A gardener at a nursery is filling pots with soil to prepare to
transplant seedlings into these larger pots. Each new pot needs about 27 cubic inches
of soil. The amount of soil s (in cubic inches) it takes to fill p pots is given by the
function s = 27p
a.
The gardener is filling the pots from a bag of soil that contains 3456 cubic
inches of soil. How many pots can be filled from the bag?
b.
Suppose the gardener needs to fill at most 109 pots. How much soil (in cubic
inches) will the gardener need?

h(x) = 4x - 10

Step-by-step explanation:

The given is:

We need to find h(x) = f(x) + g(x)

∵ f(x) = -2

∵ g(x) = 4x - 8

∵ h(x) = f(x) + g(x)

- Substitute f(x) and g(x) in h(x), and then add the like terms

∴ h(x) = (-2) + (4x - 8)

- Simplify the right hand side

∴ h(x) = -2 + 4x - 8

- Add like terms in the right hand side

∴ h(x) = 4x + (-2 - 8)

∵ -2 - 8 = -10

∴ h(x) = 4x + (-10)

∴ h(x) = 4x - 10

h(x) = 4x - 10

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Answer:

16990.616 $ you can expect to have in your account after five years.

Step-by-step explanation:

Given that,

Amount invested is principal amount (p) = $ 15000

Annual rate of interest (r) = 2.5% = 0.025

Compounded quarterly (n) = 4

Sum of the amount after 5 years (t)

We know that from compound interest formula,

[tex]\text { Final amount }(\mathrm{A})=P\left(1+\frac{r}{n}\right)^{n t}[/tex]

To find the final amount substitute the given values in the above formula,

[tex]\text { Final amount }(\mathrm{A})=15000\left(1+\frac{0.025}{4}\right)^{4 \times 5}[/tex]

[tex]\text { Final amount }(\mathrm{A})=15000\left(1+6.25 \times 10^{-3}\right)^{20}[/tex]

[tex]\text { Final amount }(\mathrm{A})=15000(1.00625)^{20}[/tex]

[tex]\text { Final amount }(\mathrm{A})=15000 \times 1.132707738[/tex]

Final amount (A) = 16990.62

The final amount that he can expect is $ 16990.62.

Answer:

$38.00

Step-by-step explanation:

164/4=41          41-3=38

Answer:

2900

Step-by-step explanation:

Very easy. Evaluate P(0).

P(0) = 2900e^0.039(0) = 2900e^0 = 2900(1) = 2900

To solve the expression, rewrite each term with the same denominator and then add them together. The final answer is 2.345.

To solve the expression 1 15/100 +1/50 +1.175, we need to rewrite all the terms with the same denominator. The least common denominator (LCD) of 100 and 50 is 100. Therefore, we can rewrite the expression as follows:

1 15/100 is equivalent to 1.15

1/50 is equivalent to 0.02

Now, we can add the three terms together:
1.15 + 0.02 + 1.175 = 2.345

Therefore, the final answer is "2.345."

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Answer:

57

Step-by-step explanation:

Write and solve a proportion.

47 / 289 = x / 350

x ≈ 57

Since the multiplicative inverse of a fraction p/q is the fraction that swaps its numerator and denominator, i.e. q/p, we have that the inverse of 2/3 is 3/2.

So, if we multiply both sides of the equation by 3/2, we have

[tex]\dfrac{3}{2}\cdot\dfrac{2}{3}a=16\cdot\dfrac{3}{2}[/tex]

3/2 and 2/3 are multiplicative inverse of each other, and by definition this means that they give 1 when multiplied:

[tex]\dfrac{3}{2}\cdot\dfrac{2}{3}a=1\cdot a=a=16\cdot\dfrac{3}{2}[/tex]

On the right hand side, we have

[tex]16\cdot\dfrac{3}{2}=8\cdot 3=24[/tex]

And so the solution is [tex]a=24[/tex]

Answer:

25 tickets were purchased ahead of time

Step-by-step explanation:

25(11)=275 which is the price of the 11 bought at the door then you  take 625-275=350 which is the amount of money that was raised through purchases ahead of time so you take 350/14=25 meaning that 25 tickets were bought ahead of time.

There are 25 tickets were purchased ahead of time.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The cost of tickets to a fundraiser when purchased ahead = $14

The cost of tickets to a fundraiser when purchased at the door = $25

And, The total amount raised from all ticket sales = $625

Now,

Let number of tickets to a fundraiser when purchased ahead = x

And, The number of tickets to a fundraiser when purchased at the

door = y

We can formulate;

⇒ $14x + $25y = $625

Since, The number of tickets to a fundraiser when purchased at the

door = 11

So, y = 11

Hence, We can formulate;

⇒ $14x + $25y = $625

⇒ $14x + $25 × 11 = $625

⇒ $14x + $275 = $625

⇒ $14x = $625 - $275

⇒ $14x = $350

⇒ x = 25

Thus, There are 25 tickets were purchased ahead of time.

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The 0.46 percentage of the number 80 is 0.368 .

Given data:

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %.

The percentage value is represented as p.

The value of p = 0.46%

So, p = 0.0046

The number is represented as q.

The value of q = 80

Now, A = p * q

On simplifying the equation:

A = 0.0046 * 80

A = 0.368

Hence, the percentage value is 0.368

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Answer:

C

Step-by-step explanation:

Let length of rectangle be "l"

Let width of rectangle be "w"

We know,

LENGTH is 2 MORE THAN WIDTH, we can write:

l = w + 2

Also, note the perimeter is the sum of all 4 sides of a rectangle, thus:

length + width + length + width

Now,

The perimeter is given as 72, so we can write:

l + l + w + w = 72

2l + 2w = 72

We have 2 equations that we need to solve and find the length (l).

The first equation is:

l = w + 2

Rearranging, we have:

w = l - 2

We put this into 2nd equation and find the value of l:

[tex]2l + 2w = 72\\2l + 2(l-2) = 72\\2l+2l-4=72\\4l-4=72\\4l=76\\l=\frac{76}{4}\\l=19[/tex]

The length is 19 meters, the correct answer is C

Answer: $37.45(to the nearest hundredths)

Step-by-step explanation:

% increase in last year living cost =5%

% increase in last year income =5%

This year income = $39.420

To calculate last year income implies

5% decrease of this year income; thus:

5/100 * $39.420 = $1.971

Last year income = $39.420 - $1.971 = $37.449 = $37.45 (to the nearest hundredths)

Answer:

37.4490 (rounded to the nearest hundredth) = 37.45

Step-by-step explanation:

ok so her bills or wateva went up 5% right and she gets a lil 5% raise or sumn from her job which made her money got up to $39.42. so if you think about it all you do is multiply 39.42 and (5%) which = 0.05 in decimal form and then after you multiply you should get 1.9710 and once you get that you gone take her money she getting now which is 39.42 - her 5% raise she got and once you subtract you gone get 37.4490 or 37.45 rounded

Answer:

Option D =[6    18]  is the correct answer

Step-by-step explanation:

Given that:

[4  2] * [-2    5; 7    -1]

For taking product:

= [4*-2 + 2*7    4*5 + 2*-1]

=[-8 + 14        20 + (-2) ]

=[6    18]

i hope it will help you!

Answer:

The restaurant sold 175 hotdogs and 525 hamburgers.

Step-by-step explanation:

Let the restaurant sold x hotdogs and y hamburgers.

Given the restaurant sold 350 more hamburgers than hotdogs.

So, we can write x + 350 = y ....... (1)

Again given that the number of total hotdogs and hamburgers sold in the restaurant is 700.

So, x + y = 700 ........ (2)

Solving equations (1) and (2) we get  

2x + 350 =700

⇒ 2x = 350

⇒ x = 175

Then from equation (1) we get,

y = 350 + 175 = 525

Therefore, the restaurant sold 175 hotdogs and 525 hamburgers. (Answer)

The equation of the line containing the given pair of points (4.6 , -8) and (6.6 , 2.2) is y = 5.1 x - 31.46

Step-by-step explanation:

The equation of a line is y = m x + b, where

∵ The line contains the points (4.6 , -8) and (6.6 , 2.2)

∴ [tex]x_{1}[/tex] = 4.6 and [tex]x_{2}[/tex] = 6.6

∴ [tex]y_{1}[/tex] = -8 and [tex]y_{2}[/tex] = 2.2

∵ [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

- Substitute the values above in the rule of m

∴ [tex]m=\frac{2.2-(-8)}{6.6-4.6}=\frac{2.2+8}{2}=\frac{10.2}{2}=5.1[/tex]

∴ The slope of the line is 5.1

∵ The equation of a line is y = m x + b

Substitute m by 5.1

∴ y = 5.1 x + b

To find b substitute x and y by the coordinates of point (4.6 , -8) OR point (6.6 , 2.2)

∵ x = 6.6 and y = 2.2

∴ 2.2 = 5.1(6.6) + b

∴ 2.2 = 33.66 + b

- Subtract 33.66 from both sides

∴ -31.46 = b

∴ y = 5.1 x + (-31.46)

∴ y = 5.1 x - 31.46

The equation of the line containing the given pair of points (4.6 , -8) and (6.6 , 2.2) is y = 5.1 x - 31.46

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Answer:

1 right angle

Step-by-step explanation:

The sides are not in common

Answer:

1 right angle

Step-by-step explanation:

They dont have the same number of sides

Answer:

48

Step-by-step explanation:

2x-1=6

2x=6+1

2x=7

x=7/2

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

4x^2-1

4(7/2)^2-1

4(49/4)-1

49-1

48

Answer: 48

Step-by-step explanation:

2x - 1 = 6

Add 1 to both sides of the equation , we have:

2x = 7

divide through by 2

x = 7/2

The value of [tex]4x^{2}[/tex] - 1 will be calculated by substituting in the value of x , that is

[tex]4x^{2}[/tex] - 1 = 4([tex](\frac{7}{2} )^{2}[/tex] - 1

= 4([tex]\frac{49}{4}[/tex]) - 1

= 49 - 1

= 48

Answer:

D)24 people

Step-by-step explanation:

Total number of people, x=300

Number of people donated blood with type A, y

[tex]=\frac{28}{100}\times x\\=\frac{28}{100} \times 300\\=84[/tex]

Number of people donated blood with type B, z

[tex]=\frac{20}{100}\times x\\=\frac{20}{100} \times 300\\=60[/tex]

⇒Number of people with Type A blood donated more than those with Type B blood= y-z=84-60= 24

Answer:

D) There are 24 more people who donated Type - A then Type -B.

Step-by-step explanation:

Total number of people who donated the blood in shelter = 300

Percentage of people who donated the type A = 28%

Percentage of people who donated the type B = 20%

Now, 28 %  of 300 = [tex]\frac{28}{100 } \times 300 = 84[/tex]

So, the total number of people who donated the Type - A  = 84 people.

Also, 20 %  of 300 = [tex]\frac{20}{100 } \times 300 = 60[/tex]

So, the total number of people who donated the Type - B  = 60 people.

So, the difference in the people who donated type A and Type B  

= Number of people who donated the {Type - A  - Type - B}

= 84 people -  60 people

= 24 people

or, the difference in the people who donated type A and Type B  = 24

Hence, there are 24 more people who donated Type - A then Type -B.

Answer:

1. false

2. true

Step-by-step explanation:

1. false because fractions are rational

2. true because it can be turned into a fraction

Answer:

P=0.39

Step-by-step explanation:

We use the Hypergeometric distribution to find the probability

The normal deck of cards has 52 cards, 26 red and 26 black

Taking 4 cards out of the whole deck can be done (without replacement) in

[tex]\begin{pmatrix}52\\4\end{pmatrix}[/tex]

different ways .

Taking 2 red cards can be done in

[tex]\begin{pmatrix}26\\2\end{pmatrix}[/tex]

different ways. Same applies to the black cards

So, the required probability can be computed as

[tex]P=\frac{\begin{pmatrix}26\\2\end{pmatrix}\begin{pmatrix}26\\2\end{pmatrix}}{\begin{pmatrix}52\\4\end{pmatrix}}[/tex]

[tex]{\begin{pmatrix}52\\4\end{pmatrix}}=\frac{52!}{4!48!}=270725[/tex]

[tex]{\begin{pmatrix}26\\2\end{pmatrix}}=\frac{26!}{2!24!}=325[/tex]

[tex]P=\frac{325x325}{270725}=0.39[/tex]

Final answer:

To find the intercepts of the given line, the equation is rearranged into the slope-intercept form, revealing the y-intercept directly and allowing for easy calculation of the x-intercept by setting y=0. Thus, the x-intercept is 4/3.

Explanation:

To determine the intercepts of the line given by the equation -3x - 4 = -5y - 8, we should find both the x-intercept and y-intercept. The general form of a line is given by y = mx + b, where m is the slope, and b is the y-intercept.

Steps to find the intercepts:

Rearrange the equation to the slope-intercept form y = mx + b by adding 3x to both sides and then adding 8, resulting in -5y = 3x - 4. By further dividing both sides by -5, we get  y = -3/5x + 4/5.

To find the y-intercept (b), set x=0 in the rearranged equation, which gives y = 4/5. Thus, the y-intercept is 4/5.

To find the x-intercept, set y=0 in the rearranged equation, resulting in 0 = -3/5x + 4/5. Multiplying both sides by 5 and then dividing by -3, we find x = 4/3. Thus, the x-intercept is 4/3.

Answer:

Answer:

2x - y = 3.

Step-by-step explanation:

0.2x = 0.1y + 0.3

Multiply through by 10:

2x = y + 3

2x - y = 3.

Answer:

[tex]\large\boxed{5\dfrac{3}{10}\ hectometers=530\ meters}[/tex]

Step-by-step explanation:

[tex]PREFIXES\\\\mega\ (M)=10^6\\\\kilo\ (k)=10^3\\\\hecto\ (h)=10^2\\\\deko\ (da)=10\\\\decy\ (d)=10^{-1}=0.01\\\\centi\ (c)=10^{-2}=0.01\\\\mili\ (m)=10^{-3}=0.001\\\\mikro\ (\mu)=10^{-6}=0.000001[/tex]

[tex]5\dfrac{3}{10}=5.3\\\\1\ hectometers=100\ meters\qquad(1\ hm=100m)\\\\5\dfrac{3}{10}\ hm=5.3\ hm=5.3\cdot100\ m=530\ m[/tex]

Answer:

1

Step-by-step explanation:

8/2*4=8/8=1

Answer:

About 300 calories

The drawing will help

Answer:

(5x+10) + (x+14) =180

6x+24=180

x=26

Angles are 140 and 40

Step-by-step explanation:

top left i guessed and got it correct

Answer:

A is correct so technically the top left hope this helps

Step-by-step explanation:

Answer:

The number of dimes = 32

The number of quarters  = 14

Step-by-step explanation:

Here, the total number of coins combined = 46

Let us assume the number of dimes = m

So, the Number of quarter = Total Coins - Number of dimes  = 46 - m

Now,as we know:

1 dime = $0.1

So, m dimes  = m x ($0.1) = $(0.1 m)

1 Quarter  = $0.25

So, ( 46 - m ) Quarters  = (46 - m ) x ( $ 0.25)   = 11.5 - 0.25 m

Also, given the total amount of coins = $ 6.70

⇒ Value of (Dimes + Quarters) = $ 6.70

or, (0.1 m) +  11.5 - 0.25 m  = 6.70

-0.15 m = - 4.8

or, m = 4.8/0.15  =  32

⇒ m = 32

Hence, the number of dimes = m = 32

And the number of quarters  = 46 - m= 46 -32 = 14

Answer:

x>=-12

Step-by-step explanation:

3x+7>=-29

3x>=-29-7

3x>=-36

x>=-36/3

x>=-12