a carpenter is fitting some bookcases to an alcove, using as much of the space as possible from floor to ceiling, a height of 2.5 m. The books to be fitted into the shelves are 210 mm high and a gap of at least 30 mm is necessary above each book so that they can be removed. The shelves are 20 mm thick. The alcove is 1.2 m wide. The bottom shelf should not be less than 300 mm from the ground, as the house-owner cannot bend down easily. How many shelves can be fitted into the alcove?

Answer:

A store pays $840 for an oil painting. The store marks up the price by 46%. What is the amount of the mark-up?

=

$386.40

Answer:

x-int = (4,0)

y-int = (0,6)

Step-by-step explanation:

to find the x intercept put y as 0 and solve for x.

to find the y intercept put x as 0 and solve for y.

The answer should be 90 degrees

Answer:

a>-21(1/3)

Step-by-step explanation:

3/4a>-16

first thing is to divide both sides by 3/4 to isolate the variable.

Since it is not negative, the sign stays the same.  

-16/0.75=-21.3 repeating or just 1/3

Answer:

1) 38

2) 18

Step-by-step explanation:

1) 4m - 2t

m = 10

t = 2

(4 * 10) - (2 * 2)

40 - 4 = 36

Answer : 36

2) t + 2m - 4

m = 10

t = 2

2 + (2 * 10) - 4

22 - 4 = 18

Answer : 18

3) m/2t

m = 10

t = 2

10/(2*2) = 2.5

Answer : 2.5

The compensating variation is $13.52.

The compensating variation is the amount of money that Greg would need to be compensated for a price increase in order to maintain his original level of utility. In this case, Greg's utility function is u = x^0.38x^0.962. His income is $83.00, and he faces these prices: (P1, P2) = (4.00, 1.00). If the price of x increases by $1.00, then the new prices are (P1, P2) = (5.00, 1.00).

To calculate the compensating variation, we can use the following formula:

CV = u(x1, x2) - u(x1', x2')

where u(x1, x2) is Greg's original level of utility, u(x1', x2') is Greg's new level of utility after the price increase, and CV is the compensating variation.

We can find u(x1, x2) using the following steps:

Set x1 = 83 / 4 = 20.75.

Set x2 = 83 - 20.75 = 62.25.

Substitute x1 and x2 into the utility function to get u(x1, x2) = 22.13.

We can find u(x1', x2') using the following steps:

Set x1' = 83 / 5 = 16.60.

Set x2' = 83 - 16.60 = 66.40.

Substitute x1' and x2' into the utility function to get u(x1', x2') = 21.62.

Therefore, the compensating variation is CV = 22.13 - 21.62 = $1.51.

To two decimal places, the compensating variation is $13.52.

Learn more about function  here: brainly.com/question/30721594

#SPJ11

Therefore, the maximum and minimum values of the function f(x, y) = xy subject to the given constraint are both 32/17.

To find the maximum and minimum values of the function f(x, y) = xy, subject to the constraint x² + y² = 8 and y = 4x, we can substitute y = 4x into the equation x² + y² = 8 to eliminate y and obtain an equation in terms of x only.

Substituting y = 4x into x² + y² = 8, we have:

x² + (4x)² = 8

x² + 16x² = 8

17x² = 8

x² = 8/17

x = ±√(8/17)

Now, we can find the corresponding values of y using y = 4x:

For x = √(8/17), y = 4√(8/17)

For x = -√(8/17), y = -4√(8/17)

We have two critical points: (√(8/17), 4√(8/17)) and (-√(8/17), -4√(8/17)).

To determine the maximum and minimum values, we evaluate the function f(x, y) = xy at these points:

For (√(8/17), 4√(8/17)):

f(√(8/17), 4√(8/17)) = (√(8/17))(4√(8/17)) = (4√8/√17)(4√8/√17) = 32/17

For (-√(8/17), -4√(8/17)):

f(-√(8/17), -4√(8/17)) = (-√(8/17))(-4√(8/17)) = (4√8/√17)(4√8/√17) = 32/17

Therefore, the maximum and minimum values of the function f(x, y) = xy subject to the given constraint are both 32/17.

To learn more about constraint visit:

brainly.com/question/17156848

#SPJ11

The two numbers are 4 and 8 and their product is 32, using algebra to solve for the unknown x and y to represent the numbers.

Let the two numbers be x and y such that we have the ratios;

x - y : x + y : x × y = 1: 3 : 8

(x + y)/xy = 3/8

3xy = 8(x +y) {by cross multiplication}

3xy = 8x + 8y ...(i)

also

(x - y)/xy = 1/8

xy = 8x - 8y {by cross multiplication}

xy = 8x - 8y ...(ii)

add equations (i) and (ii)

4xy = 16x {divide through by 4x}

y = 4

substitute the value of y = 4 in equation (ii)

4x = 8x - 8(4)

4x = 8x - 32

4x = 32 {collect like terms}

x = 32/4 {divide through by 4}

x = 8

Therefore, the unknown numbers are 4 and 8 and their product is 32.

Learn more about algebra here: https://brainly.com/question/723406

#SPJ1

Taryn saved $13.50 by shopping on tax-free weekend, since she did not have to pay any sales tax on her $180 purchase.

to calculate how much taryn saved by shopping on tax-free weekend, we first need to calculate how much she would have paid in sales tax if she had bought her school supplies on a regular day.

if the sales tax is normally 7.5%, then the amount of sales tax taryn would have paid is:

0.075 x $180 = $13.50 the answer is (b) $13.50.

Taryn bought all her school supplies on tax-free weekend and spent $180. If sales tax is normally 7. 5%,

Learn more about purchase here:

 https://brainly.com/question/31489447

#SPJ11

Answer:

B.16 mins start from home to school or school to home

Step-by-step explanation:

I. When bike is faster than walk 3 times

  Jane is in the middle of way to school

  if she walk mid point to school is 4 mins

 then mid point to home is 4 * 3 = 12 mins

 School + Home = Total Mins

 4 + 12 = 16

More discuss, leave comment below.

Silver chloride is precipitated as a white substance that is soluble through ammonium hydroxide when chlorides respond to silver nitrate solution state.

2) C cannot behave as both a reducing agent in CO32 because it has the highest oxidation state of +4, whereas every other compound are able to decolorize KMnO4 solution.

3) Conc. H2SO4 reacts with Cl, Br, I, NO3, C2O42, and CH3COO but not with dil. producing recognizable gases with H2SO4. Either with the diluted H2SO4 or concentrated H2SO4, SO42- and PO43- do not react.

4) White barium chloride precipitates are produced when sodium sulphate and barium chloride react. The precipitates in question are irresolvable in diluted HCl. It follows that SO42 is the anion present.

Ions that have a negative charge are called anions. They develop when non-metallic materials gain electrons. As many as one electron is gained.

To know more about compound click here

brainly.com/question/23781897

#SPJ4

Therefore, in either partial derivatives, we have u = 0 or v = 0.

The given information implies that two vectors u and v satisfy:

u * v = 0, where * denotes the dot product between vectors.

u X v = 0, where X denotes the cross product between vectors.

From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.

From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:

|u X v| = |u| * |v| * sin(θ)

= 0

Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).

In the case where u and v are parallel, we have:

u * v = |u| * |v| * cos(θ)

= |u|²

= 0

This implies that |u| = 0, which means that u = 0.

In the case where u and v are anti-parallel, we have:

u * v = |u| * |v| * cos(θ)

= -|u|²

= 0

This again implies that |u| = 0, which means that u = 0.

To know more about partial derivatives,

https://brainly.com/question/21661447

#SPJ11

Answer:

Step-by-step explanation:

(2x+4)° + 42° = 180°

x = 67°

Answer

-77

Step-by-step

                 11

Simplify   ——

                 2

Then

         42         11

 (0 -  ——) • ——

       3             2

Simplify

                 14

                ——

                  1

Next

                  11

 (0 -  14) • ——

                  2

Final result

-77

If this was helpful, please mark brainliest. Have a beautiful day.

Answer:

(-4 2/3) × (1 1/2) = -7

Step-by-step explanation:

Given problem,

→ (-4 2/3) × (1 1/2)

Let's solve the problem,

→ (-4 2/3) × (1 1/2)

→ (-14/3) × (3/2)

→ (-14 × 3)/(3 × 2)

→ -42/6 = -7

Hence, the answer is -7.

Answer:

a) As weekly costs are fixed at $300, we simply need to shift the function up 300 units. (the new function is shown in blue on the attached graph).

b) Reading from the (blue) graph, the total cost of producing 75 books in a week is $600.

fixed cost + variable cost = $300 + $300 = $600

Answer:

T increased by 55 =t+55

Possible options:

uppercase letter: 26

lowercase letter: 26

number: 10

upper or lowercase letter: 50

Note: I'm interpreting the "no upper or lower case letters can be repeated in the sequence" to mean you could have Aa0b, where A is used as the uppercase and a is used as the lower case letter, but then you can't use A or a for the last character.

26 · 26 · 10 · 50 = 338,000 combinations

Now is using "A" and "a" isn't allowed, then you have:

Possible options:

uppercase letter: 26

lowercase letter: 25

number: 10

upper or lowercase letter: 48

26 · 25 · 10 · 48 = 312,000 combinations

Answer:

2/4, 4/8, 8/16, 16/32

Step-by-step explanation:

2/4
2x2/4x2 = 4/8
4x2/8x2 = 8/16
8x2/16x2 = 16/32

Answer:

5+8

Step-by-step explanation:

Answer:

A) 8+2.50x=28

B) 8 rides

C) Jada can go on 8 rides before she has spent all of her money

Step-by-step explanation:

subtract the $8 fee from 28 and get 20, then divide 20 by how much each ride costs (2.50) and get 8 :)

Answer:

She went on 8 rides

Step-by-step explanation:

28-8=20÷2.50=8

Answer:

x=2

Step-by-step explanation:

3 (3 - 3x) +4= -5

Subtract 4 from each side

3 (3 - 3x) +4-4= -5-4

3 (3 - 3x)= -9

Divide by 3

3/3 (3 - 3x) = -9/3

3-3x = -3

Subtract 3 from each side

3-3x-3 = -3-3

-3x = -6

Divide by -3

-3x/-3 = -6/-3

x = 2

Answer:

3 miles per hour.

Step-by-step explanation:

To get his walking rate in miles per hour, we multiply 1/5 by its reciprocal, 5/1. We also multiply 6/10 by 5/1. This gets us 30/10 of a mile in an hour. We can simplify 30/10 to 3. This means he walks at 3 miles per hour.

Answer:

Step-by-step explanation:

1. BOC and 90 degrees and complemetary angles

2. BOC and 30 degrees

3. 30 degrees

4. 60 degrees

What's the answer to problem 19 Geometry?

Answer:

C.$0.15 I TOOK IT ON STUDY ISLAND

Step-by-step explanation:

First, you want to find an exact point on the graph.  What I mean by this is you want to go somewhere on the graph where the line goes through an exact y and x value.

Second, you want to figure out where this x and y value are.  Where the graph first goes through two points is at (20, 3).

Third, you want to figure out what the 20 and the 3 mean.  20 is the number of messages and 3 is the dollar amount.

Finally, to calculate the amount of money per message, you divide the dollar amount (3) by the number of messages (20).  So, you have 3/20.  After this, simplify 3/20 to get 0.15, or 15 cents per message.

Answer:

c. 14.4

Step-by-step explanation:

when your divide 271.4^3 by 1000 you get 7.2 and then you multiply that by  2 and get 14.4 as your answer.

Answer:

4/7 = 0.57142857……

Step-by-step explanation:

integer NO cause it has a decimal

irrational NO cause it can be written as a fraction

Natural NO cause it has decimals

Rational YES because it’s a fraction

whole NO cause decimals

Real YES cause it’s a number

The conditional distribution of X given that the first two tosses both land Heads is:

P(X = 0 | HH) = 1

P(X = 1 | HH) = 2

P(X = 2 | HH) = 0

Given that the first two tosses both land Heads, the sample space is reduced to {HH, HT}. Therefore, X can take values 0, 1, or 2, with respective probabilities P(X = 0 | HH) = P(X = 0, HH) / P(HH), P(X = 1 | HH) = P(X = 1, HH) / P(HH), and P(X = 2 | HH) = P(X = 2, HH) / P(HH).

We have:

Probability of getting two heads in a row = P(HH) = 1/2 × 1/2 = 1/4

Probability of getting one head and one tail = P(HT) = 1/2 × 1/2 = 1/4

Now, if the first two tosses are both Heads, then we can only get the following: HH. Thus, the distribution of X is:

X = 0:

- Only one way, P(X = 0, HH) = 1/4

- Hence P(X = 0 | HH) = (1/4) / (1/4) = 1

X = 1:

- Only one way, P(X = 1, HH) = 2/4 = 1/2

- Hence P(X = 1 | HH) = (1/2) / (1/4) = 2

X = 2:

- No way, P(X = 2, HH) = 0

- Hence P(X = 2 | HH) = 0

Thus, the conditional distribution of X given that the first two tosses both land Heads is:

P(X = 0 | HH) = 1

P(X = 1 | HH) = 2

P(X = 2 | HH) = 0

Know more about conditional distribution here:

https://brainly.com/question/14310262

#SPJ11

The 98% confidence interval for the true proportion is (0.506, 0.614).

Given that a local news outlet reported that 56% of 600 randomly sampled Kansas residents planned to set off fireworks on July 4th and we need to compute the 98% confidence interval for the true proportion.

The formula to find the confidence interval is given by;

\(CI = \hat{p} \pm z_{\alpha/2} \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\)

Where,

\(\hat{p}\) = Sample proportion\(n\)

= Sample size\(z_{\alpha/2}\)

= Critical value for the confidence level\(\alpha\)

= Level of significance

Let's put the given values in the above formula:

\(\hat{p} = 56\%

= 0.56\)\(n

= 600\)\(\alpha

= 0.02\) (As the level of significance is 1 - 0.98)\(z_{\alpha/2}\)

= 2.33 (From standard normal distribution table)N

ow, we will compute the confidence interval by putting the above values in the formula;

\(\begin{aligned}CI

= \hat{p} \pm z_{\alpha/2} \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\

= 0.56 \pm 2.33 \times \sqrt{\frac{0.56(1-0.56)}{600}} \\

= 0.56 \pm 0.054 \\

= (0.506, 0.614) \end{aligned}\)

Therefore, the 98% confidence interval for the true proportion is (0.506, 0.614).

Know more about 98% confidence interval here:

https://brainly.com/question/17097944

#SPJ11

The expression used  to calculate the surface area of the rectangular prism is given by option b. 2×6 + 2×10 + 2×15.

Let us consider 'l' be the length of the rectangular prism.

'w' be the width of the rectangular prism .

'h' be the height of the rectangular prism.

From the attached figure we have,

Length of the rectangular prism l = 3 units

Width of the rectangular prism w = 2 units

Height of the rectangular prism h = 5 units

Surface of the rectangular prism = 2(lw + wh + hl )

Substitute the values in the formula we get,

⇒Surface of the rectangular prism = 2 (3×2 + 2×5 + 5×3 )

⇒Surface of the rectangular prism = 2 ( 6 + 10 + 15)

⇒Surface of the rectangular prism = 2×6 + 2×10 + 2×15

Therefore, the surface area of the rectangular prism with given dimensions is equal to option b. 2×6 + 2×10 + 2×15.

Learn more about surface area here

brainly.com/question/14322585

#SPJ4

The above question is incomplete, the complete question is:

Which expression can be used to find the surface area of the following rectangular prism?

Attached figure.

The value of h(x) = -40x2 – 52x + 18. Option (b) is correct.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable is defined as a function.

Given functions

f(x) = -5x − 9

g(x) = 8x − 4

we have to determine which equation defines function h

f(x) = -5x − 9

g(x) = 8x – 4

(f x g) (x) = (-5x –9)(8x – 4)

(f x g) (x) = -40x2 + 20x – 72x + 36

(f x g) (x) = -40x2 – 52x + 18

Therefore the value of  h(x) = -40x2 – 52x + 18. Option (b) is correct.

To learn more about functions visit

https://brainly.com/question/5245372

#SPJ1