Amy has $1,000 in a savings account at the beginning of the fall. She wants to have at least $500 in the account by the end of the fall. She withdraws $100 a week for living expenses. Write an inequality for the number of weeks Amy can withdraw money, and solve.
A) 1000 - 100w ≤ 500; w ≥ 6
B) 1000 + 100w ≤ 500; w ≤ 5
C) 1000 + 100w ≥ 500; w ≥ 6
D) 1000 - 100w ≥ 500; w ≤ 5

The race-car will have to go for 730 miles

Step-by-step explanation:

The given is:

We need to find how far it will have to go

∵ The car will move around the park

- That means it moves the distance equal the perimeter of the park

∵ The dimensions of the park are 4.6 mile long and 2.7 miles wide

∵ The perimeter of the park = 2(length + width)

∴ The perimeter of the park = 2(4.6 + 2.7)

∴ The perimeter of the park = 2(7.3)

∴ The perimeter of the park = 14.6 miles

∵ The car will move around the park 50 times

∵ The distance of one round is 14.6 miles

∴ The distance for 50 rounds = 14.6 × 50

∴ The distance for 50 rounds = 730 miles

The race-car will have to go for 730 miles

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Answer:

The relationship between the number of scoops and the number of dogs is not proportional

Step-by-step explanation:

Let

x ----> the number of scoops

y ----> the number of dogs

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

First situation

You prepare 8 scoops of dog food for 4 dogs

x=8, y=4

Find the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

substitute the values of x and y

[tex]k=\frac{4}{8}=0.5[/tex]

Second situation

You prepare 12.5 scoops of dog food for 5 dogs

x=12.5, y=5

Find the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

substitute the values of x and y

[tex]k=\frac{5}{12.5}=0.4[/tex]

Compare the values of k

[tex]0.5\neq 0.4[/tex]

The values of k are not equal

therefore

The relationship between the number of scoops and the number of dogs is not proportional

Answer:

55%

Step-by-step explanation:

The percent markup is the percent increase from $300 to $465.

Subtract to find the markup: 465 - 300 = 165

Now we find the percent markup.

Divide: 165/300 = 0.55

Multiply: 0.55 * 100 = 55

Answer: 55%

Markup percentage is 55%

Old price of phone = 300

New price of phone = 465

Markup percentage

Markup = [465 - 300] /

Markup = 165 / 300

Markup = 0.55

Markup percentage = 0.55 × 100

Markup percentage = 55%

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Step-by-step explanation:

21 percent of 3,876 is 813.96$, and 17 percent of 4552 is 773.67$. 813.96>773.67

21% of $3,876 is $813.96, while 17% of $4,552 is $773.84. Therefore, 21% of $3,876 inequality sign is greater than 17% of $4,552.

Choosing between 21% of $3,876 or 17% of $4,552 involves calculating each percentage of the given amounts to compare which is greater. To do this:

Calculate 21% of $3,876: 0.21 × 3876 = $813.96.

Calculate 17% of $4,552: 0.17 × 4552 = $773.84.

Comparing these two amounts using an inequality sign, we see that $813.96 is greater than $773.84. So, you would rather have 21% of $3,876 than 17% of $4,552.

The inequality would be written as:

21% of $3,876 > 17% of $4,552

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Answer: A: 0.0031

Step-by-step explanation:

Given : In a study of wait times at an amusement park, the most popular roller coaster has a mean wait time of 17.4 minutes with a standard deviation of 5.2 minutes.

i.e. [tex]\mu=17.4[/tex] and [tex]\sigma=5.2[/tex]

We assume that the wait times are normally distributed.

samples size : n= 30

Let x denotes the sample mean wait time.

Then, the probability that the mean wait time is greater than 20 minutes will be :

[tex]P(x>20)=1-P(x\leq20)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{20-17.4}{\dfrac{5.2}{\sqrt{30}}})\\\\=1-P(z\leq2.74)\ \ [\because\ z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9969\ \ [\text{ By z table}]\\\\=0.0031[/tex]

Hence, the probability that the mean wait time is greater than 20 minutes.= 0.0031

Thus , the correct answer is A: 0.0031 .

Answer:

Answer: A: 0.0031

Step-by-step explanation:

Answer:

4x-8

Step-by-step explanation:

3/4(4x-8)+1/4(4x-8)

12/4x-24/4+4/4x-8/4

3x-6+x-2

3x+x-6-2

4x-8

Answer:

everything is on the sheet

Answer:

B)

Step-by-step explanation:

The right answer is Option D: $5.44

Step-by-step explanation:

Given,

Cost of one sun visor = $6.25

Cost of 11 sun visors = 6.25*11 = $68.75

Cost of one sunglasses = $8.90

Cost of 4 sunglasses = 8.90*4 = $35.60

Cost of one water bottle = $9.50

Cost of 8 water bottles = 9.50*8 = $76

Cost of one whistle = $1.75

Cost of 15 whistles = 1.75*15 = $26.25

Total number of items = 11+4+8+15 = 38

Total cost of items = 68.75+35.60+76+26.25 = $206.60

Average = [tex]\frac{Sum\ of\ prices}{No.\ of\ items}[/tex]

[tex]Average=\frac{206.60}{38}\\Average=\$5.436[/tex]

Rounding off to nearest hundredth

Average = $5.44

The average price of an item is $5.44

The right answer is Option D: $5.44

Keywords: average, sum

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Answer:

The coordinates of the mid-point are :

[tex](\frac{1}{2}, \frac{5}{2})[/tex]

Step-by-step explanation:

We know that, the coordinates of the mid-point (x, y) of a line segment joining the points (x₁, y₁) and (x₂, y₂) is given by

[tex](x, y) = (\frac{x_{1} +x_{2} }{2},\frac{y_{1}+y_{2} }{2} )[/tex]

Now, we have the given points as (3, 5) and (-2, 0).

By using the above formula, coordinates of the mid-point (x, y) of the line-segment joining the points (3, 5) and (-2, 0) is given by,

[tex]x = \frac{3+(-2)}{2} = \frac{3-2}{2} = \frac{1}{2}[/tex]

[tex]y = \frac{5+0}{2} = \frac{5}{2}[/tex]

∴ coordinates of the mid-point of the line-segment joining the points (3,5) and (-2,0) is [tex](\frac{1}{2}, \frac{5}{2})[/tex].

Answer:

[tex]g \leq -24[/tex]  or  [tex]g>6[/tex]

Step-by-step explanation:

Lets solve the first inequality by cross multiplying and doing algebra. THe process is shown below:

[tex]\frac{2g+63}{5} \leq  3\\2g+63 \leq 15\\2g \leq 15-63\\2g \leq -48\\g \leq -24[/tex]

Now, lets solve the next inequality with simple algebra. Process shown below:

[tex]13g-34>44\\13g>44+34\\13g>78\\g>6[/tex]

Hence, we can say:

g is less than or equal to -24  AND  g is greater than 6

Answer:

Theo Should use 1.3 cups of Sugar to make 24 cookies.

Step-by-step explanation:

Given;

Number of cookies required by recipe = 36 cookies

Number of cookies Theo wants to use = 24 cookies

Number of cups sugar recipe requires = 2 cups

We need to find Number of cups sugar Theo should use to make cookie according to recipe.

Now,

For 36 cookies = 2 cups of sugar

So For 24 cookies = Number of cups of sugar required for 24 cookies.

By Using Cross Multiplication we get;

Number of cups of sugar required for 24 cookies = [tex]\frac{24\times2}{36}= 1.33\ cups[/tex]

Hence Theo Should use 1.3 cups of Sugar to make 24 cookies.

Answer:

(∞,-5)

Step-by-step explanation:

For a line to have a slope of 0, it has to be horizontal.

Any point that has a y value of -5 could form a horizontal line along with (0,-5).

Option A

Volume of bed is [tex]2\frac{2}{3}[/tex] cubic inches

Solution:

Given are the dimensions of bed

To find: volume of bed

Since bed is generally of cuboid shape, we can use the volume of cuboid formula

volume of cuboid is given as:

[tex]\text{ volume of cuboid } = l \times w \times h[/tex]

Where, "l" is the length and "w" is the width and "h" is the height of cuboid

From attached figure in question

[tex]l = 2\frac{2}{3} inches = \frac{3 \times 2 + 2}{3} = \frac{8}{3} inches[/tex]

[tex]w = 3 inches[/tex]

[tex]h = \frac{1}{3} inches[/tex]

Substituting the values in formula,

[tex]v = \frac{8}{3} \times 3 \times \frac{1}{3}\\\\v = \frac{8}{3} = 2\frac{2}{3}[/tex]

Therefore volume of bed is [tex]2\frac{2}{3}[/tex] cubic inches

The shortest possible height of tower is 24 cm.

Tim used 4 blue blocks and his brother used 3 green blocks.

Step-by-step explanation:

Given,

Height of blue block = 6 cm

Height of green block = 8 cm

We will take least common multiple to find the shortest possible height.

6 = 2*3

8 = 2*2*2

LCM = 2*2*2*3 = 24 cm

The shortest possible height of tower is 24 cm.

Number of blue blocks used = [tex]\frac{24}{6} = 4[/tex]

Number of green blocks used = [tex]\frac{24}{8} = 3[/tex]

Tim used 4 blue blocks and his brother used 3 green blocks.

Keywords: LCM, multiplication

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Answer:

x=-5

Step-by-step explanation:

-4x-10=10

-4x=10+10

-4x=20

x=20/-4

x=-5

Answer:

Hence Proved AB = DF

Step-by-step explanation:

In the Figure:

Given;

CD = EF

AB = CE

We need to prove AB = DF

Solution:

CD = EF    ⇒ (Given)

Now Adding both side by DE we get;

CD + DE = EF + DE   ⇒by the (Addition) Property of Equality.

CE=CD + DE and DF = EF + DE ⇒(Segment Addition)

Now we know that if [tex]a=b \ and \ b =c \ so \ a=c[/tex]

CE = DF           ⇒by the (transitive) Property of Equality.

Now Given:

AB = CE

CE = DF

Now we know that if [tex]a=b \ and \ b =c \ so \ a=c[/tex]

AB  = DF    ⇒by the (Transitive) Property of Equality)

The correct options to fill in the gaps are:

From the diagram given, we have that;

We are to show that the segment AB is congruent to DF

Also from the diagram

Similarly, given that:

AB = CE and CE = DF implies AB = DF by the Transitive Property of Equality.

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answer: 3a^4 is the correct answer

Answer:3a^4

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\\\\75\%=\dfrac{75}{100}=0.75\\\\50\%=\dfrac{50}{100}=0.5\\\\\dfrac{n}{d}-\text{a fraction}\to(n-\text{numerator},\ \text{denominator})\\\\\text{numerator is decreased by 75}\%\to n-0.75n=0.25n\\\\\text{denominator is decreased by 50}\%\to d-0.5d=0.5d\\\\\text{new fraction}\ \dfrac{0.25n}{0.5d}=\dfrac{0.25\cdot100}{0.5\cdot100}\cdot\dfrac{n}{d}=\dfrac{25}{50}\cdot\dfrac{n}{d}=\dfrac{1}{2}\cdot\dfrac{n}{d}=0.5\cdot\dfrac{n}{d}\\\\\dfrac{n}{d}-0.5\dfrac{n}{d}=0.5\cdot\dfrac{n}{d}\to\ \text{it's}\ 50\%\ \text{of}\ \dfrac{n}{d}[/tex]

Answer:

They both have 3 up ig

Step-by-step explanation:

Answer:

You have to simplify the equation and find the answer

Step-by-step explanation:

[tex]4x + ( - 4) = - 2x + 8 \\ \\ 4x + 2x = 4 + 8 \\ \\ 6x = 12 \\ \\ x = 2[/tex]

Answer:

Step-by-step explanation:

4x+(-4) = -2x+8

4x - 4 = -2x + 8

Collecting like terms

4x + 2x = 8 + 4

6x = 12

Dividing through by 6

x = 12/6

x = 2

Answer:

[tex]y=1500\cdot(0.902)^T[/tex]

Step-by-step explanation:

Let T be the number of years since the start of the study and y be the area that the forest covers in [tex]\text{km}^2[/tex].

We have been given that at the beginning of an environmental study a forest cover an area of 1500 [tex]\text{km}^2[/tex]. Since then this area has decreased by 9.8% each year.

We know that an exponential function is in form [tex]y=a\cdot(1-r)^x[/tex], where,

y = Final amount,

a = Initial amount,

r = Decay rate in decimal form,

x = Time.

Let us convert 9.8% into decimal as:

[tex]9.8\%=\frac{9.8}{100}=0.098[/tex]

We have been given that initial value (a) is [tex]1500[/tex].

Upon substituting our given values, we will get:

[tex]y=1500\cdot(1-0.098)^T[/tex]

[tex]y=1500\cdot(0.902)^T[/tex]

Therefore, our required exponential function would be [tex]y=1500\cdot(0.902)^T[/tex].

Answer:

1/8

Step-by-step explanation:

1 chance of of 4 cards. * because since she draws 4 times you do 4+4 = 8.

Answer: 4

Step-by-step explanation:

The amplitude is the distance from the baseline to the maximum.

Answer:

(1,12) and (2,12).

(- 5,1) and (- 5, 2).

Step-by-step explanation:

y = 12 is a line that is parallel to the x-axis and at a constant distance of 12 units above the x-axis. Therefore, the points on the line will have any x-coordinate but have a constant y-coordinate i.e. 12.

Therefore, the two points on the line y = 12 can be (1,12) and (2,12).  

x = - 5 is a line that is parallel to the y-axis and at a constant distance of 5 units left of the y-axis. Therefore, the points on the line will have any y-coordinate but have a constant x-coordinate i.e. - 5.

Therefore, the two points on the line x = - 5 can be (- 5,1) and (- 5, 2).  (Answer)

Answer:

Neither

Step-by-step explanation:

Can be determined because there is enough information (Length, width, and height).

Not congruent because from the picture itself, the figures are in different sizes.

Not similar because:

The height ratio is not the same as the ratios of other dimensions.

1 : 4 is not similar to 6 : 12 and 4 : 8

Answer:

272,100

This is because 62 rounds up

Answer:

272,100

You get this answer by looking at the hundreds place and then looking at the right of it. The hundreds place is the 0 and the the right of it is 6, so 5 and up round up 4 and down round down and in this case, 6 is above 5, so it rounds up to 272,100!

Hope this helped!

Answer:

y-8=-3/2(x+8)

Step-by-step explanation:

y-y1=m(x-x1)

y-8=-3/2(x-(-8))

y-8=-3/2(x+8)

Final answer:

The equation of the line in the point-slope form that passes through (-8, 8) with a slope of -3/2 is y - 8 = (-3/2)(x + 8).

Explanation:

To write an equation in point-slope form for a line that passes through a given point with a known slope, we use the formula y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line.

For the line that passes through the point (-8, 8) with a slope of -3/2, we substitute these values into the point-slope form equation:

y - 8 = (-3/2)(x + 8)

This equation represents the specific line asked in the problem.

Answer:

40g of chocolate are left.

Step-by-step explanation:

3/5*100=300/5=60

100-60=40

Final answer:

To find the amount of chocolate left, subtract the amount eaten from the original 100g bar.

Explanation:

To find the number of grams of chocolate left, you need to subtract the amount Captain ate from the original 100g bar. Captain ate 3/5 of the bar, so you can calculate the amount eaten by multiplying 3/5 by 100g. This gives you 60g. To find the amount left, you subtract 60g from 100g. The answer is 40g.

Answer:

Mass Media

Step-by-step explanation:

Answer: Got an (A) on my test, it is (Mass media)

Step-by-step explanation: OOOOFFF is my word

Answer:

The fraction of trip completed by Andre is  [tex]\frac{31}{24}[/tex] km

Step-by-step explanation:

Given as :

The Total distance between the home to a festival = 1 [tex]\frac{5}{8}[/tex] km

I.e The total distance between the home to a festival =  [tex]\frac{13}{8}[/tex] km

The distance cover by Andre before taking rest =  [tex]\frac{1}{3}[/tex] km

Let The fraction of trip completed by Andre = x km

So, According to question

The fraction of trip completed by Andre = The Total distance between the home to a festival - The distance cover by Andre before taking rest

or, x =  [tex]\frac{13}{8}[/tex] km - [tex]\frac{1}{3}[/tex] km

or, x =  [tex]\frac{39 - 8}{24}[/tex] km

∴ x = [tex]\frac{31}{24}[/tex] km

Or, The fraction of trip completed by Andre = x = [tex]\frac{31}{24}[/tex] km

Hence , The fraction of trip completed by Andre is  [tex]\frac{31}{24}[/tex] km Answer

Answer:

[tex]\frac{4}{15}[/tex]

Step-by-step explanation:

We know that the total distance is

[tex]1\frac{5}{8}km[/tex] which is standard fraction would be [tex]\frac{13}{8}km[/tex].

So, Andre walks [tex]\frac{1}{3}km[/tex], that means he needs to walk the following distance to get to the festival

[tex]\frac{13}{8}-\frac{1}{3}=\frac{39-8}{24}=\frac{31}{24}km[/tex]

Now, to find the fraction of the tripe that represents the distance he already completed, we have to divide

[tex]\frac{1}{3} \div \frac{13}{8}=\frac{1}{3} \times \frac{8}{13}=\frac{8}{30}=\frac{4}{15}[/tex]

Therefore, we completed a [tex]\frac{4}{15}[/tex] part of the total distance.