)

\(2x - 3y \leqslant 6\)

Answer:

Below.

Step-by-step explanation:

The dimensions are  5.75m * 6.5 m

= 575cm * 650 cm.

Finding the GCF:

575 = 5 * 5 * 23

650 = 5 * 5 * 26

- so t he Greatest Common Factor of these 2 is 25cm.

575 / 25 = 23

650 / 25 = 26.

So we need 23 tiles along the width of the room and the length will have 26 tiles.

Each tile with be 25cm * 25 cm. in size and the number of tiles = 23*26

= 598.

Step-by-step explanation:

\( \: \: \: \: 8.563 \\ + 4.8292 \\ = 13.3922\)

Answer:

8.563 + 4.8292

=8.563 + 4.8292

=13.3922

Round it to the 10 place is 13.4

Answer:

We have the proportion: 8/10 = 100/y

We can solve for y by cross-multiplying.

That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000

Dividing both sides by 8 to solve for y, y = 125

Hence, the value of y is 125.

Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5

Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4

Therefore, y = 4√5The value of y is 4√5.

Step-by-step explanation:

Hope this helps!! Have a good day/night!!

The electric field at the point directly to the east of the negatively charged point is directed towards the charge, that is, west of the point.

The correct option is D.

A negative point charge has an electric field focused at it. Thus, the electric field at the point directly to the east of the negatively charged point is directed towards the charge, that is, west of the point.

The electric field is defined as that of the electric force per unit of charge. The direction of the field is assumed to represent the direction of the force it would impose on a positive test charge. The electric field radiates outward from the a positive charge and inward from a negative point charge.

The field lines never cross. The field lines lie parallel to the charge's surface. The quantity of charge and indeed the number of field lines are proportionate.

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I understand that the question you are looking for is:

What is the direction of the electric field directly to the east of an isolated negative point charge?

A. north

B. south

C. east

D. West

The following expression:

Can be rewritten using some notation for mixed fractions. Remember that:

Then:

Use the commutative property of the sum to bring together the integer part of the expression:

Notice that -(-3) = +3, then:

Add the integers:

Rewrite the number as a mixed fraction:

Therefore:

The phrase describes a transformation of the graph of function to create the graph of function h is vertically stretched.

The answer is option D. vertically compressed.

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Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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Explanation:

The figure preserves its size in certain transformations and only its location is changed. Examples of this kind of transformation are: translations, rotations, and reflections. The size of the figure can change with other transformations, such as dilations.

A translation is a transition that slides through a plane or through space through a figure. Both points of a diagram travel the same distance and the same direction as a translation. A TRANSLATION IS A CHANGE IN LOCATION. A translation is usually specified by a direction and a distance.

A rotation is a move that transforms a figure around a point or a line (around). Rotation involves simply rotating a shape. The center of rotation is called the point at which a figure revolves. The rotation center may be on or outside of the shape. What seems like a rotation? Rotation Core A ROTATION Implies TO Transform A FIGURE.

A transformation that flips a figure over a line is a mirror. A REFLECTION IS FLIPPED OVER A LINE. Note, it's the same but it looks like a mirror image of itself when a shape is mirrored. Remember, the line that forms a shape is flipped precisely over the same distance that is considered a line from the reflection. Reflection line on both ends. It is possible to reflect on the outline or it may be outside the shape.

Without modifying the shape, dilation shifts the scale of the shape. When you go to the eye specialist, your pupils are dilated. Let's try it by shutting the lights off. Dilations are created as you enlarge a photograph or use a copy machine to minimize a map. To render a shape larger, Widen means. Reducing involves having a shape smaller.

The scale factor shows you how much you enlarge or decrease something.

Hope this helps :D (paraphrased; no plagiarism)

Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

The value of \\(tan \theta\) when \(\cos \theta = \frac{12}{13} is \frac{5}{12}\), which corresponds to option D.

To find the value of \(\tan \theta\) when\(\cos \theta = \frac{12}{13}\), we can use the trigonometric identity:

\(\tan \theta = \frac{\sin \theta}{\cos \theta}\)

Given that \(\cos \theta = \frac{12}{13}\), we can use the Pythagorean identity to find the value of \(\sin \theta\):

\(\sin \theta = \sqrt{1 - \cos^2 \theta}\)

\(\sin \theta = \sqrt{1 - \left(\frac{12}{13}\right)^2}\)

\(\sin \theta = \sqrt{1 - \frac{144}{169}}\)

\(\sin \theta = \sqrt{\frac{169}{169} - \frac{144}{169}}\)

\(\sin \theta = \sqrt{\frac{25}{169}}\)

\(\sin \theta = \frac{5}{13}\)

Now we can substitute the values of \(\sin \theta\) and \(\cos \theta\) into the formula for\(\tan \theta\):

\(\tan \theta = \frac{\sin \theta}{\cos \theta}\)

\(\tan \theta = \frac{\frac{5}{13}}{\frac{12}{13}}\)

\(\tan \theta = \frac{5}{13} \cdot \frac{13}{12}\)

\(\tan \theta = \frac{5}{12}\)

Therefore, the value of \tan \theta when \(\cos \theta = \frac{12}{13}\) is \(\frac{5}{12}\), which corresponds to option D.

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Answer:

12.2 < 39

Step-by-step explanation:

3.2 +9 < 39

Add 3.9 and 9

It will give you 12.2 < 39

Hope this helps:) Have a great day!

The limit of the sequence is L = 2.

We have,

To find the limit of the given recursively defined sequence, we can use the fact that as n approaches infinity, approaches a common limit value. Let's denote this limit as L.

Given:

a1 = 1

an+1 = 6/(1 + an)

To find the limit, we can set the recursive equation equal to L and solve for L:

L = 6/(1 + L)

Now, let's solve this equation for L:

L(1 + L) = 6

L + L² = 6

L² + L - 6 = 0

Factorizing the quadratic equation, we have:

(L + 3)(L - 2) = 0

This gives us two possible solutions:

L + 3 = 0 -> L = -3

L - 2 = 0 -> L = 2

Since the sequence is defined as an increasing sequence starting from 1, the limit L should be greater than 1.

Therefore,

The limit of the sequence is L = 2.

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The required answer of the sequence with a1 = 1, an+1 = 6/1 + an  is the sequence converges to either -3 or 2.

To find the limit of the recursively defined sequence with a1 = 1 and an+1 = 6/(1 + an), we can assume that the sequence converges and find the value it converges to.

Let's denote the limit as L.

As n approaches infinity, an approaches L, and an+1 also approaches L. Therefore, we can write the recursive equation in terms of the limit L:

L = 6/(1 + L)

To solve for L, we can multiply both sides of the equation by (1 + L):

L(1 + L) = 6

Expanding the left side:

\(L + L^2 = 6\)

Rearranging the equation to a quadratic form:

\(L^2 + L - 6 = 0\)

Factoring the quadratic equation:

(L + 3)(L - 2) = 0

Setting each factor equal to zero:

L + 3 = 0 or L - 2 = 0

Solving for L:

L = -3 or L = 2

Therefore, the sequence converges to either -3 or 2.

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The answer are: a. Total outflows: $2,007,901, b. Total inflows: $827,080, c. Net present value: $824,179, d. Should the old issue be refunded with new debt? Yes

To determine whether the old bond issue should be refunded with new debt, we need to calculate the present value of total outflows, the present value of total inflows, and the net present value (NPV). Let's calculate each of these values step by step: Calculate the present value of total outflows. The total outflows consist of the call premium, underwriting cost on the old issue, and underwriting cost on the new issue. Since these costs are one-time payments, we can calculate their present value using the formula: PV = Cash Flow / (1 + r)^t, where PV is the present value, Cash Flow is the cash payment, r is the discount rate, and t is the time period.

Call premium on the old issue: PV_call = (7% of $22 million) / (1 + 0.1)^16, Underwriting cost on the old issue: PV_underwriting_old = $530,000 / (1 + 0.1)^16, Underwriting cost on the new issue: PV_underwriting_new = $680,000 / (1 + 0.1)^16. Total present value of outflows: PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. Calculate the present value of total inflows. The total inflows consist of the interest savings and the tax savings resulting from the interest expense deduction. Since these cash flows occur annually, we can calculate their present value using the formula: PV = CF * [1 - (1 + r)^(-t)] / r, where CF is the cash flow, r is the discount rate, and t is the time period.

Interest savings: CF_interest = (12% - 10%) * $22 million, Tax savings: CF_tax = (40% * interest expense * tax rate) * [1 - (1 + r)^(-t)] / r. Total present value of inflows: PV_inflows = CF_interest + CF_tax.  Calculate the net present value (NPV). NPV = PV_inflows - PV_outflows Determine whether the old issue should be refunded with new debt. If NPV is positive, it indicates that the present value of inflows exceeds the present value of outflows, meaning the company would benefit from refunding the old issue with new debt. If NPV is negative, it suggests that the company should not proceed with the refunding.

Now let's calculate these values: PV_call = (0.07 * $22,000,000) / (1 + 0.1)^16, PV_underwriting_old = $530,000 / (1 + 0.1)^16, PV_underwriting_new = $680,000 / (1 + 0.1)^16, PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. CF_interest = (0.12 - 0.1) * $22,000,000, CF_tax = (0.4 * interest expense * 0.4) * [1 - (1 + 0.1)^(-16)] / 0.1, PV_inflows = CF_interest + CF_tax. NPV = PV_inflows - PV_outflows.  If NPV is positive, the old issue should be refunded with new debt. If NPV is negative, it should not.

Performing the calculations (rounded to the nearest whole dollar): PV_call ≈ $1,708,085, PV_underwriting_old ≈ $130,892, PV_underwriting_new ≈ $168,924, PV_outflows ≈ $2,007,901,

CF_interest ≈ $440,000, CF_tax ≈ $387,080, PV_inflows ≈ $827,080.  NPV ≈ $824,179.  Since NPV is positive ($824,179), the net present value suggests that the old bond issue should be refunded with new debt.

Therefore, the answers are:

a. Total outflows: $2,007,901

b. Total inflows: $827,080

c. Net present value: $824,179

d. Should the old issue be refunded with new debt? Yes

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Answer:

12 hours

Step-by-step explanation:

using the relationship

D = ST ( D is distance, S is average speed and T is time in hours )

calculate average speed by dividing both sides by T

S = \(\frac{D}{T}\) = \(\frac{469}{7}\) = 67 mph

calculate time by dividing both sides by S

T = \(\frac{D}{S}\) = \(\frac{804}{67}\) = 12 hours

Answer:

Step-by-step explanation:

Distance travelled by Kala in 7 hours= 469 mi.

Distance travelled by Kala in 1 hour=  \(\frac{469}{7}\)

                                                          = 67 mi.

Time taken by Kala to travel 804 miles= \(\frac{804}{67}\)

                                                                = 12 hours

∴ it will take her 12 hours to cover a distance of 804 miles.

Answer:

10=20. divisible by 2 (2,5 = 10) both of the factor are prime

Step-by-step explanation:

BIG BRAIN

4 gallons

If half covers an eighth, then you need half a total if 8 times. So multiply half by 8 and you get 4.

If this helped please mark branliest

II. Firms may utilize databases other than relational databases.

III. In mapping an E-R diagram to a set of tables in a relational database, only the entities in the E-R diagram are mapped to tables in the database.

II. The statement that firms may utilize databases other than relational databases is true. While relational databases are widely used, there are other types of databases available, such as hierarchical databases, network databases, and object-oriented databases. Each type has its own characteristics and may be suitable for different purposes or specific requirements of an organization.

III. The statement that, in mapping an E-R diagram to a set of tables in a relational database, only the entities in the E-R diagram are mapped to tables in the database is also true. In the entity-relationship (E-R) model, entities represent objects or concepts in the real world, and relationships define the associations between entities. When designing a relational database based on an E-R diagram, the entities are typically mapped to tables, and the relationships are represented through foreign keys and join operations between tables. Other elements, such as attributes and keys, are also considered in the mapping process, but not all of them are necessarily represented as separate tables.

IV. The statement that each attribute of an entity is given a separate table in the mapping of an E-R diagram to a set of tables in a relational database is not true. In a relational database, attributes are typically represented as columns within a table, where each row represents a record or instance of the entity. Attributes are not given separate tables, but rather they contribute to the structure and content of the table associated with the entity.

Therefore, the correct statements are II and III.

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