Volume and surface area

Answer:

  k ≠ -14/3

Step-by-step explanation:

A square matrix is invertible if and only if its determinant is not zero.

The determinant of a 2×2 matrix is the difference of the products of the diagonal terms and the off-diagonal terms:

  det = (6)(k) -(-7)(4) = 6k +28

The requirement that the determinant is not zero places a restriction on k.

  6k +28 ≠ 0

  k +14/3 ≠ 0 . . . . . . divide by 6

  k ≠ -14/3 . . . . . . . . subtract 14/3

For the matrix to be invertible, the value of k must not be -14/3.

1. The computation of the net present value of each project is as follows:

                                     Project A           Project B

NPV                               $36,523            $9,000

2. Based on the net present value approach, Project A should be adopted, instead of Project B.

The net present value is the difference between the costs and the annual cash inflows discounted to their present values.

                                      Project A           Project B

Initial costs                     $103,000          $41,000

Annual cash inflows         $34,441          $12,522

Project live                       5 years            5 years

Rate of return                    8%                    8%

Annuity factor                   3.993             3.993

PV of cash inflows       $139,523          $50,000

NPV                               $36,523            $9,000

1. Compute the net present value of each project.

2. Which project should be adopted based on the net present value approach?

Thus, based on the net present value approach, Project A should be adopted.

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Answer:

Ordinal, 3,355th. This number as US currency, three thousand three hundred fifty-five dollars ... 3355 is NOT a triangle number ... Base 6

It takes 1.7 x 10 ^4 for light from the sun to reach the comet.

The number is written in the form  [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]

Scientific notations have some of the profits as:

Better readability due to compact representation

Its value in terms of the power of 10 is known, which helps in the easy comparison of quantities differing by a large value.

A comet is about  [tex]5.1 \times 10 ^9[/tex] km from the sun.

Light travels at about [tex]3.0 \times 10 ^5[/tex] km per second.

[tex]\dfrac{5.1 \times 10 ^9}{3.0 \times 10 ^5}[/tex]

= [tex]1.7 \times 10 ^4[/tex]

Hence, It takes 1.7 x 10 ^4 for light from the sun to reach the comet.

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Answer: 8 pieces

Step-by-step explanation:

- if there are 24 pieces of sushi in 6 packages then 24/6 = 4 so there’s 4 pieces of sushi in each package

- since there’s 4 pieces of sushi in each pack just do 4 x 2 = 8

- so there’s 8 pieces of sushi in 2 packages

hope this helps :)

Answer: [tex]f(x) > 0[/tex]

Step-by-step explanation:

The range of all exponential functions without a vertical shift is the set of positive real numbers.

Answer:

(x/0.2)(7)-2.8=-499.8

x=-14.2

Step-by-step explanation:

(x/0.2)(7)-2.8=-499.8

7x/0.2 -2.8 = -499.8

35x -2.8 = -499.8

35x = -499.8 +2.8

35x = -497

35x/35 = -497/35

x = -14.2

you probably already got it solved, but at least this can help anyone else!

Answer:

see image

Step-by-step explanation:

I did two different problems depending on whether the 4 beside the log is a base or not.

If the log IS the base, I got x = 1 as you did. But if the 4 is not the base then there is no base written and that means the base is 10.

For log problems that have log on one side of the equation only, then a good strategy is to change the equation from logarithmic form to exponential form. See image for work. Hope this helps.

The rate of 9 kilometers per hour in kilometers per minute is 0.15 km/min. The cyclist would travel 2.25 km in 15 minutes.

An equation is an expression that shows the relationship between two or more numbers and variables.

60 km/h = 1 km/min

Hence:

9 km/h = 9 km/h * (1 km/min) / ( 60 km/h) = 0.15 km/min

In 15 minutes, distance = 0.15 km/min * 15 min = 2.25 km

The rate of 9 kilometers per hour in kilometers per minute is 0.15 km/min. The cyclist would travel 2.25 km in 15 minutes.

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The first three terms of the sequence are 10, 20, and 30.

The function given is 10n. In this case, the terms will be:

First term = 10n = 10 × 1 = 10

Second term = 10 × 2 = 40

Third term = 10 × 3 = 30

In this case, the first three terms of the sequence are 10, 20, and 30.

It an arithmetic sequence as there is a common difference of 10.

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The sentence that best supports the reason for youth recreational sports is (3) The US Department of Agriculture recommends that young people ages 6–17 should engage in 60 minutes of physical activity each day.

Recreational sports are competitive physical games played for fun and physical exercise with friends or as part of extra-curricular activities.

They do not involve professional sports persons.

Read this source of information. (1) American youth have school commitments and extracurricular activities. (2) Many also enjoy leisure activities, such as reading and playing video games. (3) The US Department of Agriculture recommends that young people ages 6–17 should engage in 60 minutes of physical activity each day. (4) The specific amount of activity needed for a healthy lifestyle depends on daily caloric intake.

Thus, the sentence that best supports the reason for youth recreational sports is Sentence 3.

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Answer:

ez 3

Step-by-step explanation:

Answer:

480 Hectares potatoes, 340 Hectares corn

Step-by-step explanation:

Let x be the land used to plant potatoes in hectares.

Let y be the land used to plant corn in hectares.

Given the information from the question, we know that:

x + y = 820 - Equation 1

and

x - y = 140 - Equation 2

as you can see here we have 2 equations, means we can solve them simulteanously to solve for both. We will use elimination method.

We will use Equation 1 - Equation 2.

x-x+y-(-y)=820-140

2y = 680

y = 680 ÷ 2 = 340 hectares

We substiture y into equation 1 to find x

x + 340 = 820

x = 820 - 340

= 480 hectares

Therefore, 480 hectares of potatoes and 340 hectares of corn were planted.

Answer:

The interest rate Cindy will be charged with money factor 0.00354 is approximately 8.5% which is option b.

Given The factor included in lease is 0.00354.

Interest is the amount that a bank or person who gives loan charges from loan taker.

Money factor is a method for finding the financing charges on a lease with monthly payments. The money factor can be translated into the annual percentage rate by multiplying the money factor by 2400.

Money factor=0.00354.

So the interest rate that Cindy will charge is equal to 2400*0.00354

The interest rate Cindy will be charged =8.496%

=8.5%

Hence the interest rate charged is approximately 8.5%.

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The transformation was a 180° rotation about the origin.

We can solve this question by plotting the points R (1, 1)

S (3, 1) T (1, 6) and R' (–1, –1) S' (–3, –1) T' (–1, –6) on the graph as shown below.

As we can see from the graph, the original triangle RST which was in quadrant 1, now becomes triangle R’S’T’ in quadrant 3. Thus, when triangle RST was transformed using the rule (x, y) → (–x, –y), from quadrant 1 to quadrant 3 it is a 180° rotation about the origin.

Hence, the transformation was a 180° rotation about the origin.

Your question was incomplete. Please check below for full content.

Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown. R (1, 1) S (3, 1) T (1, 6) R' (–1, –1) S' (–3, –1) T' (–1, –6)

Which best describes the transformation?

The transformation was a 90° rotation about the origin.

The transformation was a 180° rotation about the origin.

The transformation was a 270° rotation about the origin.

The transformation was a 360° rotation about the origin.

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There are 2 trucks are between Joe's hardware truck in a super supplier's truck.

The reasoning is the capacity to make logical judgments based on newly available or previously known information.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

The blue truck from the old time is part to the right truck from hit road the green truck from super suppliers is part to the right of all time.

According to the information provided, there are only two trucks between the Super Suppliers truck and the Joe's Hardware truck.

Joe's Hardware is essentially on the left and Super Suppliers is on the right, with 2 trucks in between.

Thus, there are 2 trucks are between Joe's hardware truck in a super supplier's truck.

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The graph of the exponential function in discuss whose base is; e would have a y-intercept t at point (0, 1), with a domain as the set of all real numbers and its range as the set of all positive numbers.

It follows from the task content that the function in discuss can be written as;

y = e^x.

Consequently, the y-intercept of the graph which corresponds to x= 0 is; (0, 1).

The domain and range of the graph as with other exponential functions are therefore given as the set of all real numbers and all real positive numbers respectively.

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According to the empirical rule, the percent of the data points that are above 76 is; 2.28%

We are given;

Mean; μ = 88

Standard deviation; σ = 6

Sample mean; x' = 76

Formula for z-score is;

z = (x' -  μ)/σ

z = (76 - 88)/6

z = -2

Now, from the empirical rule of normal distribution graph attached, we see that at z = -2, the percentage is 95.44%. However, we want to find the percentage that lie above 27. Thus, this is (100% - 95.44%)/2 = 2.28%

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Answer:

2 miles

Step-by-step explanation:

6X + 10 = 22

X = (22-10)/6 = 12/6 = 2 miles

Answer: 4

Step-by-step explanation:

[tex]f(4)=\frac{1}{4} \cdot 2^{4}=\frac{1}{4} \cdot 16=4[/tex]

The function that is a  tangent to the graph of f is [tex]f(x) = (5/4)x^4+60[/tex]

The definite integral can be interpreted as the resulting area of a region. In addition, it is a value in its result, that is, it does not depend on the variable x, which can be exchanged for any other variable without changing the value of the integral.

Knowing that :

therefore, f'(x)|x=a = -40, so only look for a we have:

[tex]5a^3 = -40\\a^3 = -8\\a = -2[/tex]

if, x = -2, then y = 80 (since, 40x + y = 0), therefore, f(x) passes through (-2,80), so in the equation:

[tex]f'(x) = 5x^3\\f(x) = (5/4)x^4 + c\\80 = (5/4)(-2)^4 + c\\c = 60[/tex]

Therefore,

[tex]f(x) = (5/4)x^4+60[/tex]

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Answer:

t = 4.0

Step-by-step explanation:

1.) P(t) = 1578

2.) Divide both sides by 1400

3.) Take the natural log of both sides (to remove the "e")

4.) Divide both sides by 0.03

5.) Properly round to the 1st decimal place

Answer:

no

Step-by-step explanation:

there are somethings you need to know. The given height is the combined height of the cylinder and hemisphere. but we need to use the height of cylinder in the formula so we subtract the original height by radius.

Next thing is that the formula 2πrh is for C.S.A of the cylinder but we need the base area as well for surface area of this combined solid. So we add base area (i.e πr²) to 2πrh.

The expression that is equivalent to √1,120y is: 4√70y.

Expressions are said to be equivalent when the value of one is the same as the value of the other when evaluated or simplified.

Given the expression, √1,120y, we can simplify as shown below:

√(16 × 70 × y)

= 4√70y

Thus,  4√70y is equivalent to √1,120y .

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By "number of Power set of A" I wonder if you mean the cardinality of the power set.

For any finite set with [tex]n[/tex] elements, its power set contains [tex]2^n[/tex] elements.

Here [tex]|A| = 5[/tex], so the power set will contain [tex]|\mathcal P(A)| = 2^5 = \boxed{32}[/tex] elements.

Recall that the power set is the set of all subsets of a given set

• subsets of [tex]A[/tex] of size 0 (1):

[tex]\emptyset[/tex]

• subsets of size 1 (5):

[tex]\{a\}\\ \{b\}\\ \{\{a\}\}\\ \{3\}\\ \{\{3\}\}[/tex]

• subsets of size 2 (10):

[tex]\{a,b\}\\ \{a,\{a\}\}\\ \{a, 3\}\\ \{a, \{3\}\}\\ \{b,\{a\}\}\\ \{b,3\}\\ \{b,\{3\}\}\\ \{\{a\},3\}\\ \{\{a\}, \{3\}\}\\ \{3,\{3\}\}[/tex]

• subsets of size 3 (10):

[tex]\{a,b,\{a\}\}\\ \{a,b,3\}\\ \{a,b,\{3\}\}\\ \{a,\{a\},3\}\\ \{a,\{a\},\{3\}\} \\ \{a,3,\{3\}\}\\ \{b,\{a\},3\}\\ \{b,\{a\},\{3\}\}\\ \{\{a\},3,\{3\}\}[/tex]

• subsets of size 4 (5):

[tex]\{a,b,\{a\},3\}\\ \{a,b\{a\},\{3\}\}\\ \{a,b,3,\{3\}\}\\ \{a,\{a\},3,\{3\}\}\\ \{b,\{a\},3,\{3\}\}[/tex]

• subsets of size 5 (1):

[tex]\{a,b,\{a\},3,\{3\}\}[/tex]

Answer:

the x value is 13 and the y value is 10. x=13 and y=10