A number is multiplied by 5 and the answer when divided by 3 gives 1315 . what is the number ?

Answer:

A) 10%

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Sam's monthly bills are normally distributed with mean 2700 and standard deviation 230.9.

This means that [tex]\mu = 2700, \sigma = 230.9[/tex]

What is the probability that his expenses will exceed his income in the following month?

Expenses above 2*1500 = $3000, which is 1 subtracted by the p-value of Z when X = 3000.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3000 - 2700}{230.9}[/tex]

[tex]Z = 1.3[/tex]

[tex]Z = 1.3[/tex] has a p-value of 0.9032.

1 - 0.9032 = 0.0968 that is, close to 10%, and thus the correct answer is given by option A.

The linear regression model which models the data is :

y = -6.41053X + 103.83509

Obtaining the regression equation could be performed using either the formula method or using technology (excel, calculator, online regression calculators )

Using technology :

• Enter the data into the columns provided ;

The regression equation obtained for the data is : y = -6.41053X + 103.83509

Where ;

Slope = -6.41053

Intercept = 103.83509

X = Rank

y = probability percentage

Hence, from the linear regression equation obtained, we could see that a negative linear relationship exists between rank and probability as implied from it's negative slope value.

Learn more on linear regression : https://brainly.com/question/12164389

Answer:

x = 5

Step-by-step explanation:

I'm taking all bases as b so not typing it

2/3 log 125 = log (125^2/3) = log 25

1/2 log 9 = log (9^1/2) = log 3

So we can rewrite the equation as,

log x = log 25 + log 3 - log 15

or, log x = log (25×3) - log 15

or, log x = log 75 - log 15

or, log x = log (75/15)

or, log x = log 5

or, x = 5

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

f(n) = 8 + 3(n) - 3

f(n) = 5 + 3n

f(1) = 5 + 3(1)

f(1) = 8

f(2) = 5 + 3(2)

f(2) = 5  + 6

f(2) = 11

f(3) = 5 + 3*3

f(3) = 14

f(4) = 5 + 3*4

f(4) = 17

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Answer:

Step-by-step explanation:

The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.

1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)

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2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)

Answer and Explanation:

Odds ratio is the odds that an outcome would happen given a level of exposure in comparison to the occurrence of that outcome without exposure. Odds ratio is calculated by dividing odds of event occurring with exposure(the first group) by odds of event(usually disease) occurring without exposure. Odds is different from probability(denoted p/1-p). While probability is the number of favorable events divided by total number of events, odds is number of favorable events/number of unfavorable events.

Relative risk, also measuring relationship between exposure and outcome, is the ratio of the probability that an outcome would occur without exposure and probability that an outcome would occur with exposure.

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Answer:

  27%

Step-by-step explanation:

The price multiplier for the first discount is (1 -55%) = 0.45.

The price multiplier for the second discount is (1 -40%) = 0.60.

Then the price multiplier for the two discounts together is ...

  (0.45)(0.60) = 0.27

You end up paying 27% of the original price.

Answer:

3

Step-by-step explanation:

common ratio

2.1/0.7=3

6.3/2.1=3

18.9/6.3=3

therefore common ratio is equal to 3

Answer:

2 sqrt(2) = x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 45 = x/4

4 sin 45 = x

4 ( sqrt(2)/2) =x

2 sqrt(2) = x

Answer: D

Use sine to find the x-value:

[tex]sin(45)=\frac{x}{4} \\\\4*sin(45)=x\\\\x=\frac{\sqrt{2} }{2} *4=2\sqrt{2}[/tex]  

Answer:

Following are the solution to the given points:

Step-by-step explanation:

Normal Distribution:

[tex]\mu=50\\\\\sigma= 6\\\\Z=\frac{X-\mu}{\sigma} \sim N(O,l)[/tex]

For point a:

[tex]P(X< 56)=\frac{(56-50)}{6}= \frac{6}{6}=1\\\\[/tex]

[tex]=P(Z<1)\ From\ \sigma \ Table=0.8413\\\\P(X>= 56)=(1-P(X< 56))=1-0.8413=0.1587\\\\[/tex]

For point b:

[tex]P(X< 49)=\frac{(49-50)}{6}=-\frac{1}{6} =-0.1667\\\\=P(Z<-0.1667)\ From\ \sigma \ Table\\\\=0.4338[/tex]

For point c:

To Find [tex]P(a\leq Z\leq b)= F(b) - F(a)\\\\[/tex]

[tex]P(X< 45)=\frac{(45-50)}{6}=\frac{-5}{6} =-0.8333\\\\P (Z<-0.8333) \ From \ \sigma \ Table\\\\=0.20233\\\\P(X< 55)=\frac{(55-50)}{6} =\frac{5}{6}=0.8333\\\\P ( Z< 0.8333) \ From \ \sigma\ Table\\\\=0.79767\\\\P(45 < X < 55) =0.79767-0.20233 =0.5953[/tex]

Answer:

The zeroes are -6, 1/2 and 2.

Step-by-step explanation:

f(x) = 2x3 + 7x2 - 28x + 12 = 0

From the first and last coefficient 2 and 12, one guess for a zero is x = 2.

So substituting x = 2:

f(2) = 16+ 28 - 56 + 12 = 0

So x = 2 is a zero and x - 2 is a factor of f(x)

Performing long division:

x - 2)2x3 + 7x2 - 28x + 12( 2x2 + 11x - 6 <------- Quotient

       2x3  - 4x2

                 11x2 - 28x

                 11x2 - 22x

                          - 6x + 12

                           -6x + 12

                            .............

Now we solve

2x2 + 11x - 6 = 0

(2x - 1)(x + 6) = 0

2x - 1 = 0 or x + 6 = 0, so:

x = 1/2,  x = -6.

Answer: -6, 1/2, 2.

Step-by-step explanation:

{(x) = 2x3 + 7x2 - 28x + 12 = 0

From the first and last coefficient 2 and 12, one

guess for a zero is x=2.

So substituting x=2:

{(2) = 16+ 28 - 56 + 12 = 0

So x = 2 is a zero and x - 2 is a factor of f(x)

Performing long division:

X - 2)2x3 + 7x2 - 28x + 12(2x2 + 11x - 6 <

Quotient

Answer:

The value of [tex]x[/tex] is 10.

Step-by-step explanation:

Both angles ABC and CBD are complementary, that is, the sum of the measures of both angles equals 90°, that is:

[tex]\angle ABC + \angle CBD = 90^{\circ}[/tex] (1)

If we know that [tex]\angle ABC = 5\cdot x[/tex] and [tex]\angle CBD = 4\cdot x[/tex], then the value of [tex]x[/tex] is:

[tex]5\cdot x + 4\cdot x = 90^{\circ}[/tex]

[tex]9\cdot x = 90^{\circ}[/tex]

[tex]x = 10[/tex]

The value of [tex]x[/tex] is 10.

Answer:

Step-by-step explanation:

Arranging the data in the ascending order:

108.6 98.3 103.7 112 117.4 120 121.5 123.2 128.4

The median is the middle value of the data set:

a)

Hence,

median = 117.4

b)

When the value of blood pressure is 117.7 instead of 117.4 then the median will be:

Median = 117.7

c)

This indicates that the median of a well sorted set of data is depends upon the middle value of the data set.

Answer:

6 samples

Step-by-step explanation:

Given :

Sample size, = n

Standard deviation, = 6000

Margin of Error = 2000

Confidence interval, α = 95%

Zcritical at 95% = 1.96

n = (Zcritical * σ) / margin of error

n = (1.96 * 6000) /2000

n = 11760 / 2000

n = 5.88

n = 6 samples

Answer:

Hypothenus = 22

Step-by-step explanation:

From the question given above, we were told that the triangles are congruent (i.e same size). Thus,

AC = EF

BC = DE

To obtain the length of each Hypothenus, we shall determine the value of y and x. This can be obtained as follow:

For y:

AC = y + 3

EF = 2y + 1

AC = EF

y + 3 = 2y + 1

Collect like terms

3 – 1 = 2y – y

2 = y

y = 2

For x:

BC = 5x + 7

DE = 6x + 2y

y = 2

DE = 6x + 2(2)

DE = 6x + 4

BC = DE

5x + 7 = 6x + 4

Collect like terms

7 – 4 = 6x – 5x

3 = x

x = 3

Finally, we shall determine the length of each Hypothenus. This can be obtained as follow:

Hypothenus = BC

Hypothenus = 5x + 7

x = 3

Hypothenus = 5x + 7

Hypothenus = 5(3) + 7

Hypothenus = 15 + 7

Hypothenus = 22

OR

Hypothenus = DE

DE = 6x + 2y

y = 2

x = 3

Hypothenus = 6(3) + 2(2)

Hypothenus = 18 + 4

Hypothenus = 22

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Answer:

Step-by-step explanation:

Let x and y represent the cost of a hot dog and a hamburger, respectively. The the two purchases can be described by ...

  3x +2y -9.75 = 0

  2x +3y -10.25 = 0

We can list the coefficients of these general-form equations in 2 rows, listing the first one again at the end:

  3, 2, -9.75, 3

  2, 3, -10.25, 2

Now, we can form differences of cross-products in adjacent pairs of columns:

  d1 = (3)(3) -(2)(2) = 9 -4 = 5

  d2 = (2)(-10.25) -(3)(-9.75) = -20.50 +29.25 = 8.75

  d3 = (-9.75)(2) -(-10.25)(3) = -19.50 +30.75 = 11.25

Then the solutions are found from ...

  1/d1 = x/d2 = y/d3

  x = d2/d1 = 8.75/5 = 1.75

  y = d3/d1 = 11.25/5 = 2.25

The cost of one hot dog is $1.75; the cost of one hamburger is $2.25.

_____

Additional comment

This is my simplification of the "cross-multiplication method" of solving a pair of linear equations. That method can be found described on web sites and in videos. This version, and the versions described elsewhere, are variations on Cramer's Rule and on the Vedic Maths method of solving equations. Each of those do similar differences of cross products, perhaps in less-easily-remembered fashion.

For a given pair of columns with coefficients ...

  a b

  c d

The cross-product we form is ad -cb.

Answer:

3 e^t/2 + 4 = 27

e^t/2 = 23 / 3

Taking natural log of both sides

t/2 = ln 23/3 = ln 7.667 = 2.037

t = 4.074

Check:

3 e^4.074/2 + 4 = 27

27 = 27

Answer:

24 and 45

Step-by-step explanation:

Okay, now that I can answer this question with the right answers:

The easy way to do this is to first solve the left hand side of the equation.

1/2 of 12 is the same as 12/2 = 6.

So 6 = 1/4 * x

To solve for that unknown x, just multiply both sides by 4 to cancel out the fraction:

6*4 = 4* 1/4*x

24 = x

For the other equation, do the same thing:

1/3 * 90 = 90/3 = 30

30 = 2/3*x

30*3 = 3* 2/3 *x

90 = 2x

90/2 = 2x/2

45 = x

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Answer:

  x = 36

Step-by-step explanation:

The interior angle at E is (180-2x). The interior angle at F is (180-4x). The sum of the interior angles of the triangle is 180, so we have ...

  (180 -2x) +x +(180 -4x) = 180

  180 = 5x . . . . . . add 5x-180 to both sides

  36 = x . . . . . . . divide by 5

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Additional comment

This value of x makes the exterior angles at E and F be 72° and 144°, respectively. The internal angles at E, F, G are then 108°, 36°, 36°, making the triangle isosceles with EF = EG.

Answer:

x = 5

Step-by-step explanation:

Your goal is to isolate x

3x + 7 = 22

Subtract 7 from both sides and you are left with

3x = 15

In order to isolate x divide both sides by 3

x = 5

Answer:

Step-by-step explanation:

Hope this helps :)!

Answer: The probability would be zero

Step-by-step explanation:

There are two children and one is a boy, so the probability of both being girls is a zero

the answer is d ( square root 3 )

tan = oposite / adjacent

tan 60° = √3 / 1

= √3

so

82-(-2)

=84

then ur answer is 84

Answer:

The answer is "[tex]\frac{5\pi}{6}[/tex]"

Step-by-step explanation:

Please find the graph file.

[tex]h= y=2x-x^2\\\\r= x\\\\Area=2\pi\times r\times h\\\\= 2 \pi \times x \times (2x-x^2)\\\\= 2 \pi \times 2x^2-x^3\\\\volume \ V(x)=\int \ A(x)\ dx\\\\= \int^{x=1}_{x=0} 2\pi (2x^2-x^3)\ dx\\\\= 2\pi [(\frac{2x^3}{3}-\frac{x^4}{4})]^{1}_{0} \\\\= 2\pi [(\frac{2}{3}-\frac{1}{4})-(0-0)] \\\\= 2\pi \times \frac{5}{12}\\\\=\frac{5\pi}{6}\\\\[/tex]

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Answer:

  (a)  2

Step-by-step explanation:

Each inch is 2.54 cm, so 5.08 cm is ...

  x / (5.08 cm) = (1 in) / (2.54 cm)

  x = (1 in)(5.08/2.54) = (1 in)(2)

  x = 2 in

5.08 cm equals 2 inches.

Answer:

Here you go

Ans is in pictures.

Answer:

see below

Step-by-step explanation:

10 + 15k

Factor out the greatest common factor 5

5( 2+3k)

Rewriting

5(3k+2)

Rami is correct if a=2 then his expression is 5(3k+2)

Kenneth

yk+6+8k+4

Add the terms together

k(y+8) + 10

If y =7 then Kenneth is correct otherwise he is incorrect

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Answer:

  B. $1044.28

Step-by-step explanation:

Putting the given numbers into the given formula, we have ...

  A(8) = $700•e^(0.05•8) ≈ $1044.28