Please help ASAP. Thanks so much.

Answer:

40x+24y-56=

8(5x+2y-7)

Step-by-step explanation:

Answer:

\(S(q)= 105\)

Step-by-step explanation:

Given

\(p =S(q) = 2q\)

Required

Calculate S(q) when p = 105

The given equation can be rewritten as:

\(S(q) = p\)

\(S(q) = 2q\)

\(p= 2q\)

Using: \(S(q) = p\)

Substitute 105 for p

\(S(q)= 105\)

The Volume of the box is 3.75in³

The volume of the box is dependent on the volume of the cube in it.

To obtain the volume of a cube, we use the relation, V = s³

s = side of the cube

Volume = 0.5³ = 0.125 in³

Number of cubes in box = 30

Volume of each cube × Number of cubes

0.125 × 30 = 3.75 in³

Hence, the volume of the box is 3.75in³

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Answer:

x = 62 words

Explanation:

→ We write the data problems.

372 words .............6 minutes

→ We must find: What's Cynthia typing rate in words per minute?

372 words .............6 minutes

x words ..................1 minute

x = 372 words * 1 minute/ 6 minutes

x = 62 words

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Expression: \(\displaystyle\sf (6-2x) +(15-3x)\)

Substituting \(\displaystyle\sf x=0.2\):

\(\displaystyle\sf (6-2(0.2)) +(15-3(0.2))\)

Simplifying the expression inside the parentheses:

\(\displaystyle\sf (6-0.4) +(15-0.6)\)

\(\displaystyle\sf 5.6 +14.4\)

Calculating the sum:

\(\displaystyle\sf 20\)

Therefore, \(\displaystyle\sf (6-2x) +(15-3x)\) evaluated at \(\displaystyle\sf x=0.2\) is equal to \(\displaystyle\sf 20\).

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

The mean value of the chemical to be added to every bottle of syrup so that the bottle wont be rejected would be = 1.41750 ml

Step-by-step explanation:

Standard deviation ( σ )= 0.250 ml

assume the required amount of chemical to be deposited in each syrup bottle to be X

Hence the distribution of X in each bottle can be represented as :

X Г N ( u , 0.250 )

for a bottle not to be rejected  :  P ( X ≤ 2 )

To determine the setting so that no more than 1% of the bottles of cough syrup prepared by this machine will be rejected we have to standardize the variable X

at X = 2 ml

\(\frac{x - u }{std} = \frac{2 - u}{std}\)

z = \(\frac{2-u}{0.250}\) = z ----------- ( 1 )

probability for a bottle to be rejected : P( x >2 ) = 1 - P ( x ≤ 2 )

                                                                             = 0.01

attached below is a normal distribution curve showing probability values

from the curve

p( 0 < Z < z ) = 0.5 - 0.01 = 0.49  

Area = 0.49 hence from the Normal table where area = 0.49 the value of z = 2.33

Referring back to equation 1 above:  z = \(\frac{2-u}{0.250}\) = 2.33 --------- (2)

u = mean value that should be added so that the bottle will not be rejected

make u subject of the equation : u = 2 - ( 2.33 * 0.250 )

                                                       u = 1.41750

The mean value of the chemical to be added to every bottle of syrup so that the bottle wont be rejected would be = 1.41750 ml

\(\bold{\huge{\underline{ Solution }}}\)

- I have used different colours for indicating different process

- I used brown colour to indicate steps

- I used green colour for explaining solution

- Pink colour for known properties of integration

- Purple colour for the middle steps that are optional.

[Note :- For solving such questions it is mandatory that you should know all the functions and it's derivatives ]

\(\sf{=}{\sf{\dfrac{ x^{2}}{2}}}{\sf{ + 7x + 67x .In| x - 4 | - 30.In| x - 3 | + c }}\)

Answer:

\(\displaystyle \large{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}\)

Step-by-step explanation:

To find an integration of this function, first, you must know these integration methods and differences of them.

These methods above are common when it comes to integrating fractional functions, except there are differences when to use these methods.

Examples (of these integrands that require partial fraction technique)

\(\displaystyle \large{\int \frac{3}{x^2-5x+6} \ dx}\\\displaystyle \large{\int \frac{x+2}{x^2-4} \ dx}\)

Examples (of these integrands that require long division)

\(\displaystyle \large{\int \frac{x^2+5x+6}{x+2} \ dx}\\\displaystyle \large{\int \frac{x^4+3}{x} \ dx }\)

Therefore, from the given integral, the integrand requires long division method. (See attachment for long division.)

After long division, we should get:

\(\displaystyle \large{\int x+7+\frac{37x-81}{x^2-7x+12} \ dx}\)

Recall important properties of integral such as:

\(\displaystyle \large{\int [f(x) \pm g(x)] \ dx = \int f(x) \ dx \pm \int g(x) \ dx}\)

Hence:

\(\displaystyle \large{\int x \ dx + \int 7 \ dx + \int \frac{37x-81}{x^2-7x+12} \ dx}\)

Recall important integration formula for polynomial and constant:

\(\displaystyle \large{\int x^n \ dx = \frac{x^{n+1}}{n+1} + C}\\\displaystyle \large{\int x \ dx = \frac{x^2}{2} + C}\\\displaystyle \large{\int k \ dx = kx + C \ \ \tt{(k \ \ is \ \ a \ \ constant.)}\)

Therefore:

\(\displaystyle \large{\frac{x^2}{2}+7x+\boxed{\int \frac{37x-81}{x^2-7x+12} \ dx}}\)

From the boxed integral above, we cannot evaluate it by default. From what I said, if the degree of numerator is less than the degree of denominator, we’ll use partial fraction technique.

Therefore, factor the denominator:

\(\displaystyle \large{\frac{37x-81}{(x-4)(x-3)}}\)

Set to A/x-4 and B/x-3

\(\displaystyle \large{\frac{37x-81}{(x-4)(x-3)} = \frac{A}{x-4} + \frac{B}{x-3}}\)

Multiply both sides by (x-4)(x-3).

\(\displaystyle \large{\frac{37x-81}{(x-4)(x-3)} \cdot (x-4)(x-3)= \frac{A}{x-4} \cdot (x-4)(x-3) + \frac{B}{x-3} \cdot (x-4)(x-3)}\\\displaystyle \large{37x-81= A(x-3) + B(x-4)}\\\displaystyle \large{37x-81= Ax-3A+Bx-4B}\\\displaystyle \large{37x-81= (A+B)x-(3A+4B)}\)

Then compare the coefficients:

\(\displaystyle \large{\left \{ {{A+B=37} \atop {3A+4B=81}} \right}\)

Solve the simultaneous equation for A and B.

\(\displaystyle \large{\left \{ {{A=37-B} \atop {3A+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {3(37-B)+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {111-3B+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {111+B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {B=81-111}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {B=-30}} \right}\\\displaystyle \large{\left \{ {{A=67} \atop {B=-30}} \right}\\\)

Therefore, A = 67 and B = -30. Substitute the values in:

\(\displaystyle \large{\int \frac{67}{x-4}-\frac{30}{x-3} \ dx}\\\displaystyle \large{\int \frac{67}{x-4} \ dx -\int \frac{30}{x-3} \ dx}\)

Recall the integration formula for above:

\(\displaystyle \large{\int \frac{k}{x-a} \ dx = \int k \cdot \frac{1}{x-a} \ dx = k\ln |x-a| + C}\)

Therefore:

\(\displaystyle \large{\int \frac{37x-81}{x^2-7x+12} \ dx = \int \frac{67}{x-4}-\frac{30}{x-3} \ dx = 67\ln |x-4| - 30\ln |x-3|}\)

Back from this:

\(\displaystyle \large{\frac{x^2}{2}+7x+\boxed{\int \frac{37x-81}{x^2-7x+12} \ dx}}\)

Substitute in:

\(\displaystyle \large{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}\)

Therefore the solution is:

\(\displaystyle \large \boxed{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}\)

The inequality that represents the value of x is (b)  x > 80

from the question, we have the following parameters that can be used in our computation:

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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======================================================

Explanation:

From 1:45 to 2:15 is a span of 30 minutes, or 30/60 = 1/2 = 0.5 hour.

From 2:15 to 3:15 is a span of 1 hour

In total, the entire duration is 0.5 hr + 1 hr = 1.5 hours

------------

Multiply the speed with the time value to get the distance traveled

distance = rate*time

distance = (65 mph)*(1.5 hrs)

distance = (65*1.5) miles

distance = 97.5 miles

Answer:

slope (m) = 2/3

Step-by-step explanation:

slope = change in x /change in y

Also, slope is y2 - y1 / x2 -x1. That is what I apply for this activity, hence:

slope = 3 - (-1) / 0 - (-6)

         = 3 + 1 / 0 + 6

         = 4 / 6

         = 2/3

∴ slope(m) = 2/3

Answer:

62.33 degrees Fahrenheit.

Anytime bestie <3

Answer:

56

Step-by-step explanation:

P=2(l+w)=2·(16+12)=56

Answer:

Area of the total garden is: given by: 4 x^2 +56 x + 192

Step-by-step explanation:

Complete the product

(2x + 16)* (2x + 12) = 4x^2 +24 x +32 x + 192 =

= 4 x^2 +56 x + 192

Answer:

10

Step-by-step explanation:

divide the numbers for a anser

a) Using the standard divisors according to Jefferson's apportionment method, the number of salespeople assigned to work each shift is as follows:

Shift                              Morning     Midday     Afternoon     Evening   Total

Number of

salespeople assigned  1               3                  5                 7                16

b) The modified or adjusted divisor used represents the average number of customers for each shift divided by the standard divisor.

The standard divisor shows the ratio of the total population to the number of seats.

The standard divisor gives an insight about the number of people each seat represents.

Standard divisor = Total number of customers / Total number of salespeople

The total number of customers = 1,425

The number of salespeople = 16

a) Standard divisor = 1,425 ÷ 16

= 89.0625

Shift                              Morning     Midday     Afternoon     Evening   Total

Average number of

customers                     125            280             460             560       1,425

Standard divisor      89.0625     89.0625      89.0625      89.0625

b) Modified divisor     1.4035        3.1438          5.165           6.288

Number of

salespeople assigned  1               3                  5                 7                16

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Answer:

Thanks

Step-by-step explanation:

Thanks

Tanisha takes 5/6 hours longer to mow all the lawns last week than this week.

Here, we are given that Tanisha mowed 5 lawns last week in 7/ 12 hours each.

Thus, the total time taken by her to mow 5 lawns = 5(7/12)

= 35/ 12 hours

Now, this week she mows the five lawns in 5/12 hours each

Thus, the total time taken by her = 5(5/12)

= 25/12 hours

Therefore, the difference between the time taken by her last week and this week will be-

35/ 12 - 25/ 12

= (35 - 25)/ 12

= 10/ 12

= 5/6

Thus, Tanisha takes 5/6 hours longer to mow all the lawns last week than this week.

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

True

Step-by-step explanation:

Angles 1 and 5 match each other; they are congruent and in the same positions. There are therefore corresponding.

Answer:

9,500,000. the ten thousands place has a two, which is one less than 3, rendering the 6 in the thousand's place ineffective

Step-by-step explanation:

4 or less let it rest, 5 or more let it score

Answer:

b

Step-by-step explanation:

Answer:

working on a answer one second

Step-by-step explanation:

Answer:

Trapezoid

Step-by-step explanation:

It's a quadrilateral and it only has one pair of parallel sides.

Answer:

multiply by 6

Step-by-step explanation:

Answer:

a(t)= 2000(1+r)^T

*make sure to add the power to t

a(t)=2000(1+.10)^5

= 3221.02

Hope this helps!

The exponential decay function is given by  y=2000×0.9ˣ and the stock will be worth $1180.98 after a period of 5 years.

In mathematics, exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y=a(1-b)ˣ wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.

Given here: The value of the stock in 2012 was $2000 and the value decreases each year by 10%

We know the exponential decay is given by  y=a(1-b)ˣ

where x is the number of years and 1-b is the decreasing factor

Thus based on the given information we can construct the exponential decay function as y=2000(1-10%)ˣ

or y=2000×0.9ˣ

Therefor in 5 years i.e in 2017 the stock will be worth

y=2000×0.9⁵

=$1180.98

Hence, The exponential decay function is given by  y=2000×0.9ˣ and the stock will be worth $1180.98 after a period of 5 years.

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Answer:

8x - 58 ≤ 500

8x ≤ 500 + 58

8x ≤ 558

x ≤ 69.74

The amount of the sales tax is $9.75.

The percentage is defined as a ratio expressed as a fraction of 100.

The taxable amount of the sale: $150

Sales tax percentage: 6.5%

To calculate the sales tax, you can multiply the taxable amount of the sale by the sales tax percentage.

Sales Tax = Taxable Amount × Sales Tax Percentage

Sales Tax = $150 × 6.5%

Sales Tax = $150 × 0.065

Apply the multiplication operation, and we get

Sales Tax = $9.75

So, the amount of the sales tax is $9.75.

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Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

The intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

Option (D) is correct.

What is the intersection of two sets?

The intersection of two sets, A and B, is the set of elements that are common to both sets. It is often represented by A ∩ B.

In this case, Set A = {2, 4, 6, 8} and set B = {1, 2, 3, 4, 5, 6, 7, 8}. The set that represents A ∩ B is {2, 4, 6, 8} because these are the elements that are common to both sets A and B.

So the correct answer is {2, 4, 6, 8}

Hence, the intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

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