14. You start an investment account with $3000 and save $100 each month. Write a
rule to represent the total amount of money you invest into your account as an
arithmetic sequence. How much money will you have invested after 12 months?​

Length of sides of quadrilateral are 8 feet, 8 feet, 16 feet, 24 feet

Given that length of the sides of a quadrilateral are in extended ratio 1:1:2:3

Perimeter of the quadrilateral = 56 feet

Need to determine length of the sides

As length of the sides of a quadrilateral are in extended ration 1: 1: 2: 3  

lets assume that four sides of rectangle = 1x, 1x, 2x and 3x

Perimeter of quadrilateral = sum of length of four sides  

=> Perimeter of quadrilateral = 1x + 1x + 2x + 3x = 7x

As given that perimeter = 56 feet

=> 56 = 7x

x = 8

Then the length of sides are:

1x = 1(8) = 8 feet

1x = 1(8) = 8 feet

2x = 2(8) = 16 feet

3x = 3(8) = 24 feet

Answer: The perimeter of the scale drawing is [tex]30[/tex].

Step-by-step explanation:

You need to analize the information provided in the exercise.

You know that the perimeter of rectangle is [tex]450[/tex] and the scale factor Natalie used to create the scale drawing, was:

[tex]scale\ factor=\frac{1}{15}[/tex]

From this you can identify that, in order to find the perimeter of the scale drawing of the triangle (Which can be represented with [tex]P_2[/tex]), you must multiply the original perimeter ((Which can be represented with [tex]P_1[/tex]), by the scale factor Natalie used.

Therefore, you get that the perimeter is:

[tex]P_{2}=\frac{1}{15}P_1\\\\P_2(\frac{1}{15})(450)\\\\P_2=30[/tex]

Answer:

a) 21 nickels and 2 dimes

b) [tex]5x+10y=125[/tex]

c) There are 13 nickels and 6 dimes

d) The point (13,6) a solution to the equation you wrote

Step-by-step explanation:

Let x be the number of nickels and y be the number of dimes in Priya's pocket.

1 nickel = 5 cents

x nickels = 5x cents

1 dime = 10 cents

y dimes = 10y cents

b. Total amount in nickels and dimes is [tex]5x+10y[/tex] cents that is $1.25. Convert $1.25 into cents:

[tex]\$1.25=125\ cents,[/tex]

so the equation that describes the relationship between the number of dimes and number of nickels is

[tex]5x+10y=125[/tex]

a. To find one possible solution, substitute an arbitrary value of y and find x. Let y = 2, then

[tex]5x+10\cdot 2=125\\ \\5x+20=125\\ \\5x=125-20\\ \\5x=105\\ \\x=21[/tex]

21 nickels and 2 dimes

c. The point (13,6) means that there are 13 nickels and 6 dimes.

d. Substitute x = 13 and y = 6 intoe the equation and check whether it is true:

[tex]5\cdot 13+6\cdot 10=65+60=125[/tex]

True, so the point (13,6) a solution to the equation you wrote

Answer:

1. Figure 4

2. Figure 2

3. Figure 4

Answer:

1. Figure 2

2. Figure 3

3. Figure 1

Step-by-step explanation:

Brainlest?

Mrs. Bailey had a 75% decrease in the number of candies she had after giving away 9 out of the original 12 pieces.

To calculate the percent decrease of candy Mrs. Bailey had, we begin by identifying the initial amount and the final amount of candy. Mrs. Bailey started with 12 pieces and ended with 3 pieces, which means she gave away 12 - 3 = 9 pieces of candy. To find the percent decrease, we use the formula: “part over total, times one hundred, equals percent.” Here, the “part” is the amount of candy she gave away (9), and the “total” is the original amount she had (12).

The formula for the percent decrease is:

9 / 12 × 100 = 75%

So, the percent decrease in the number of candies Mrs. Bailey had is 75%.

Answer:

9

Step-by-step explanation:

gave picture to explain

9 out of 400 phones are likely to be defective.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

If the probability of a phone being defective is 2.1%, we can use this probability to predict how many of the 400 new phones are likely to be defective.

The expected number of defective phones can be found by multiplying the probability of a phone being defective by the total number of phones ordered:

Expected number of defective phones = probability of a phone being defective × total number of phones ordered

In this case, the probability of a phone being defective is 2.1%, or 0.021 as a decimal.

The total number of phones ordered is 400.

So, we can write:

Expected number of defective phones = 0.021 × 400 = 8.4

We can't have a fractional number of defective phones, so we need to round to the nearest whole number.

Since 0.4 is greater than or equal to 0.5, we round up to 9. Therefore, we can predict that 9 of the 400 new phones are likely to be defective.

Learn more about percentages here:

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Answer:

Step-by-step explanation:

1x117 = 117

3x39 = 117

9x13 = 117

The result of the division , 117 divided by 13 is 9.

Given the parameters which can be used in our calculation:

We can write the expression thus :

Now we have :

The result of the division operation is 9

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Answer:

y<[tex]\frac{-1}{3}[/tex]x+1 is inequality shown on graph.

Step-by-step explanation:

The graph shows representation of inequality,

Here, Line passes through points say, A(3,0) and B(0,1)

The slope of line is given by m=[tex]\frac{Y2-Y1}{X2-X1}[/tex]

m=[tex]\frac{Y2-Y1}{X2-X1}[/tex]

m=[tex]\frac{1-0}{0-3}[/tex]

m=[tex]\frac{-1}{3}[/tex]

and Y-intercept is c=1

The equation of line is given by y=mx+c

y=[tex]\frac{-1}{3}[/tex]x+1 is equation of line in graph.

To decide which side you are going to shaded area on the graph

Take test of origin.

If (0,0) is statisfy the equation then, shaded the graph towards the origin.

Let suppose,

Take, y<[tex]\frac{-1}{3}[/tex]x+1

0<[tex]\frac{-1}{3}[/tex](0)+1

0<1

TRUE,

Therefore, y<[tex]\frac{-1}{3}[/tex]x+1 is inequality shown on graph.

Answer:

there are 2100 seconds in 35 minutes

There are 60 seconds in a minute, if you times 60 by how many minutes there are, you get how many seconds there are. Here is how I got the answer:

60 x 35 = 2100

I hope this helps you and you can use it for future reference! :)

Answer:

1 meter is 100 centimeters

Henry misread the meters part and assumed his desk was 1 centimeter, which is why he thought his nametag was 7 cm longer.

In reality, his desk is 92 cm longer (100 cm - 8 cm = 92 cm)

Answer:

byzantine style of architecture is an example of haggis sophias style

Step-by-step explanation:

Final answer:

To find out how much stock is needed for 4 servings of Mrs. Young's haggis recipe, we use proportional relationship calculations to arrive at 3/4 cup of stock.

Explanation:

The student needs to determine how much stock Mrs. Young will need for 4 servings of her haggis recipe if the original recipe, which serves 12, calls for 2 1/4 cups of stock. To solve this, a proportional relationship can be used, as follows:

Multiply the number of servings in the original recipe by the amount of stock to find the stock per serving.

Divide the original number of servings (12) from the result to find the stock needed for one serving.

Multiply the amount of stock for one serving by the new number of servings (4) to determine the total stock needed.

The calculation would be: (2 1/4 cups ÷ 12 servings) × 4 servings. Since 2 1/4 cups is equal to 9/4 cups, the arithmetic gives us: (9/4 cups ÷ 12) × 4 = 3/4 cup of stock needed for 4 servings.

Answer:5/3

Step-by-step explanation: plug in 1/2 for x

Answer

ITS A (–∞, –3)

Step-by-step explanation:

Answer:

28/8=3.5...so probably just 3

Step-by-step explanation:

1. 40 units___16 workers

20 units___x= 8 workers

(20*16)/40=8

2. 40 units___16 workers

25 units___x= 10 workers

(25*16)/40=10

3. 40 units___16 workers

100 units___x= 40 workers

(100*16)/40=40

Step-by-step explanation:

1. 40 units: 16 workers    2. 40 units: 16 workers

   20 units: 8 workers          25 units: 10 workers

(20 x 16) /40= 8 workers       (25 x 16) /40= 10 workers

3. 40 units: 16 workers

  100 units: 40 workers

(100 x 16) / 40= 40 workers

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Answer:

negative

Step-by-step explanation:

The slope of a line graphed to represent the volume of water in a pool over time will be 6 and the equation of the line representing the table

y = - 6x + 50

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have a table as given in the question as follows -

Time (in minutes)         Water (in gallons)

0                                         50

1                                          44

2                                         38

3                                         32

4                                         26

5                                         20

We can write the slope of the line as follows -

The slope of the line will be -

m = (y₂ - y₁)/(x₂ - x₁)

m = (44 - 50)/(1 - 0)

m = -6

At [x] = 0, the [y] coordinate is 50. Therefore, the equation of the line representing the table -

y = - 6x + 50

Refer to the graph attached.

Therefore, the slope of a line graphed to represent the volume of water in a pool over time will be 6 and the equation of the line representing the table y = - 6x + 50

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Answer:

The zeros of the function are x=-7 and x=2

Step-by-step explanation:

we have

[tex]A(x)=(x-2)(x+7)[/tex]

we know that

The zeros or roots of the function are the values of x when the value of the function is equal to zero (also is called the x-intercepts)

so

For A(x)=0

[tex](x-2)(x+7)=0[/tex]

Remember that

The Zero Product Property states that

if ab = 0, then either a = 0 or b = 0, or both a and b are 0

so

Let

[tex](x-2)=0[/tex] ----> [tex]x=2[/tex]

[tex](x+7)=0[/tex] ----> [tex]x=-7[/tex]

therefore

The zeros of the function are x=-7 and x=2

Answer:

130°

Step-by-step explanation:

DEF is an isosceles triangle with base DE and DF = EF.

By definition, base angles of an isosceles triangle are equal.

Hence ∠FDE = ∠DEF = 25°

Angle F = 180° - ∠FDE - ∠DEF

= 180° - 25° - 25°

= 130°

Answer:

None of these choices are correct.

Step-by-step explanation:

The quoted value of 99.875, means that this bond is sold at 99.875%  of the face value and not at a price of  $99.875.

Therefore, calculate price;

Price = 0.99875 * 1000

Price = $998.75

Since brokerage fees is 5.5% of the selling price, Leona will pay additional cost to the quoted price making the total cost to be more than $998.75;

Brokerage fees = (0.055*998.75) = $54.93

Total cost = $998.75 +$54.93

= $1053.68

Therefore, none of the choices is correct.

Answer:

The value of y is 5 , and The value of x is - 5

Step-by-step explanation:

Given as :

The line passes through point ( - 2, 5)

The slope of line is m =  [tex]\frac{2}{3}[/tex]

Equation of line is written as

y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex])

Since line passes through line ( - 2 , 5 ) and have slope [tex]\frac{2}{3}[/tex]

So, y - 5 =   [tex]\frac{2}{3}[/tex]  × (x + 2)

Or, 3 × ( y - 5 ) = 2 × ( x + 2 )

Or, 3 y - 15 = 2 x + 4

Or, 3 y - 2 x - 19 = 0 is the equation of line

Now points ( x , 3 ) lies on the line 3 y - 2 x - 19 = 0

So, 3 × 3 - 2 x - 19 = 0

or, 9 - 2 x - 19 = 0

or, 2 x = - 10

∴  x = - [tex]\frac{10}{2}[/tex]

I.e x = - 5

Again points ( - 2 , y )  lies on the line 3 y - 2 x - 19 = 0

So, 3 × y + 2 × 2 - 19 = 0

Or,  3 × y + 4 -19 = 0

or, 3 y = 15

∴  y = [tex]\frac{15}{3}[/tex]

I.e y = 5

Hence The value of y is 5 , and The value of x is - 5   .  Answer

Answer:

$12 per hour

Step-by-step explanation:

3600/6=600

600/50=12

Answer:

20.397

Step-by-step explanation:

The expression below shows a number in expanded form:

[tex](2\times 10) + \left(3\times  \dfrac{1}{10}\right)+ \left(9 \times \dfrac{1}{100}\right) +\left (7 \times \dfrac{1}{1,000}\right)[/tex]

This expanded form tells you that the number has

Hence, this number is [tex]20.397[/tex]

Dependent variable: Hot chocolate sales

Independent variable: Outside temperatures

If it is 75°F I don't think people will be buying hot chocolate

But if it's 35°F more people will be buying hot chocolate. The sales of the hot chocolate depends on what the outside temperature is. While the temperature depends on nothing

Answer:

I just did it and got it right so hoped it helped you ;)

1/2

1/2

1/4

Step-by-step explanation:

The probability that both coins will land heads up when Miranda flips them twice, assuming each coin is fair and has an equal chance of landing heads or tails, is 1/4. Each flip has a probability of 1/2 for heads, and these probabilities multiply for sequential independent events.

If Miranda flips a coin twice, the probability that both coins will land heads up needs to be calculated by multiplying the probability of the first coin landing heads up by the probability of the second coin doing the same. Since the chance of a coin landing on heads (assuming it is a fair coin) is usually 50%, that is 1/2 for each flip. Therefore, to find the probability of both coins landing heads up, we multiply these probabilities together: 1/2 × 1/2 = 1/4.

In a broader context, the more times you flip a coin, the closer you are likely to get to 50% heads due to the law of large numbers. Notably, in experiments such as one conducted by Karl Pearson, after 24,000 coin flips, the relative frequency of heads was 12,012/24,000 ≈ 0.5005, closely aligning with the theoretical probability of 1/2. An essential assumption in determining these probabilities is that the coin is fair and each flip is independent of the others.

Answer:

x=4

Step-by-step explanation:

-3x+4x=2*4-x

x=8-x

8=x+x

8=2x

x=8/2

x=4

Answer:

2 pennies 2 nickels and a dime 22 cents

Answer:

4/35

Step-by-step explanation:

5/7-3/5=

find common denominator =35

5/7*5/5=25/35

3/5*7/7=21/35

25/35-21/35=4/35

Answer:

[tex]x + \frac{3}{5} = \frac{5}{7}[/tex]

[tex] \times = \frac{5}{7} - \frac{3}{5} [/tex]

[tex]x = \frac{25}{35} - \frac{21}{35} [/tex]

[tex]x = \frac{4}{35} [/tex]

Answer: B

Step-by-step explanation:

Slope = rise/run (aka change in y/change in x)

Slope = (-9-(-9.75))/(-4-(-1)) = 0.75/-3 = -1/4

Answer:

The speed of River's mom drove for 10 miles distance is 0.234 mph

The speed of  River's mom drove for 25 miles is 10.234 mph  

Step-by-step explanation:

Given as :

The first distance cover by River's mom = 10 miles

The rate of speed = x mph

The second distance cover by river's mom = 25 miles

The rate of speed = x + 10 mph

The total driving time = 45 min

Now, According to question

Time = [tex]\dfrac{\textrm Distance}{\textrm speed}[/tex]

So, 45 = [tex]\dfrac{10}{x}[/tex] +  [tex]\dfrac{25}{x + 10}[/tex]

Or, 9 = [tex]\dfrac{2}{x}[/tex] +  [tex]\dfrac{5}{x + 10}[/tex]

Or, 9 × x × ( x + 10 ) = 2 × ( x + 10 ) + 5 x

Or, 9 x² + 90 x = 2 x + 20 + 5 x

Or, 9 x² + 90 x = 7 x + 20

Or, 9 x² + 90 x - 7 x - 20 = 0

Or, 9 x² + 83 x - 20 = 0

Solving this quadratic equation

x = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]

Or, x = [tex]\frac{-83\pm \sqrt{83^{2}-4\times 9\times (-20)}}{2\times 9}[/tex]

Or, x = [tex]\frac{-83\pm \sqrt{7609}}{18}[/tex]

∴  x = [tex]\frac{-83+87.22}{18}[/tex] , tex]\frac{-83-87.22}{18}[/tex]

I.e x = 0.234 , - 9.4567

We consider x = 0.234

So, The speed for 10 miles distance = x = 0.234 mph

and The speed of 25 miles = x + 10 = 0.234 + 10 = 10.234 mph

Hence The speed of River's mom drove for 10 miles distance is 0.234 mph

and The speed of  River's mom drove for 25 miles is 10.234 mph   Answer

Final answer:

To find the two driving speeds, use the distance formula and set up two equations. Simplify the equations to find the speeds.

Explanation:

To find the two driving speeds at which River's mom drove, we can use the formula distance = speed x time. We know that the total driving time was 45 minutes. We can set up two equations using the given information:

10 = x ⋅ (45/60)

25 = (x + 10) ⋅ (45/60)

Simplifying the equations, we get:

x = 20 mph

x + 10 = 30 mph

Therefore, River's mom drove at speeds of 20 mph and 30 mph.

Answer:

(x^2-6)(x+2)(x-2)

Step-by-step explanation:

x^4-10x^2+24

(x^2-6)(x+2)(x-2)