The numerator of a fraction is 5 less than its denominator. If 1 is added to the numerator and to the denominator, the new fraction is \(\frac{2}{3\\}\) Find the fraction.

Solution:

Step 1:

Factor out the common term

The common term is 3x

By doing this, we will have

Step 2:

Factorise the quadratic expression in the bracket

By doing this, we will have to look for two factors to multiply to give i4 and if we add them together, we will have -3

The two factors are -4 and +1

therefore,

Replace -3x with -4x + x

Hence,

The final answer is = (x-4)

Answer:

Graph?

Step-by-step explanation:

Answer:

Step-by-step explanation: I need help now pls

Answer:

50

Step-by-step explanation:

\text{SOH-CAH-TOA}

SOH-CAH-TOA

\cos D = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{59}{91}

cosD=

hypotenuse

adjacent

​

=

91

59

​

\cos D = \frac{59}{91}

cosD=

91

59

​

D=\cos^{-1}(\frac{59}{91})

D=cos

−1

(

91

59

​

)

D=49.583\approx 50^{\circ}

D=49.583≈50

∘

Type into calculator and round to the nearest degree.

D

E

F

59

91

(adjacent to ∠D)

Explanation:

The given system of equations is

(4/5)x + 6y = 15

-x + 18y = 11

To solve the system, we will use the substitution method, so first, we need to solve the second equation for x

-x + 18y = 11

-x + 18y - 18y = 11 - 18y

-x = 11 - 18y

-x(-1) = 11(-1) - 18y(-1)

x = -11 + 18y

Now, we can replace x = -11 + 18y on the first equation

(4/5)x + 6y = 15

(4/5)(-11 + 18y) + 6y = 15

(4/5)(-11) + (4/5)(18y) + 6y = 15

-8.8 + 14.4y + 6y = 15

-8.8 + 20.4y = 15

Then, solve the equation for y

-8.8 + 20.4y + 8.8 = 15 + 8.8

20.4y = 23.8

20.4y/20.4 = 23.8/20.4

y = 7/6

Finally, we can find the value of x as follows

x = -11 + 18y

x = -11 + 18(7/6)

x = -11 + 21

x = 10

So, the solution to the system is x = 10 and y = 7/6

Answer:

The  confidence interval is  \(-11.34 < \mu_1 -\mu_2 < -10.86\)

Step-by-step explanation:

From the question we are told that

    The first sample size is  \(n_1 = 146\)

    The second sample size is \(n_2 = 180\)

    The first sample mean is \(\= x_1 = 51.6\)

    The second  sample  mean is  \(\= x_2 = 62.7\)

     The first standard deviation is  \(\sigma _1 = 9.42\)

     The second standard deviation is  \(\sigma _2 = 14.5\)

Given that the confidence level is  98% then the significance level is mathematically evaluated as

      \(\alpha = (100 -98 )\%\)

       \(\alpha = 2 \%\)

        \(\alpha = 0.02\)

Next we obtain the critical value of  \(\frac{\alpha }{2}\) from the z-table , the value is  \(Z_{\frac{\alpha }{2} } = 2.33\)

The reason we are obtaining critical value of  

 \(\frac{\alpha }{2}\)

instead of  

\(\alpha\)

is because  

 \(\alpha\)

represents the area under the normal curve where the confidence level interval (

\(1-\alpha\)

) did not cover which include both the left and right tail while  

 \(\frac{\alpha }{2}\)

is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

      \(E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\sigma_1^2}{n_1^2} + \frac{\sigma_2^2}{n_2^2} }\)

substituting values

      \(E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }\)

substituting values

     \(E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }\)

     \(E = 0.2405\)

The 98% confidence interval is mathematically represented as

      \((\= x _ 1 - \= x_2 ) - E < \mu_1 -\mu_2 < (\= x _ 1 - \= x_2 ) + E\)

substituting values

      \((51.6 - 62.7) - 0.2405 < \mu_1 -\mu_2 < (51.6 - 62.7) + 0.2405\)

     \(-11.34 < \mu_1 -\mu_2 < -10.86\)

Answer:

2508

Step-by-step explanation:

28.5% of 8800 is 2508.

so at the end of the year she had a total of 11308.

The city which had more noon temperatures above 76°F is City A.

The city which had noon temperatures with a larger interquartile range (IQR) is that: both had the same number.

The city which had a larger median noon temperature is City B.

The city which had the highest noon temperature is City A.

IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.

Mathematically, interquartile range (IQR) is the difference between first quartile (Q₁) and third quartile (Q₃):

IQR = Q₃ - Q₁

Based on the given box and whisker plot, we can logically deduce the following quartile ranges for City A:

Third quartile, Q₃ = 75

First quartile, Q₁ = 68

Now, we can calculate the interquartile range (IQR) for City A:

Interquartile range, IQR = Q₃ - Q₁

Interquartile range, IQR = 75 - 68

Interquartile range, IQR = 7

For City B, we have:

Interquartile range, IQR = Q₃ - Q₁

Interquartile range, IQR = 80 - 73

Interquartile range, IQR = 7

For the median, which is the middle number (50%), we have:

Median of City A = 70.

Median of City B = 78.

Therefore, City B had a larger median noon temperature while City A had the highest noon temperature of 85°F.

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Answer:

  17 bars

Step-by-step explanation:

Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.

The error in a rounded number is assumed to be as much as half of the least significant digit of the number.

Peter's load limit may actually be as low as ...

  1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100

Peter's bar weight might be as high as ...

  60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10

If Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...

  (1150 kg) / (65 kg/bar) ≈ 17.7 bars

The greatest number of bars Peter can load safely is 17.

Answer:

…, −3.5, −2.5, −1.5, 0, 1.5, 2.5, 3.5, …

Step-by-step explanation:

0, 1, 2, 3, 4, …

…, −4, −3, −2, −1, 0

…, −3, −2, −1, 0, 1, 2, 3, …

…, −3.5, −2.5, −1.5, 0, 1.5, 2.5, 3.5, …

Answer: 15.6

Step-by-step explanation:

In 15.56, the digit in the tenths place is the second 5. 15.56. So look at the hundredths place (6). If the digit in the hundredths place is smaller than 5, round down. If it's 5 or more, round up. 6 > 5, so we round the tenths place up by one number to get 15.6.

Answer:

Larger number = 21.5

Step-by-step explanation:

One number = x

Larger number = x + 2

x + x +2 = 41

2x + 2 = 41

       2x = 41 - 2

       2x = 39

         x = 39/2

         x = 19.5

Larger number = x + 2

                        = 19.5 +2

                        = 21.5

The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say that number is x,

Quotients of 20 and x will be given as 20/x

20/x - 4 = 0

20/x = 4

x = 20/4 = 5

Hence"The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5".

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Answer:

x = 5

Step-by-step explanation:

We know that AB = 2x - 3 and AB = 7, therefore:

2x - 3 = 7

2x - 3 + 3 = 7 + 3

2x = 10

2x / 2 = 10 / 2

x = 5

Answer: 8 units.

Step-by-step explanation:

Split apart the figure into two sets, starting from the y value of 2. The part of the shape in Quadrant one has a area of 2, and the same on the other side giving us a area of 4.

Under it, we have 2 other halves of a unit, meaning we now have 1 unit, and adding the other three we have 4 units, giving us a total of 8 units.

The solution for the system of equation is (8, 1), Hence the correct option is c.

The given system of equations is:

–3x + 2y = –22

–5y = –4x + 27

We can solve for x and y using elimination method:

–3x + 2y = –22

⇒ -3x + 2y = -22

–5y = –4x + 27

⇒  –4x + –5y = - 27

Eliminate x,

-3x + 2y = -22

-4x  - 5y = -27

That is

-12x + 8y = -88

-12x - 15y = −81

0  −7y = −7

or

-7y = -7

y = 7/7

y = 1

Solve for x by substituting the value of y in –3x + 2y = –22

–3x + 2(1) = –22

–3x + 2 = –22

–3x  = –22 - 2

–3x  = −24

x = 24/3

x = 8

Thus, The solution for the system of equation is (8, 1), Hence the correct option is c.

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Complete question:

Select the statement that correctly describes the solution to this system of equations.

–3x + 2y = –22

–5y = –4x + 27

A

There is no solution.

B

There are infinitely many solutions.

C

There is exactly one solution at (8, 1).

D

There is exactly one solution at (1, 8)

Answer: I think it would have to be c) Sublimation

Answer:

-0.25 units

Step-by-step explanation:

144x^2 - 72x + 9 = 0

common factor: 9

16x^2 - 8x + 1 = 0

(4x + 1)^2 = 0

4x +1 = 0

4x = -1

x = -0.25 units

Answer:

60

Step-by-step explanation:

\(a+b+c=180\\\frac{b+c}{2}=a \rightarrow b+c=2a\\\\a+2a=180\\3a=180\\a=60\)

Therefore, the value of a is 60 degrees

Answer:

-0.4k + 14

Step-by-step explanation:

hope that helped!

The Length of the rectangle is: B. 6 2/3.

The area of a rectangle is calculated as: Area = (length)(width). Therefore, if we known the area of a rectangle and its width, we can find the length of the rectangle using:

Length of rectangle = area of rectangle / width of rectangle.

Given the following:

Area of a rectangle = 21 and 2 over 3 square inches

Width = 3 and 1 over 4 inches

Length of the rectangle = 21 2/3 ÷ 3 1/4

Length of the rectangle = 65/3 ÷ 13/4

Length of the rectangle = 65/3 × 4/13

Length of the rectangle = 260/39 = 6 2/3.

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Answer:

550

Step-by-step explanation:

Srry if im wrong but if im right will you consider giving me brainly

Hope it helps

:D

Answer:

thx for free poins

Step-by-step explanation:

Answer:

3645

Step-by-step explanation:

The odd one is \(3645\).

Let the given numbers are,

 \(3861,8712,5247,4356,1485,3645\)

The given numbers are divisible by \(99\) except \(3645\).

Now,      

The number \(3681\) is divisible by \(99\).  

The number \(8732\) is divisible by \(99\).  

The number \(8732\) is divisible by \(99\).  

The number \(4356\) is divisible by \(99\).  

The number \(1485\) is divisible by \(99\).  

The number \(3645\) is  not divisible by \(99\).  

Hence, the odd number is \(3645\).

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The total cost of chocolate sprinkles is $800

This is an implementation of the numeral system that shows the value of each digit in a number using their positions

From the complete question, we have the following parameters:

So, the total cost of chocolate sprinkles is calculated using the following formula

\(Unit = \frac{Total}{Pounds}\)

This gives

\(\$8.00= \frac{Total}{100}\)

Multiply both sides of the equations by 100

\(Total = \$8.00 \times 100\)

\(Total = \$800\)

Hence, the total cost of chocolate sprinkles is $800

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There will be no change in the price of the car.

A number line is a representation of a graduated straight line used to abstract real numbers in elementary mathematics. Its points are considered to correspond to real numbers and vice versa.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Let the sticker price = x, Price reduced by $300

Hence the new price is,

N= x-$300

The cost of additional features = $900

Hence the new price for selling will be.

=x-$300+$900

=x+$600

Dealer also provides a discount of $600

Hence Final  selling price will be

=x+$600-$600

Hence there seems to be no change in the sticker price as the sticker price and the final selling price are the same.

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Answer:

x = 360 - 49 - 136 - 69 = 106°

Answer:

  2c -7 = 31

Step-by-step explanation:

You want an equation for the points Carlos scored, given that Fabio scored 31 points, which was 7 less than 2 times Carlos's score.

We are told to represent the points Carlos scored using the variable c. Double Carlos's score is then 2c, and 7 points less is 2c-7. The is said to be the amount of Fabio's score, which is also given as 31. Equating these two descriptions of Fabio's score gives the equation ...

  2c -7 = 31

Answer:

  \(a=\dfrac{\Delta v}{t}\)

Step-by-step explanation:

Acceleration is the change in velocity per unit time. It is usually represented by the letter "a". An appropriate formula is ...

  \(\boxed{a=\dfrac{\Delta v}{t}}\)

The required equation for determining the acceleration from a velocity-time graph is \(a=\dfrac{\Delta v}{t}\)equation is a=delta v over t.

We know that,

Acceleration is known as the rate of change of velocity per unit time.

The velocity vs time graph is the graph plotted between the change in velocity with the change in time.

\(a=\dfrac{\Delta v}{t}\)

Hence the required equation for determining the acceleration from a velocity-time graph is \(a=\dfrac{\Delta v}{t}\).

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Answer:

-1  2/3

Step-by-step explanation:

The probability that a randomly selected female is taller than 67 inches is 0.8133, or approximately 81%.

To calculate this probability, we need to standardize the height of 67 inches using the formula:

z = (x - mu) / sigma

where x is the height we're interested in, mu is the mean, and sigma is the standard deviation.

z = (67 - 64.5) / 2.8 = 0.8929.

Then, we can look up the area to the right of z = 0.8929 in the standard normal distribution table, which is 0.1867.

Finally, we subtract this value from 1 to get the probability that a randomly selected female is taller than 67 inches:

P(X > 67) = 1 - 0.1867

P(X > 67) = 0.8133

So, the probability that a randomly selected female is taller than 67 inches is 0.8133, or approximately 81%.

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