Kyra has £60 more than Donna. Donna spends 1/3 of her money. Kyra now has twice as much money as Donna. How much did Donna spend?

Answer:

Step-by-step explanation:

Given the equation j – 16 = 7, If Nolan is using substitution to determine if 23 is a solution to the equation, then Nolan need to make j the subject of the formula from the equation. The following statements must therefore be made by Nolan.

First, Nolan must substitute for the value of j in the equation.

To simplify, Nolan must subtract the value of  7 from both sides to have;

j – 16 - 7= 7 - 7

j – 23 = 0

Then Nolan must add 23 to both sides of the equation to get the value of j as shown;

j – 23 + 23 = 0+23

j = 23

23 is therefore a solution to the equation

Answer:First, Nolan must substitute 23 for j.To simplify, Nolan must subtract 16 from 23. 23 is a solution of the equation.

Step-by-step explanation:

I got it right on Edge

Answer:

8 + 2x

Step-by-step explanation:

You are adding 8 to 2 times an unknown number.

Answer:

y = -8.5

Step-by-step explanation:

Answer:-8.5

Step-by-step explanation:

5.4y=-45.9

y=-8.5

Answer:

7 donkeys

Step-by-step explanation:

Given

A system consisting of donkeys and tourists

Heads = 50

Legs = 114

Required

Calculate number of donkeys.

Represent donkeys with D and tourists with T.

By means of identification; donkeys and tourists (human) both have 1 head.

This implies that

Number of Heads = D + T

50 = D + T ----- Equation 1

While each donkey have 4 legs, each tourists have 2 legs.

This implies that

Number of legs = 4D + 2T

114 = 4D + 2T ---- Multiply both sides by ½

114 * ½ = (4D + 2T) * ½

57 = 4D * ½ + 2T * ½

57 = 2D + T ----- Equation 2

Subtract equation 1 from 2

57 = 2D + T

- (50 = D + T)

---------------------

57 - 50 = 2D - D + T - T

7 = D

Recall that D represents the number of donkeys.

So, D = 7 implies that

The total number of donkeys are 7

Answer:

[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} =  \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants.

Step-by-step explanation:

Consider the differential equation [tex]y''+6y'+9y = 4e^{x}[/tex]. To find the homogeneus solution, we assume that [tex]y = Ae^{rt}[/tex] and replace it in the equation [tex]y''+6y'+9y = 0[/tex]. If we do so, after using some properties of derivatives and the properties of the exponential function we end up with the equation

[tex]r^2+6r+9 = 0 = (r+3)^2[/tex]

which leads to r = -3. So, one solution of the homogeneus equation is [tex]y_h = c_1e^{-3x}[/tex], where c_1 is a constant.

To use the order reduction method, assume

[tex] y = v(x)y_h(x)[/tex]

where v(x) is an appropiate function. Using this, we get

[tex]y'= v'y+y'v[/tex]

[tex]y''=v''y+y'v'+y''v+v'y'=v''y+2v'y'+y''v[/tex]

Plugging this in the original equation we get

[tex]v''y+2v'y'+y''v + 6(v'y+y'v) +9vy=4e^{x}[/tex]

re arranging the left side we get

[tex]v''y+2v'y'+6v'y+v(y''+6y'+9y)=4e^{x}[/tex]

Since y is a solution of the homogeneus equation, we get that [tex]y''+6y'+9y=0[/tex]. Then we get the equation

[tex]yv''+(2y'+6y)v' = 4e^{x}[/tex]

We can change the variable as w = v' and w' = v'', and replacing y with y_h, we get that the final equation to be solved is

[tex] e^{-3x}w'+(6e^{-3x}-6e^{-3x})w =4e^{x}[/tex]

Or equivalently

[tex]w' = 4e^{4x}[/tex]

By integration on both sides, we get that w = e^{4x}+ k[/tex] where k is a constant.

So by integration we get that v = [tex]e^{4x}{4} + kx+d[/tex] where d is another constant.

Then, the final solution is

[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} =  \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants

Answer:

x + 8 ≤ (x − 4)2

Step-by-step explanation:

Let the number be x,

The sum of the number and 8 is

(x + 8)

The square of the difference of the number and 4 is

(x - 4) {}^{2}  

Hence the inequality is

(x + 8) \leqslant (x - 4) {}^{2}

Answer:

21

Step-by-step explanation:

The 5 smallest prime numbers are 1, 2, 3, 5, and 7.

So when multiplied it equals 105.

Divide by 42 and you get 2 21/42

So you have a remainder of 21

Answer:

6.75 GB

Step-by-step explanation:

Given the probability mass function of the amount of memory X (GB) in a purchased flash drive.

[tex]\left|\begin{array}{c|ccccc}x&1&2&4&8&16\\p(x)&0.05&0.15&0.30&0.35&0.15\end{array}\right|[/tex]

Expected Value of X, [tex]E(X)=\sum x \cdot P(x)[/tex]

[tex]=(1 \times 0.05)+(2 \times 0.15)+(4 \times 0.30) +(8 \times 0.35) +(16 \times 0.15)\\=0.05+0.3+1.2+2.8+2.4\\=6.75[/tex]

The expected value of X is 6.75 GB.

Answer:

[tex]\frac{25}{16}[/tex]

Step-by-step explanation:

[tex](-\frac{5}{4})^2\\\\ \text {Apply power of a fraction rule: } (\frac{a}{b})^x=\frac{a^x}{b^x}\\\\(-\frac{5}{4})^2 = \frac{-5^2}{4^2}=\frac{25}{16}\\\\\boxed{(-\frac{5}{4})^2=\frac{25}{16}}[/tex]

Answer:

  appropriately writing the proportion can reduce or eliminate steps required to solve it

Step-by-step explanation:

The proportion ...

  [tex]\dfrac{A}{B}=\dfrac{C}{D}[/tex]

is equivalent to the equation obtained by "cross-multiplying:"

  AD = BC

This equation can be written as proportions in 3 other ways:

  [tex]\dfrac{B}{A}=\dfrac{D}{C}\qquad\dfrac{A}{C}=\dfrac{B}{D}\qquad\dfrac{C}{A}=\dfrac{D}{B}[/tex]

  Effectively, the proportion can be written upside-down and sideways, as long as the corresponding parts are kept in the same order.

I find this most useful to ...

  a) put the unknown quantity in the numerator

  b) give that unknown quantity a denominator of 1, if possible.

__

The usual method recommended for solving proportions is to form the cross-product, as above, then divide by the coefficient of the variable. If the variable is already in the numerator, you can simply multiply the proportion by its denominator.

Example:

  x/4 = 3/2

Usual method:

  2x = 4·3

  x = 12/2 = 6

Multiplying by the denominator:

  x = 4(3/2) = 12/2 = 6 . . . . . . saves the "cross product" step

__

Example 2:

  x/4 = 1/2 . . . . we note that "1" is "sideways" from x, so we can rewrite the proportion as ...

  x/1 = 4/2 . . . . . . written with 1 in the denominator

  x = 2 . . . . simplify

Of course, this is the same answer you would get by multiplying by the denominator, 4.

The point here is that if you have a choice when you write the initial proportion, you can make the choice to write it with x in the numerator and 1 in the denominator.

Answer:

$37.50

Step-by-step explanation:

50*.25=12.50

Take $50 - 12.50  = 37.50

Answer:

[tex]\boxed{\sf \ \ age = 10\ \ }[/tex]

Step-by-step explanation:

Hello,

let's write the mean computation, we note x the age of the additional person

[tex]\dfrac{14+14+18+18+22+x}{6}=16[/tex]

[tex]<=> 14+14+18+18+22+x = 6*16=96\\\\<=> x = 96 - ( 14+14+18+18+22)= 10[/tex]

So the age of the person is 10

hope this helps

Answer:

10

Step-by-step explanation:

The mean is the sum of terms divided by number of terms.

Let x be the age of the person who entered the room.

(14+14+18+18+22+x)/6 = 16

(x + 86)/6 = 16

x + 86 = 96

x = 10

The age of the person who entered the room is 10.

Answer:

please see the attached picture for full solution...

Hope it helps...

Good luck on your assignment....

Answer:

The probability that operator A gets the job even though both operators have equal ability is 0.0001.

Step-by-step explanation:

We are given that an experiment is designed to test whether operator A or operator B gets the job of operating a new machine. If the sample means for the 75 trials differ by more than 5 seconds, the operator with the smaller mean gets the job.

Suppose the standard deviations of times for both operators are assumed to be 2 seconds.

The z score probability distribution for the two-sample normal distribution is given by;

                   Z  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1}+\frac{\sigma_2^{2} }{n_2} } }[/tex]  ~ N(0,1)

where, [tex]\bar X_1[/tex] = sample mean for operator A

[tex]\bar X_2[/tex] = sample mean for operator B

[tex]\sigma_1[/tex] = standard deviations of times for operator A = 2 seconds

[tex]\sigma_2[/tex] = standard deviations of times for operator B = 2 seconds

[tex]n_1=n_2[/tex] = sample of independent trials for both operators = 75

Now, the probability that operator A gets the job even though both operators have equal ability is given by = P([tex]\bar X_1 -\bar X_2[/tex] > 5 seconds)

    P([tex]\bar X_1 -\bar X_2[/tex] > 5 sec) = P( [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1}+\frac{\sigma_2^{2} }{n_2} } }[/tex] > [tex]\frac{5-0}{\sqrt{\frac{2^{2} }{75}+\frac{2^{2} }{75} } }[/tex] )

                                    = P(Z > 15.31) = 1 - P(Z [tex]\leq[/tex] 15.31)

                                                          = 1 - 0.9999 = 0.0001

As in the z table, the highest critical value for x is given for x = 4.40 so we will take this value's probability area for x = 15.31.

Answer:

If the mean was 7 for the first 4 days that means the sum of temperatures of the first 4 days was 7 * 4 = 28. Similarly, the sum of temperatures of the first 5 days was 9 * 5 = 45 so that means that the temp. on the 5th day was 45 - 28 = 17°C.

Answer:

11 C

Step-by-step explanation:

To find the mean (average), you have to add all and divide by 2, so if you reverse this, you get (7 + X)/2  = 9 , 9 * 2 - 7 = 11

Answer:

Concave

Step-by-step explanation:

The length of the pool would be 8.5 x 4.5 = 38.25 meters.

Using the Pythagorean theorem the diagonal is:

Diagonal = sqrt(38.25^2 + 8.5^2)

Diagonal = 39.183 meters

You swim it 6 times.

Total distance = 39.183 x 6 = 235.098 meters.

Round to 2 decimals = 235.10 meters

Answer:

0.48% probability that all four are new

Step-by-step explanation:

The homes are chosen "without replacement", which means that after a home is visited, it is not elegible to be visited again. So we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Total of 10 homes, so N = 10.

We want 4 new, so x = 4.

In total, there are 4 new, so k = 4.

Sample of four homes, so n = 4.

Then

[tex]P(X = 4) = h(4,10,4,4) = \frac{C_{4,4}*C_{6,0}}{C_{10,4}} = 0.0048[/tex]

0.48% probability that all four are new

The calculated probability is "0.0048".

From a total of [tex]N=10\ \ \text{homes},\ r=4[/tex] are completely new while 6 are not.

Let X indicate the series of innovative dwellings in a sample of[tex]n=4[/tex] homes.

X is the next step. Algebraic distribution for parameters[tex]N=10, r=4, \ \ and\ \ n = 4[/tex] Only integer values in this range: can be given to a hypergeometric random variable.

[tex]\to [ \max {(0,\,n+r-N)}, \min {(n,\,r)} ] = [ 0, 4 ] \\\\ \to P( X = 4) \\\\ \to N=10\\\\ \to r=4\\\\ \to n = 4[/tex]

[tex]\to \bold{P(X=k) = \dfrac{\binom{r }{ k}{\binom{N-r} {n-k}}}{\binom{N}{n}}} \\\\\to P(X =4 ) = \dfrac{\binom{r }{ 4}{\binom{N-r} {n-4}}}{\binom{N}{n}} \\\\[/tex]

                   [tex]= \dfrac{\binom{4 }{ 4}{\binom{10-4} {4-4}}}{\binom{10}{4}}\\\\= \dfrac{\binom{4 }{ 4}{\binom{6} {0}}}{\binom{10}{4}} \\\\= \dfrac{ 1 \times 1}{210} \\\\= \dfrac{ 1}{210} \\\\= \dfrac{1}{210} \\\\= 0.004762[/tex]

Using the excel function:

[tex]\text{HYPGEOM.DIST( k, n, r, N. cumulative)}[/tex]  for calculating the [tex]P_{X} (4)[/tex]:

[tex]\to \text{HYPGEOM.DIST( 4, 4, 4, 10, FALSE) = 0.0047619047619}[/tex]

[tex]\to P(X= 4 ) = \frac{1}{210} = { 0.0048 }[/tex]

Find out more information about the probability here:

brainly.com/question/2321387

Answer:

A

Step-by-step explanation:

f(x) – g(x)

Set up the expression.

2x² - 3x + 4 - x² - 4x - 5

Add or subtract the like terms.

2x² - x² -3x - 4x + 4 - 5

x² - 7x -1

Answer:

The first five terms of the sequence are: 2000, 2100, 2205, 2315.25, 2431.01.

Step-by-step explanation:

The sequence is modeled by the equation:

[tex]a_{n} = 2000(1.05)^{n}[/tex]

(a) Find the first five terms of the sequence {an}.

[tex]a_{n} = 2000(1.05)^{n}[/tex]

[tex]a_{0} = 2000(1.05)^{0} = 2000[/tex]

[tex]a_{1} = 2000(1.05)^{1} = 2100[/tex]

[tex]a_{2} = 2000(1.05)^{2} = 2205[/tex]

[tex]a_{3} = 2000(1.05)^{3} = 2315.25[/tex]

[tex]a_{4} = 2000(1.05)^{4} = 2431.01[/tex]

The first five terms of the sequence are: 2000, 2100, 2205, 2315.25, 2431.01.

Answer:

(56 )log3 x

Step-by-step explanation:

We know that  log a^b = bloga

8log3 x^7 = (7*8 )log3 x = 56 log3 x

Answer:

56 log3 x

Step-by-step explanation:

8 log3 x^7 can be rewritten as log3 x^(7*8) = log3 x^56 or 56 log3 x

Answer:

a. They are empty set.

b. they are finite set.

Solution,

a. A={ prime number between 6 and 7}

There are not any number between 6 and 7.

So there will be no Elements.

A={ }

It is empty set.

Empty set are those set which doesn't contain any Element.

b.B={multiples of 2 less than 20}

B={2,4,6,8,10,12,14,16,18}

It is a finite set.

Finite set are those set which we can count easily.

Hope this helps...

Good luck on your assignment...

Step-by-step explanation:

Zero has one square root which is 0. Negative numbers don't have real square roots since a square is either positive or 0. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can't be written as the quotient of two integers.

Answer:

i). 10 levels of the bricks

ii). 320 bricks

Step-by-step explanation:

First level contains number of bricks = 50

Second level will contain = 50 - 4 = 46 bricks

Similarly, 3rd level will contain number of bricks = 46 - 4 = 42

Therefore, sequence formed for the number of bricks in each level of the wall will be,

50, 46, 42........14

This sequence is an arithmetic sequence having,

First term 'a' = 50

Common difference 'd' = 46 - 50 = (-4)

Last term of the sequence [tex]T_{n}[/tex]= 14

i). Expression representing last term will be,

  [tex]T_{n}=a+(n-1)d[/tex]

  Here [tex]T_{n}[/tex] = nth term

  a = first term

  n = number of term (Number of level of the wall)

  d = common difference

  By substituting these values in the formula,

  14 = 50 + (n - 1)(-4)

  14 - 50 = (-4)(n - 1)

  -36 = -4(n - 1)

  9 = (n - 1)  

  n = 9 + 1

  n = 10

ii). Number of bricks used in the wall = Sum of the sequence

   Expression for the sum of an arithmetic sequence is,

   [tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]

   [tex]S_n=\frac{10}{2}[2\times 50+(10-1)(-4)][/tex]

        = 5(100 - 36)

        = 320 bricks

Answer:

[tex]\boxed{\sf \ \ \ \dfrac{4}{5} \ \ \ }[/tex]

Step-by-step explanation:

when the equation is like y = ax + b

the slope is a

in this case we have

[tex]y \ = \ \dfrac{4}{5}x\ \ - \ 3[/tex]

so the slope is

[tex]\dfrac{4}{5}[/tex]

Answer:

96 ft^2

Step-by-step explanation:

volume=l^3

l=4

4x4x4=64

Surface area (4x4)=16

16x6=96

Answer:

SA =96 ft^2

Step-by-step explanation:

The volume of a cube is given by

V = s^3

64 = s^3

Take the cube root of each side

64 ^ 1/3 = s^3 ^ 1/3

4 =s

The side length si 4

The surface area of a cube is

SA = 6 s^2

SA = 6 * 4^2

SA = 6 * 16

SA =96 ft^2

Answer: 10.9

Step-by-step explanation:

You would use Pythagorean theorem:

5x5+12x12=c

5x5=25

12x12=144

Now, 25+144=169

Now find the square root of 169 which is 13 which isn't an answer choice, which means your prolly after a leg.

I assume 12 is the hypotenuse

A(squared)+5x5=12x12

A+25=144

144-25=119

Square root of 119=10.9

So I'm going to go with answer 10 in or 11 if you round.

Answer:

i think its c

Step-by-step explanation:

Answer:

D. 41

Step-by-step explanation:

Use Pythagorean Theorem: a² + b² = c²

With that in mind, we already have a and b, so:

40² + 9² = c²

√(40² + 9²) = c

c = 41

And we have our final answer!