The sum of two positive integers is 67. When the smaller integer is subtracted from twice the larger, the result is 38. Find the two integers.

The number two is a function

First rule of function: for each element of A there is one and only one element of B

For example, in the first one -5 is "collegated" to -2 and 3. So this isn't a function.

Naturally,  every element of B can have more element of A

Answer:

7.00864

Step-by-step explanation:

The upper control limit for R -chart can be computed by using following formula

UCL=Rbar*D4.

We are given that average range R bar is

Rbar=3.76.

The value of D4 for n=8 is also given that is

D4=1.864.

Thus, the required computed upper control limit is

UCL=3.76*1.864=7.00864.

9514 1404 393

Answer:

Step-by-step explanation:

Their age total is 15+10=25, so Ram will get 15/25 = 0.6 of the total. Kalpana will get the remaining 0.4 of the total.

  Ram receives 0.6 × ₹2000 = ₹1200

  Kalpana receives 0.4 × ₹2000 = ₹800

Answer:

-3

Step-by-step explanation:

[tex]8+3y = -1\\3y = -9\\y = -3[/tex]

Answer:

y = -3

Step-by-step explanation:

-1=3y+8

3y+8=-1

3y=-9

y=-3

Answer:

50%

Step-by-step explanation:

Girls                                            Boys

total:                 59                     total:                              41

- Chemistry       35                   - Physics                           2

                       = 24                                    =                     39

                                                 - Chemistry ( 30 - 6 )      24

                                                                   =                     15

Total boys and girls for Biology = 35 + 15 = 50

% = 50/100*100

   = 50%

Answer:

Yes you can

Step-by-step explanation:

To eliminate the denominator

Answer:

No

Step-by-step explanation:

We cannot be certain that x + 3 > 0

If it was negative then the sign of the inequality would change.

To solve find the critical values of the numerator/ denominator, that is

x = 2 and x = - 3

The domain is the split into 3 intervals

(- ∞, - 3 ), (- 3, 2), (2, + ∞ )

Use test points from each interval to determine valid solution

Answer:

See below.

Step-by-step explanation:

The degree is simply the number of the exponent (or the sum) and the coefficient is simply the number in front of the term.

First Term: -7; Deg=0, Co=-7.

-7 is the same as saying -7x^0. Thus, the degree is 0.

Second Term: -x^4; Deg=4, Co=-1

-x^4 is the same as saying -1(x^4). Thus, the degree is 4 while the coefficient is -1.

Third Term: -5x^3; Deg=3, Co=-5

Again, this is the same as saying -5(x^3). Thus, the degree is 3 while the coefficient is -1.

Fourth Term: 7x; Deg=1, Co=7

7x is the same as saying 7x^1. Thus, the degree is 1 while the coefficient is 7.

Fifth Term: x^2; Deg=2, Co=2

x^2 is the same as 1(x^2). Thus, the degree is 2 while the coefficient is 1.

The leading coefficient is the first coefficient when the polynomial is placed in descending order based on degree number. First, arrange the polynomial into descending order based on the degree:

[tex]-x^4-5x^3+x^2+7x-7[/tex]

Thus, the leading coefficient is -1 (belonging to the x^4).

The degree of the leading term will always be the highest. In this case, it is 4.

The degree of the polynomial is the highest degree. In this case, it is 4.

Answer:

3800 meters

Step-by-step explanation:

(i) False. If two lines are parallel, then they never intersect.

(ii) True. We can draw infinitely many different lines through a single point. We can think of rotating a line around a single point to form a circular fan of lines.

(iii) True. Any line is defined uniquely by two distinct points.

Answer:

[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]

Step-by-step explanation:

([tex]a^{8}[/tex]) * [tex]\frac{3}{2}[/tex]

Remove the parenthesis by multiplying

[tex]\frac{3}{2}[/tex][tex]a^{8}[/tex]

This expression cannot be simplified further

[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]

Hope this helps :)

Answer:

1300 and 700 respectively.

Step-by-step explanation:

Let x be invested in first account and y be invested in second account.

ATQ, x+y=2000 and 101=(4)*x/100+7*y/100. Solving it will give us x=1300 and y=700

Answer: 45

Step-by-step explanation: The range is the difference between the greatest number in the data set and the least number in the data set which in this case is 99 - 54 or 45. So the range of this data set is 45.

Answer:

Step-by-step explanation:

Given data:

83 , 71 , 62 , 86 , 90 , 95 , 61 , 60 , 87 , 72 , 95 , 74 , 82 , 54 , 99 , 62 , 78 , 76 , 84 , 92

largest value = 99

Smallest value = 54

Let's find the range:

Range = Largest value - smallest value

= 99 - 54

= 45

Extra information:

Range

It is the simple method of measuring the variations. A range is defined as the difference between the largest and the smallest value of distribution. If the data are arranged in ascending or descending order, then the difference between the largest and smallest value is called the range.

The range is defined by

Range = Largest value - smallest value i.e ( highest value - lowest value )

= L - S

Range is the absolute measure of dispersion = L - S

Thus, if a₁ , a₂ , a₃ ...............aₙ are n term in a sequence arranged in ascending order, the range is given by

R = aₙ - a₁ where a₁ is the smallest value and aₙ is the highest value or R = L - S , where L is the largest value and S is the smallest value.

Hope I helped!

Best regards!

Answer:

a line that cuts a segment into two pieces of equal length.

Answer:

Step-by-step explanation:

eq. of directrix is y=4 or y-4=0

perpendicular distance of (x,y) from directrix =distance of (x,y) from focus (-3,2)

[tex]| \frac{y-4}{1}|=\sqrt{(x+3)^2+(y-2)^2} \\squaring~both~sides\\y^2-8y+16=(x+3)^2+(y-2)2\\(x+3)^2=y^2-8y+16-(y-2)^2\\(x+3)^2=y^2-8y+16-(y^2-4y+4)\\(x+3)^2=y^2-8y+16-y^2+4y-4\\(x+3)^2=-4y+12\\(x+3)^2=-4(y-3)[/tex]

Answer:

cos F = adjacent/hypotenuse

= 15/28

Answer: 9/2

Step-by-step explanation: Find explanation in the attached file

Answer:

316.08 inches

Step-by-step explanation:

There are 3 feet in a yard, and there is 12 inches in 1 foot, so there are 36 inches in one yard. If there is 8 7/9 yards it is the same at 8.78 yards, and  8.78 x 36 = 316.08 inches. Therefore 8 7/9 yards = 316.08 inches.

let each box length be 1

for white triangle

area = ½bh

=½(4)(2)

=4

for orange triangle

area=½(2)(3)

=3

for blue marked boxes

each of the box

area=l²

=(1)²

=1

there are 16 boxes

so the total area will be 16

total area of the hexagon = 4+3+16

=23 square units

[tex]A_1=\dfrac{1}{2}(3+5)\cdot 3=12\\A_2=1\cdot5=5\\A_3=\dfrac{1}{2}(5+1)\cdot 2=6[/tex]

So the area of the whole shape is [tex]12+5+6=23[/tex]

Answer:

(9,-2)

Step-by-step explanation:

5 is the x coordinate, and 4 is the y coordinate. When you go right a certain amount of units, you add those units to your x coordinate. If you were to go left a certain amount of units, you'd subtract them. Since we're going right, 5 + 4 = 9. When you go up a certain amount of units, you add those units to you y coordinate. If you were to go down a certain amount of units, you'd subtract them.  Since we're going up, -6 + 4 = -2. So, x = 9 and y = -2, or (9,-2)

Answer and Step-by-step explanation:

Suppose that we have a number y which is a positive integer and that:

y = [tex]x_n...x_5x_4x_3x_2x_1x_0[/tex]

Where;

[tex]x_{0}[/tex] = digit at 10⁰ => one's place (units place)

[tex]x_1[/tex] = digit at 10¹ => 10's place (tens place)

[tex]x_{2}[/tex] = digit at 10² => 100's place (hundreds place)

[tex]x_{3}[/tex] = digit at 10³ => 1000's place (thousands place)

.

.

.

[tex]x_{n}[/tex] = digit at 10ⁿ place

Then;

y = [tex]x_{0}[/tex] * 10⁰ + [tex]x_1[/tex] * 10¹ + [tex]x_{2}[/tex] * 10² + [tex]x_{3}[/tex] * 10³ + [tex]x_{4}[/tex] * 10⁴ + [tex]x_5[/tex] * 10⁵ + . . . + [tex]x_{n}[/tex] * 10ⁿ

Since 10⁰ = 1, let's rewrite y as follows;

y = [tex]x_{0}[/tex]  + [tex]x_1[/tex] * 10¹ + [tex]x_{2}[/tex] * 10² + [tex]x_{3}[/tex] * 10³ + [tex]x_{4}[/tex] * 10⁴ + [tex]x_5[/tex] * 10⁵ + . . . + [tex]x_{n}[/tex] * 10ⁿ

Now, to test if y is divisible by 11, replace 10 in the equation above by -1. Since 10 divided by 11 gives -1 (mod 11)     [mod means modulus]

y = [tex]x_{0}[/tex]  + [tex]x_1[/tex] * (-1)¹ + [tex]x_{2}[/tex] * (-1)² + [tex]x_{3}[/tex] * (-1)³ + [tex]x_{4}[/tex] * (-1)⁴ + [tex]x_5[/tex] * (-1)⁵ + . . . + [tex]x_{n}[/tex] * (-1)ⁿ

=> y =  [tex]x_{0}[/tex]  - [tex]x_1[/tex] + [tex]x_{2}[/tex] - [tex]x_{3}[/tex] + [tex]x_{4}[/tex] - [tex]x_5[/tex] + . . . + [tex]x_{n}[/tex] (-1)ⁿ (mod 11)

Therefore, it can be seen that, y is divisible by 11 if and only if alternating sum of its digits [tex]x_{0}[/tex]  - [tex]x_1[/tex] + [tex]x_{2}[/tex] - [tex]x_{3}[/tex] + [tex]x_{4}[/tex] - [tex]x_5[/tex] + . . . + [tex]x_{n}[/tex] (-1)ⁿ is divisible by 11

Let's take an example

Check if the following is divisible by 11.

i. 1859

Solution

1859 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (1 - 8 + 5 - 9) is divisible by 11.

1 - 8 + 5 - 9 = -11.

Since -11 is divisible by 11 so is 1859

ii. 31415

Solution

31415 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (3 - 1 + 4 - 1 + 5) is divisible by 11.

3 - 1 + 4 - 1 + 5 = 10.

Since 10 is not divisible by 11 so is 31415 not divisible.

Answer:

The fraction [tex]\displaystyle \frac{55}{22}[/tex] is indeed a rational number.

Step-by-step explanation:

A number [tex]x[/tex] is rational if and only if there exist two integers [tex]p[/tex] and [tex]q[/tex] (where [tex]q \ne 0[/tex]) such that [tex]x = \displaystyle \frac{p}{q}[/tex].

[tex]\displaystyle \frac{55}{22}[/tex], the number in question here is already written in the form of a fraction. The two integers [tex]p = 55[/tex] and [tex]q = 22[/tex] ([tex]q \ne 0[/tex]) meet the requirement that [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]. Therefore, [tex]\displaystyle \frac{55}{22}\![/tex] is indeed a rational number.

Side note: the [tex]p[/tex] and [tex]q[/tex] here ([tex]q \ne 0[/tex]) don't have to be unique. For example:

because [tex]\displaystyle \frac{55}{22} = \frac{5 \times 11 }{2 \times 11} = \fraac{5}{2}[/tex], both of the following pairs could satisfy [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]:

Hey there! I'm happy to help!

We have a 5x is one equation and a -5x in another equation. We can combine the two equations to cancel out the x and then solve! This is called solving by elimination.

5x-4y=6

+

-5x+4y=-10

0= -4

Since we lost our x and y while solving, there cannot be any solution.

Therefore, the answer is no solution.

Have a wonderful day!

Answer:

65%

Step-by-step explanation:

If 14 are male, then 26 are female.

To find the percent female, divide the number of females by the total.

26/40 = 0.65

So, the percentage of the class that is female is 65%

Answer:

C. 65%

Step-by-step explanation:

We know that of the 40 total students, 14 are male, which means the remaining students are female.

To find how many are female, we subtract 14 from 40:

40 - 14 = 26 females

Percentage is simply a part divided by a whole, multiplied by 100. Here, the "part" is the number of females, which is 26. The "whole" is the total number of students, which is 40. So, we have:

(26 / 40) * 100 = 65

The answer is thus C, 65%.

~ an aesthetics lover

Answer:

x = 6

Step-by-step explanation:

In the third line of the solution on right side of the equal sign, middle term should be 8x instead of 4x.

The final value of x will be 6.

[tex] PQ^2 + QO^2 = PO^2 \\

x^2 + 8^2 = (4+x)^2 \\

x^2 + 64 = 16 + 8x + x^2 \\

64 = 16 + 8x \\

64 - 16 = 8x \\

48 = 8x \\

6 = x\\[/tex]

Hello, there!!!!

Given that,

80°,3x° and 2x°are three angles on a st.line.

we have,

2x°+3x°+80°= 180° {The total sum of angles on a st. line is 180°}.

or, 5x°= 180°-80°

or, 5x°=100°

or, x= 100°/5

Therefore the value of x is 20°.

Hope it helps...

Answer:36

Step-by-step explanation:

Answer:

The probability that the assembly line will be shut down is 0.00617.

Step-by-step explanation:

We are given that a soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification.

Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration.

Let X = Number of bottles in the sample that are not within specification.

The above situation can be represented through binomial distribution;

[tex]P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r};x=0,1,2,3,.....[/tex]

where, n = number of trials (samples) taken = 12 bottles

             x = number of success  = 2 or more bottles

            p = probabilitiy of success which in our question is probability that  

                 bottles are not within specification, i.e. p = 0.01

So, X ~ Binom (n = 12, p = 0.01)

Now, the probability that the assembly line will be shut down is given by = P(X [tex]\geq[/tex] 2)

  P(X [tex]\geq[/tex] 2) = 1 - P(X = 0) - P(X = 1)

                 = [tex]1-\binom{12}{0} \times 0.01^{0}\times (1-0.01)^{12-0}-\binom{12}{1} \times 0.01^{1}\times (1-0.01)^{12-1}[/tex]

                 = [tex]1-(1 \times 1\times 0.99^{12})-(12 \times 0.01^{1}\times 0.99^{11})[/tex]

                 = 0.00617

Answer:

D. 359 nm

[tex]{ \boxed{ \bf{ energy = \frac{hc}{ \lambda} }}} [/tex]

lambda is the wavelength

c is the speed of light

h is the Planck's constant

[tex]{ \sf{5.53 \times {10}^{ - 19} = \frac{(6.626 \times {10}^{ - 34}) \times (3.00 \times { {10}^{8} }) }{ \lambda} }} \\ \\ { \sf{\lambda = 3.59 \times {10}^{ - 7} }} \\ { \sf{\lambda = 359 \: nm}}[/tex]

Answer:

Simple Interest : $ 4400

Step-by-step explanation:

We want to calculate the interest on $ 10,000, at 5.5% interest rate per year, over a course of 8 years.

We can use the simple interest formula here, or :

I = P × r × t,

Where P is the principle amount, $ 10,000, r is the interest rate, 5.5% each year, or in decimal form 5.5 / 100 = 0.055. t is the time, 8 years.

Simple Interest : 10000 × 0.055 × 8 =  $4400.00

Then again the interest can be added to the principal amount ( $10,000 ) to receive some new amount after 8 years, which is $ 14,000. However the simple interest earned in 8 years at a rate of 5.5% should be $4400.

The simple interest earned on the amount is $4,400

Interest is the total amount that would be paid or earned from making an investment or taking a loan over a period of time.

Simple Interest  = principal x time x interest rate

principal = amount borrowed = $10,000

time = 8 years

Interest rate = 5.5%

10,000 x 0.055 x 8 = $4,400

To learn more about simple interest, please check: https://brainly.com/question/9352088?referrer=searchResults

Answer:

24.8

Step-by-step explanation:

sin75 = 24/x

x = 24 / sin75 = 24.846628...