Type this number in decimal form. (6×1000)+(2×100)+(1×10)+(7×1)+(8×110)+(5×1100)

In order to solve using substitution, we'll need to first isolate one variable in one equation. I will be using 7x - 2y = 3 and solving for y to begin.

7x - 2y = 3

-2y = -7x + 3

2y = 7x - 3

y = 3.5x - 1.5

Next, we'll plug in our value of y (found above) into the equation 3x + 4y = 11 and solve for x.

3x + 4(3.5x - 1.5) = 11

3x + 14x - 6 = 11

17x = 17

x = 1

Finally, we'll plug our value of x in to the first equation (7x - 2y = 3) and solve for y.

7(1) - 2y = 3

7 - 2y = 3

-2y = -4

y = 2

The solution to these equations is (1, 2).

Hope this helps! :)

Answer:

Daily: $5,389.41

Monthly: $5,389.00

Semi-annually: $5,386.92

Annually:$5,384.45

Step-by-step explanation:

Answer:

The volume of a cone that fits perfectly inside the soda can is 7.

Volume of a can:

21 = r² π h

21 = 3² π h

21 = 9 π h

h = 21/ 9π = 7/ 3π 

Volume of a cone that fits perfectly inside a can:

V = 1/3 r² π h = 1/3 · 9 π · 7 / 3π = 7

Or you can use: V cone = 1/3 V cylinder ( with the same basis )

V cone = 1/3 * 21 = 7

Step-by-step explanation:

Since we have given that

Volume of soda can = 21

Diameter of can = 6

As we know the formula for "Volume of cylinder:"

Now, we have to find the volume of a cone that fits perfectly inside the soda can.

so, its radius will be 3 cm and height will be

As we know the formula for "Volume of cone":

Hence, the volume of a cone that fits perfectly inside the soda can is 7.

60% of 94 is calculated by multiplying 94 by 0.60, which results in 56.4.

To find 60% of 94, you will multiply 94 by 0.60. Performing this calculation:

60% of 94 = 0.60 * 94

0.60 * 94 = 56.4

So, 60% of 94 equals 56.4.

There are 45 oranges and 90 apples in the beginning.

Step-by-step explanation:

Let the no. of orange be 'b'

Let the no. of apples be 'a'

Given that,

2b = a

3(b-15) = a

3b - 45 = a

3b - 45 = 2b

3b - 2b = 45

b = 45

2b = a

2(45) = a

a = 90

There are 45 oranges and 90 apples in the beginning.

Answer:

154 millimeters

Step-by-step explanation:

Answer:

154

Step-by-step explanation:

Plato test said i was right

Answer:

answer is c

Step-by-step explanation:

Formula: h=2A/b1+b2

95(2)/(7+12)=h

190/19=h

10m=h

answer is c

Explanation:

If the data wasn't sorted, then the first step would be to arrange the elements from smallest to largest. However, that is already done for us.

The middle most value in the set {15, 19, 20, 25, 31, 38, 41} is 25 because there are three values below it {15,19,20} and three values above it {31,38,41}

Focus on the lower half {15,19,20} and note the middle of this subset is element 19. This is the value of Q1 or the first quartile.

The third quartile Q3 is 38 because the middle of the upper half data set {31,38,41} is 38.

We now subtract the values of Q3 = 38 and Q1 = 19 to get the interquartile range (IQR)

IQR = Q3 - Q1 = 38 - 19 = 19

Answer:

19

Step-by-step explanation:

Hope this helps and I got it right on the quiz on edge

Answer:

The equation of the line is y = 3 x - 5.

Step-by-step explanation:

The slope intercept form of the equation of a straight line is:

[tex]y=mx + b[/tex]

Here,

m = slope

b = intercept.

The two points are:

A = (2, 1)

B = (3, 4)

Use two-point form method to determine the equation of straight line.

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

 [tex](y-1)=\frac{4-1}{3-2}\ (x-2)[/tex]

    [tex]y-1=3(x-2)\\y-1=3x-6[/tex]

          [tex]y=3x-5[/tex]

Thus, the equation of the line is y = 3 x - 5.

The equation of the line in slope-intercept form is y = 3x - 5.

To find the equation of the line containing the points (2, 1) and (3, 4) in slope-intercept form (y = mx + b), you first need to determine the slope (m) and then use one of the points to solve for the y-intercept (b).

The slope (m) can be found using the formula:

m = (y2 - y1) / (x2 - x1)

Let's plug in the coordinates of the two points:

Point 1: (x1, y1) = (2, 1)

Point 2: (x2, y2) = (3, 4)

Now, calculate the slope (m):

m = (4 - 1) / (3 - 2)

m = 3 / 1

m = 3

Now that you have the slope (m), you can use one of the points, for example, (2, 1), and the slope to find the y-intercept (b). You can use the point-slope form of the equation:

y - y1 = m(x - x1)

Using the point (2, 1):

y - 1 = 3(x - 2)

Now, distribute the 3 on the right side:

y - 1 = 3x - 6

Next, add 1 to both sides to isolate y:

y = 3x - 6 + 1

Simplify:

y = 3x - 5

for such more question on slope-intercept form

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Answer:

8,760

Step-by-step explanation:

If Kaylah is reading 142 words in one minute, there is 60 minutes in an hour.

therefore,

142 x 60 = 8,760

Answer:

8520 minutes

Step-by-step explanation:

To solve, make a proportion

142 words in 1 minute, and x words in 60 minutes (1 hour).

142/1=x/60

Cross multiply

142*60=1*x

8520=x

Another way to solve is to know that each hour has 60 minutes, and she can read 142 words in 1 minute. So, we can just multiply 60 and 142.

60*142=8520

Answer:

1/3

Step-by-step explanation:

Answer:

13.5 mi/h

Step-by-step explanation:

The average speed of the car can be written as

[tex]v=\frac{d}{t}[/tex]

where

d = 4.8 miles is the total distance covered

[tex]t=6\cdot (8 min) = 48 min \cdot \frac{1}{60}=0.8 h[/tex] is the  time elapsed

So the average speed is

[tex]d=\frac{4.8}{0.8}=6 mi/h[/tex]

We also know that the total time consists of 6 8-minutes interval, and the speed of the car decreased by 3 mi/h each interval.

Calling [tex]v_1[/tex] the average speed in the 1st interval, we have:

[tex]v_2=v_1-3\\v_3=v_1-6\\v_4=v_1-9\\v_5=v_1-12\\v_6=v_1-15[/tex]

The average speed in each interval can be written as [tex]v_i=\frac{d_i}{t}[/tex], where [tex]d_i[/tex] is the distance covered in each interval and [tex]d_i = 8 min =0.133 h[/tex] is the duration of each interval, so we can write

[tex]\frac{d_2}{t}=\frac{d_1}{t} -3 \rightarrow d_2 = d_1 -3t[/tex]

And similarly,

[tex]d_3=d_1-6t\\d_4=d_1-9t\\d_5=d_1-12t\\d_6=d_1-15t[/tex]

Since the total distance is [tex]d=d_1+d_2+d_3+d_4+d_5+d_6[/tex], we have:

[tex]d=6d_1 - 3t-6t-9t-12t-15t=6d_1-45t[/tex]

And since we know that

d = 4.8 miles

and t = 0.133h, we can find d1:

[tex]d_1=\frac{d+45t}{6}=\frac{4.8+(45)(0.133)}{6}=1.8 mi[/tex]

So the average speed in the first 8-minute interval is:

[tex]v_1=\frac{d_1}{t_1}=\frac{1.8}{0.133}=13.5 mi/h[/tex]

Answer:

[tex]=81[/tex]

Step-by-step explanation:

[tex]\left(-3\right)^4[/tex]

Use exponent rule [tex]\left(-a\right)^n=a^n[/tex]:

[tex]=3^4[/tex]

[tex]=81[/tex]

Answer:

[tex] Standard \: form :\:y= {x}^{2} - 4x - 5\\

Factored\: from:\:y = (x + 1) (x - 5)[/tex]

Step-by-step explanation:

[tex]y = (x - 2)^{2} - 9 \\ y= {x}^{2} - 4x + 4 - 9 \\ \red{ \boxed{ \bold{y= {x}^{2} - 4x - 5}}} \\ is \: in \: standard \: form \\ \\ y = (x - 2)^{2} - 9 \\ y = (x - 2)^{2} - {3}^{2} \\ y = \{(x - 2) + 3\} \{(x - 2) - 3 \} \\ y = \{x - 2 + 3\} \{x - 2- 3 \} \\ \purple{ \boxed{ \bold{y = (x + 1) (x - 5)}}} \\ is \: in \: factored \: form[/tex]

Answer:

Large - 24

Small - 15

Step-by-step explanation:

Answer:

7x7x7x7x7

    7x7

Step-by-step explanation:

7 to the fifth power is equal to 7x7x7x7x7

7 to the second power is equal to 7x7

Answer:

D, (7 x 7 x 7 x 7 x 7) / (7 x 7)

Step-by-step explanation:

Look at the numerator of the fraction. You will see 7^5, or 7 to the 5th power. This means you must multiply 7 by itself 4 times, to get yourself the numerator of 7 x 7 x 7 x 7 x 7. This means your choices are B (or the second option from the top) or D (or the last option from the top).

However, take note that your original equation is a fraction, meaning you would divide, and not multiply. This means B, or the second option, is incorrect, because they are multiplying in that expression, when a fraction means to divide.

Your only other option is D, where they have portrayed both 7 to the fifth correctly in the numerator, and then 7 squared in the denominator.

Answer:

7

Step-by-step explanation:

it is the 7th figure

Answer:

⅓

Step-by-step explanation:

For two perpendicular lines,

m1 × m2 = -1

-3 × m2 = -1

m2 = -1/-3

m2 = 1/3

Answer:

Lily babysit for less than 4 hours.

Step-by-step explanation:

Given:

Lucy spends in a week babysitting for 4 hours.

Lily spends seven-eighths of 4 hours.

Now, to find whether Lily babysit for more than 4 hours or less than that.

Number of hours Lucy babysit = 4 hours.

So, to get the hours Lily babysit:

[tex]\frac{7}{8}\ of\ 4\ hours.[/tex]

[tex]=\frac{7}{8}\times 4\\\\=\frac{28}{8} \\\\[/tex]

On simplifying we get:

[tex]=\frac{7}{2} \\\\=3\frac{1}{2}\ hours.[/tex]

Thus, Lily spends [tex]3\frac{1}{2}\ hours[/tex]  for babysitting which is less than 4 hours.

Therefore, Lily babysit for less than 4 hours.

Lily babysits for 3.5 hours weekly, which is less than Lucy's 4 hours of babysitting.

Lucy spends 4 hours a week babysitting, and Lily spends seven eighths as much time babysitting. To calculate how much time Lily spends, we multiply Lucy's hours by seven eighths:

4 hours × (7/8) = 28/8 hours = 3.5 hours.

So, Lily babysits for 3.5 hours a week, which is less than 4 hours.

Answer:

1 and 2/15

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

It is 18 because 14 x 2 equal 28 so that would mean you need one stick to make 2 pizzas. Then you divide 36 by 2 and get 18

Pat needs 18 sticks of pepperoni to make 36 pizzas

The unitary method is a method in which you find the value of a unit and then the value of a required number of units

According to the problem,

Using unitary method,

To make 28 pizzas Pat needs 14 sticks of pepperoni.

∴ To make 1 pizza, Pat need  [tex]\frac{14}{28}[/tex] sticks of pepperoni

∴ To make 36 pizzas, Pat needs [tex]\frac{(14)(36)}{28}[/tex]  sticks = 18 sticks of pepperoni

So, Pat needs 18 sticks of pepperoni to make 36 pizzas

Find more about "Unitary Method Problems" here: https://brainly.com/question/24587372

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Answer:$253

Step-by-step explanation: A=220(1+(0.05*3))=253

Answer:

FIRST FOUR (4) TERM = 6, 18, 54,162.

COMMON RATIO = 3

Step-by-step explanation:

In geometric expression.

Tn = the nth term

a = first term

r = common ratio.

Let's take the First term of the G.P as 6 and the third term as 54. Let's find the common ratio.

3rd term will be written as:

T3 = ar² = 54

Given the first term as 6.

T3 = 6r² = 54

6r² = 54

r² = 54 / 6

r² = 9

r= √9

r = 3

Therefore common ratio = 3.

Let's use this information to get the fourth term.

T4 = ar³

when a = 6

and r = 3.

T4 = 6 * 3³

T4 = 6 * 27

T4 = 162

The first four terms of the geometric sequence are [tex]\(a_1 = 5\), \(a_2 = 15\), \(a_3 = 45\), and \(a_4 = 135\).[/tex]  The common ratio is r= 3 and the rule for the nth term is [tex]\(a_n = 5 \cdot 3^{(n-1)}\).[/tex]

To find the common ratio r of a geometric sequence, one divides a term in the sequence by the previous term.

Given the first four terms as [tex]\(a_1 = 5\), \(a_2 = 15\), \(a_3 = 45\), and \(a_4 = 135\),[/tex] we can calculate the common ratio using the first two terms:

[tex]\[ r = \frac{a_2}{a_1} = \frac{15}{5} = 3 \][/tex]

We can verify this by calculating the ratio of the third term to the second term:

[tex]\[ r = \frac{a_3}{a_2} = \frac{45}{15} = 3 \][/tex]

And again with the fourth term and the third term:

[tex]\[ r = \frac{a_4}{a_3} = \frac{135}{45} = 3 \][/tex]

Since the ratio is consistent across these terms, we can confirm that the common ratio r is indeed 3.

The rule for the nth term of a geometric sequence is given by:

[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]

[tex]\[ a_n = 5 \cdot 3^{(n-1)} \][/tex]

This is the rule for the nth term of the given geometric sequence.

Answer:

B) 65°

Step-by-step explanation:

The formula for this would be x = 1/2 (a -b)

X being the angle you're trying to find

a being the larger arc and b being the smaller arc

Since a circle has 360°, and 245 is the larger arc, the smaller arc would be 115°

Now, just plug that into the equation; x = 1/2 (245-115)

This gives you x = 1/2 (130)

x = 65°

Answer:

The answer is x= 7 good luck though. also what you want to do it get the x's together and also get rid of the 42

Answer:160

Step-by-step explanation:

4*4=16

16+16=32

8*4=32

32*4=128

128+32=160

Answer:

T is 13.9 years to the nearest 10th of a year

Step-by-step explanation:

In this question, we are to calculate the number of years at which someone who invests a particular amount will have a particular amount based on compound interest.

To calculate the number of years, what we do is to use the compound interest formula.

Mathematically,

A = P(1+ r/n) ^nt

Where A is the final amount after compounding all interests which is $19,200 according to the question

P is the initial amount invested which is $10,000 according to the question

r is the rate which is 4.75% according to the question = 4.75/100 = 0.0475

n is the number of times per year in which interest is compounded. This is 2 as interest is compounded semi-annually

t= ?

we plug these values;

19200 = 10,000(1+0.0475/2)^2t

divide through by 10,000

1.92 = (1+0.02375)^2t

1.92 = (1.02375)^2t

We find the log of both sides

log 1.92 = log [(1.02375)^2t)

log 1.92 = 2tlog 1.02375

2t = log 1.92/log 1.02375

2t = 27.79

t = 27.79/2

t = 13.89 years

The question asks to give answer to the nearest tenth of a year and thus t = 13.9 years

Answer:

20% or 1/5

Step-by-step explanation:

20% is equal to 1/5. That means that out of 5 marbles, there is only 1 red one.