There are some rabbits and some hutches. If eight rabbits are put in each hutch, one rabbit is left over. If eleven rabbits are put in each hutch, one hutch is left empty. How many rabbit hutches are there, and how many rabbits are there?

Answer:

30 times

Step-by-step explanation:

There's a 50% chance that they will get heads.

60 divided by 2 is 30

50% of 60 is 30

Answer:

We expect 30 heads.

Step-by-step explanation:

There are 2 sides  to a coin, heads and tails.  They are equally likely.  So the probably of getting a heads is 1/2

If we want to know how many times we will get heads, we multiply the number of flips by the probability of getting heads.

number of heads = 60 * 1/2

                              = 30

Answer: 19.04 divided by 5.6 is 3.4

Step-by-step explanation:

The interest earned is approximately $50.06.

To calculate the amount of interest earned in a simple interest problem, we can use the formula:

[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Time}}{\text{Total days in a year}} \][/tex]

Given:

- Principal (P) = $1,295

- Rate (R) = 7% or 0.07

- Time (T) = 180 days

- Total days in a year = 365 days

Plugging these values into the formula:

[tex]\[ \text{Interest} = 1295 \times 0.07 \times \frac{180}{365} \]\[ \text{Interest} = 1295 \times 0.07 \times \frac{180}{365} \]\[ \text{Interest} \approx 1295 \times 0.07 \times 0.493150685 \]\[ \text{Interest} \approx 50.05958904 \][/tex]

Answer:

70%

Step-by-step explanation:

We assume, that the number 550 is 100% - because it's the output value of the task.

We assume, that x is the value we are looking for.

If 100% equals 550, so we can write it down as 100%=550.

We know, that x% equals 385 of the output value, so we can write it down as x%=385.

Now we have two simple equations:

1) 100%=550

2) x%=385

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=550/385

Now we just have to solve the simple equation, and we will get the solution we are looking for.

Solution for 385 is what percent of 550

100%/x%=550/385

(100/x)*x=(550/385)*x       - we multiply both sides of the equation by x

100=1.4285714285714*x       - we divide both sides of the equation by (1.4285714285714) to get x

100/1.4285714285714=x

70=x

x=70

Answer:

15x^3+26x^2-3x+42

Step-by-step explanation:

The multiplication is 15x³ +26x² - 3x + 42.

Multiplication is the process of adding a number up to a given number.

The multiplication (3x + 7)(5x²-3x+6) is as shown:

(3x + 7)(5x²-3x+6)

= 15x³ - 9x² + 18x +35x²- 21x +42

= 15x³ +26x² - 3x + 42

Hence, the multiplication is 15x³ +26x² - 3x + 42.

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Answer:

The temperature yesterday was -6 because 7-13 is -6.

Step-by-step explanation:

Answer:

The yesterday’s temperature is 6°C below the zero degree Celsius or (-6) degree Celsius.

Step-by-step explanation:

The temperature today is 7 degrees Celsius. Yesterday was 13 degrees Celsius cooler. That the temperature is colder means that the temperature was lower than today's temperature. This means that to obtain the temperature on the previous day, 13°C must be subtracted from today's temperature.

yesterday’s temperature=today’s temperature-13°C

It is now possible to replace today's temperature with 7 ° C

yesterday’s temperature=7°C-13°C

Remember that to subtract two integers of a different sign (one positive and the other negative), as in this case, you must subtract their absolute values (that is, subtract 13-7 = 6), and the answer will have the same sign as the number with the highest absolute value (absolute value or module of any real number is the same number but with a positive sign). As in absolute value 13 is greater than 7, the answer to the subtraction will be negative

yesterday’s temperature=7°C-13°C

So, finally, the yesterday’s temperature is 6°C below the zero degree Celsius or (-6) degree Celsius.

Answer:

15/100

Step-by-step explanation:

If the the number as a decimal is in the hundredths place you put the number over 100

Answer:

Average cost per year = 400 + 180/x

Step-by-step explanation:

Using the formula y=mx+b

We know that b is the y intercept or  initial value.  That would be the start up costs

m is the slope on costs each time x increases, that would be 400 per year

Costs = 400x + 180

To find the average cost per year, we need to divide by x

Average cost per year = (400x + 180)/x

                        = 400 + 180/x

Answer:

answer to this question is f(x)  = (180 + 400x)/x

[tex]\dfrac{7x+42}{x^2+13x+42}=\dfrac{7(x+6)}{x^2+7x+6x+42}=\dfrac{7(x+6)}{x(x+7)+6(x+7)}\\\\=\dfrac{7(x+6)}{(x+7)(x+6)}=\boxed{\dfrac{7}{x+7}}[/tex]

Your answer should be 2(10x^3+21x^2+21) over X^2 2(10x^3+21x^2+21)/X^2 unless the / was a fraction symbol and not a division symbol then your answer would be 7 over x+7 7/x+7

Answer:

17.922

Step-by-step explanation:

first you plug it in

y=0.860(17) + 3.302

then u simplify

y=14.62+3.302

then add them

y=17.922

Answer:

17.922 inches long

Step-by-step explanation:

y=0.860x + 3.302

y= 0.860(17) + 3.302

y= 14.62 + 3.302

y=  17.922

Hope it helps!!

Step-by-step explanation:

Answer:

All geometric figures, shapes and solids can be named as a sets of surface regions and plane regions and they all lie in three dimensional spaces.

Step-by-step explanation:

Answer:

$2000 invested in first fund

$1500 invested in second fund

Step-by-step explanation:

An investor invested a total of ​$3,500 in two mutual funds.

Let x be the amount invested in first fund

first fund earned a 4​% profit (4%= 0.04)

So interest is 0.04x for first fund

Let x be the amount invested in first fund

first fund earned a 4​% profit (4%= 0.04)

So interest is 0.04x for first fund

Let y be the amount invested in second fund

second fund earned a =2​% profit (2%= 0.02)

So interest is 0.02y for second fund

An investor invested a total of ​$3,500 in two mutual funds.

So x+y = 3500----> equation 1

y= 3500-x

the​ investor's total profit was ​$110

0.04x + 0.02y = 110----> equation 2

Plug in 3500 -x for y

0.04x + 0.02(3500-x) = 110

0.04x + 70 - 0.02x = 110

0.02x + 70 = 110

Subtract 70 onboth sides

0.02x = 40

Divide both sides by 0.02

x= 2000

y= 3500-x

so y= 3500 - 2000 = 1500

$2000 invested in first fund

$1500 invested in second fund

Answer:

x = - 3, x = 2

Step-by-step explanation:

Since x = 1 is a zero then (x - 1) is a factor of the polynomial

dividing x³ - 7x + 6 ÷ (x - 1)

= (x - 1)(x² + x - 6)

= (x - 1)(x + 3)(x - 2)

equating (x + 3)(x - 2) = 0 gives the other zeros

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

Answer:

17-i

--------

29

Step-by-step explanation:

To simply fractions with complex numbers, we have to multiply by the complex conjugate of the denominator.

The denominator is 5+2i, so the complex conjuate is 5-2i

3+i         5-2i

------  * ---------------

5+2i     5-2i

Simplifying the numerator

(3+i) * (5-2i) = 3*5 + 5i -3*2i -2i^2 = 15 +5i -6i -2(-1) = 15-i+2 = 17-i

Simplifying the denominator

(5+2i) (5-2i) = 25 -10i + 10i -4i^2 = 25 -4(-1) = 29

17-i

--------

29

Answer:

- [tex]\frac{1}{29}[/tex] i + [tex]\frac{17}{29}[/tex]

Step-by-step explanation:

to simplify the fraction ewe require to rationalise the denominator.

This is done by multiplying the numerator/ denominator by the conjugate of the denominator.

the conjugate of 5 + 2i is 5 - 2i, hence

= [tex]\frac{(3+i)(5-2i)}{(5+2i)(5-2i)}[/tex]

= [tex]\frac{15-i-2i^2}{25-4i^2}[/tex]

[ i² = ([tex]\sqrt{-1}[/tex])² = - 1 ]

= [tex]\frac{-i+17}{29}[/tex] = - [tex]\frac{1}{29}[/tex] i + [tex]\frac{17}{29}[/tex]

Answer:

Multiply 1/4 ; dividing 4

Step-by-step explanation:

Note that in each number going from left to right, it decreases by dividing 4 each time (or multiplying 1/4)

8/4 = 2 ; 2/4 = 1/2 ; (1/2)/(4) = 1/8 ; etc.

(8)(1/4) = 2 ; (2)(1/4) = 1/2 ; etc.

~

Answer: 1/4

Step-by-step explanation:

Answer: 1.996666666666667

Step-by-step explanation:

3ounces divided by 5.99

Answer:If you round 5.99 it would be 6.00 and then dived 3 and 6.00 its going to be 1.5 because you have to split it up

Step-by-step explanation:

24 = 2 · 2 · 2 · 3

36 = 2 · 2 · 3 · 3

GCF(24, 36) = 2 · 2 · 3 = 12

24 = 12 · 2

36 = 12 ·3

24 + 36 = 12 × 2 + 12 × 3 = 12 × (2 + 3)

The result of factoring out the Greatest Common Factor (GCF) from the expression (24 + 36) is 12 × (2 + 3).

To factor out the Greatest Common Factor (GCF) from the expression (24 + 36), we first need to determine the largest number that divides evenly into both 24 and 36. The GCF of 24 and 36 is 12. We divide each term by the GCF to factor out it from the expression:

24 ÷ 12 = 2

36 ÷ 12 = 3

Thus the expression factored out by the GCF is 12 × (2 + 3).

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Hey there!

"Which quantity is proportional to [tex]\frac{35}{80}[/tex]?"

The easier way, I figured out how to solve  this particular problem is simplify the fraction to decimal

[tex]\frac{35}{80}[/tex] [tex]= 0.4375[/tex]

[tex]\boxed{Answer: \frac{21}{48} AND \frac{7}{16}}[/tex]

Good luck on  your assignment and enjoy your day!

~[tex]LoveYourselfFirst:)[/tex]

Answer:

3/5 no

14/36 no

26/52 no

21/48 yes

7/16 yes

Step-by-step explanation:

Answer:

b=2 or b=-2.5

Step-by-step explanation:

We solve absolute value equations the same as any other equation using inverse operations. However, the inverse operation for absolute value requires one special condition. Since absolute values change a number to a positive regardless if it has a negative sign, we have two possible answers. When we have the absolute value operation isolated, we will set it equal to both the negative and positive option.  

[tex]-10-|1+4b|=-19\\-10+10-|1+4b|=-19+10\\-|1+4b|=-9\\\frac{-|1+4b|}{-1} =\frac{-9}{-1} \\|1+4b|=9[/tex]

We now have the absolute value isolated. We will set it equal to both 9 and -9.

[tex]1+4b=9\\1-1+4b=9-1\\4b=8\\b=2[/tex]

and

[tex]1+4b=-9\\1-1+4b=-9-1\\4b=-10\\b=\frac{-10}{4}=\frac{-5}{2}=  -2.5[/tex]

Answer:

it's 1/3

Step-by-step explanation:

5/6+(-1/2)

5/6-1/2

LCM= 6

(5-3)/6

2/6

1/3

Answer:

sqrt(x)

Step-by-step explanation:

1/ ( x^(-3/6))

We can simplify the fraction

1/ ( x^(-1/2))

A negative exponent means that since it is in the denominator, it goes to the numerator.  It still keeps the exponent.

x^ (1/2)

sqrt(x)

Answer:

-96 or 96

Step-by-step explanation:

this is because the distance from zero is twelve, so it could be -12 or 12, plug both into the problem and then solve.

the absolute value |x| of a real number x is the non-negative value of x without regard to its sign.

|x| = x for x ≥ 0.

|x| = -x for x < 0.

Examples:

|2| = 2

|-5| = -(-5) = 5

If is -8 × |12| = -8 × 12 = -96

If is 8 × |12| = 8 × 12 = 96

Answer:

20% tip

Step-by-step explanation:

Dinner:  $48.00

Tax:  0.05($48.00) = $2.40

Total (final) bill before tip:  $50.40

Tip:  $10.08

Percentage tip was then $10.08 (100%) / $50.40 = 20%

The family left a 20% tip.

Answer:

49 inches

Step-by-step explanation:

Write and solve an equation of ratios, as follows:

7 inches               x

-------------- = -----------------

8 inches        56 inches

Then (8 ")x = (7 ")(56 "), and

x = 392/8 inches = 49 inches.

The actual width of the helicopter is 49 inches.

The actual width is found to be 49 inches, which corresponds to answer choice B.

The question is asking us to determine the actual width of a helicopter given its scale model dimensions and the actual length. To solve the problem, we use the concept of ratios or proportions. The scale model is 8 inches long and 7 inches wide, and the actual helicopter is 56 inches long.

We set up a proportion to find the actual width:

To solve for x, we cross multiply:

8 * x = 56 * 7

x = (56 * 7) / 8

x = 392 / 8

x = 49 inches

Therefore, the correct answer is B: 49 inches, which is the actual width of the real helicopter.

Answer:

0

Step-by-step explanation:

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

  = (-5--5)/ (9--8)

 = (-5+5)/(9+8)

 = 0/17

=0

The slope it 0

This is a horizontal line because the y value doesn't change.  If the y value doesn't change, the slope it zero.

Answer:

Point-Slope form: The equation of line is given by:

[tex]y-y_1=m(x-x_1)[/tex]              ......[1]

where m is the slope and [tex](x_1,y_1)[/tex] is the point on the line.

From the given graph:

Consider two points i.e,

[tex](0, 1)[/tex] and (-0.5, 0)

Calculate slope:

Formula for slope is given by;

[tex]\text{Slope}(m) = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given values we have;

[tex]m = \frac{0-1}{-0.5-0} = \frac{-1}{-0.5} = \frac{10}{5} =2[/tex]

Now, substitute the value of m = 2 and (0, 1) in equation [1] we have;

[tex]y-1 = 2(x-0)[/tex]

y-1 = 2x

Add 1 to both sides we get;

y = 2x+1

On comparing equation y = 2x+1 with the slope intercept form of a line (i.e, y = mx+b) then we have;

slope(m) = 2

y-intercept(b) = 1

therefore, the slope of the function:

m = 2

y-intercept(b) = 1

and the equation represents the graph: y = 2x+1

Answer:

2

1

y = 2x + 1

Step-by-step explanation:

Final answer:

The multiplication of (3.4x10²) and (2x10³) results in 6.8x10⁵ after multiplying the coefficients and adding the exponents. Therefore, the correct answer is option (B).

Explanation:

Considering, the question it has asked to solve the following arithmetic operation in scientific notation: (3.4x10²)x(2x10³).

To solve this the following steps can be used :

we multiply the coefficients (3.4 and 2) and then add the exponents (2 and 3).

Multiplication of coefficients: 3.4 * 2 = 6.8

Addition of exponents: 2 + 3 = 5

Combining both parts: 6.8 x 10^5

The correct answer in scientific notation is therefore 6.8x10⁵, which corresponds with option B.