Which of these fractions is an improper fraction? 5/3 or 3/5

Answer:

  (x, y) = (7, 4) meters

Step-by-step explanation:

The area of the floor without the removal is x^2, so with the smaller square removed, it is x^2 -y^2.

The perimeter of the floor is the sum of all side lengths, so is 4x +2y.

The given dimensions tell us ...

  x^2 -y^2 = 33

  4x +2y = 36

From the latter equation, we can write an expression for y:

  y = 18 -2x

Substituting this into the first equation gives ...

  x^2 -(18 -2x)^2 = 33

  x^2 -(324 -72x +4x^2) = 33

  3x^2 -72x + 357 = 0 . . . . write in standard form

  3(x -7)(x -17) = 0 . . . . . factor

Solutions to this equation are x=7 and x=17. However, for y > 0, we must have x < 9.

  y = 18 -2(7) = 4

The floor dimension x is 7 meters; the inset dimension y is 4 meters.

Answer:

c. The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

A variable is said to be continuous if it can take on any value in an interval. Examples are lengths, temperature, etc

A discrete variable, on the other hand, can only take on specific values. Examples of discrete variables are the number of students and age.

The exact lengths (in kilometers) of the ocean coastlines of different countries is a continuous variable because it can take on any value in an interval.

A stated earlier, Lengths are in general, continuous variables.

Answer:

[tex] = \frac{3}{2} [/tex]

Step-by-step explanation:

[tex]y = mx + c[/tex]

Here,

In this equation ,

[tex]2y - 3x = 8[/tex]

to find the value of m or the value of slope we have to solve for y

Let's solve,

[tex]2y - 3x = 8 \\ 2y = 8 + 3x \\ \frac{2y}{2} = \frac{8 + 3x}{2} \\ y = 4 + \frac{3x}{2} \\ y = \frac{3x}{2} + 4[/tex]

So, the slope is,

[tex] = \frac{3}{2}[/tex]

Answer : The correct statements are,

AC = 5 cm

BA = 4 cm

The perimeter of triangle ABC is 12 cm.

Step-by-step explanation :

As we know that a, b, and c are midpoints of the sides of right triangle that means midpoint divide the side in equal parts.

Now we have to calculate the sides of triangle ABC by using Pythagoras theorem.

Using Pythagoras theorem in ΔACF :

[tex](AC)^2=(FA)^2+(CF)^2[/tex]

Now put all the values in the above expression, we get the value of side AC.

[tex](AC)^2=(3)^2+(4)^2[/tex]

[tex]AC=\sqrt{(9)^2+(16)^2}[/tex]

[tex]AC=5cm[/tex]

Using Pythagoras theorem in ΔDAB :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](BD)^2=(AD)^2+(BA)^2[/tex]

Now put all the values in the above expression, we get the value of side BA.

[tex](5)^2=(3)^2+(BA)^2[/tex]

[tex]BA=\sqrt{(5)^2-(3)^2}[/tex]

[tex]BA=4cm[/tex]

Using Pythagoras theorem in ΔBEC :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](BE)^2=(CE)^2+(CB)^2[/tex]

Now put all the values in the above expression, we get the value of side CB.

[tex](5)^2=(4)^2+(CB)^2[/tex]

[tex]CB=\sqrt{(5)^2-(4)^2}[/tex]

[tex]CB=3cm[/tex]

Now we have to calculate the perimeter of ΔABC.

Perimeter of ΔABC = Side AB + Side CB+ Side AC

Perimeter of ΔABC = 4 + 3 + 5

Perimeter of ΔABC = 12 cm

Now we have to calculate the area of ΔABC.

Area of ΔABC = [tex]\frac{1}{2}\times 4\times 3=6cm^2[/tex]

Now we have to calculate the area of ΔDEF.

Area of ΔDEF = [tex]\frac{1}{2}\times 8\times 6=24cm^2[/tex]

Area of ΔABC = [tex]\frac{6}{24}\times[/tex] Area of ΔDEF

Area of ΔABC = [tex]\frac{1}{4}[/tex] Area of ΔDEF

Answer:

a) Probability that a team will win the match given that it has won the first game = 0.66

b) Probability that a team will win the match given that it has won the first two games= 0.81

c) Probability that a team will win the match, given that it has won two out of the first three games = 0.69

Step-by-step explanation:

There are a total of seven games to be played. Therefore, W and L consists of 2⁷ equi-probable sample points

a) Since one game has already been won by the team, there are 2⁶ = 64 sample points left. If the team wins three or more matches, it has won.

Number of ways of winning the three or more matches left = [tex]6C3 + 6C4 + 6C5 + 6C6[/tex]

= 20 + 15 + 6 + 1 = 42

P( a team will win the match given that it has won the first game) = 42/64 = 0.66

b)  Since two games have already been won by the team, there are 2⁵ = 32 sample points left. If the team wins two or more matches, it has won.

Number of ways of winning the three or more matches left = [tex]5C2 + 5C3 + 5C4 + 5C5[/tex] = 10 + 10 + 5 +1 = 26

P( a team will win the match given that it has won the first two games) = 26/32 = 0.81

c) Probability that a team will win the match, given that it has won two out of the first three games

They have played 3 games out of 7, this means that there are 4 more games to play. The sample points remain 2⁴ = 16

They have won 2 games already, it means they have two or more games to win.

Number of ways of winning the three or more matches left = [tex]4C2 + 4C3 + 4C4[/tex] = 6 + 4 + 1 = 11

Probability that a team will win the match, given that it has won two out of the first three games = 11/16

Probability that a team will win the match, given that it has won two out of the first three games = 0.69

Answer:

Correct statement: "the number is divisible by 3".

Step-by-step explanation:

The statement provided is:

When a number is divisible by 9, the number is divisible by 3.

The general form of a conditional statement in if-then form is:

[tex]p\rightarrow q[/tex]

This implies that if p, then q.

The part after the "if" is known as the hypothesis and the part after the "then" is known as the conclusion.

The if-then form of the provided statement is:

If a number is divisible by 9, then the number is divisible by 3.

So, the conclusion is:

"the number is divisible by 3"

Answer:

a

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

The last percentile always contains 25% of the observations.

Answer:

$23.64

Step-by-step explanation:

12 * $1.97 = $23.64

Answer: The solution  is [tex](-2,\frac{5}{3} )[/tex]

Step-by-step explanation:

it already gives you the solution for x so just plot it into the equation to solve for y.

y= [tex]\frac{2}{3} *\frac{-2}{1}+3[/tex]  

y= [tex]\frac{-4}{3}+\frac{3}{1}[/tex]

y= [tex]\frac{5}{3}[/tex]

Answer: -2 5/3

Step-by-step explanation:

y= 2/3*-2/1+3

y= -4+3/1

-2 5/3

Answer:

The value of the sample mean resonance frequency is 112Hz

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

In this problem, we have that:

Lower bound: 111.6

Upper bound: 112.4

Sample mean: (111.6 + 112.4)/2 = 112Hz

The value of the sample mean resonance frequency is 112Hz

The value of the sample mean resonance frequency is 112 Hz.

The value of the sample mean resonance frequency is equivalent to the average of the upper limit and the lower limit.

The sample mean resonance frequency = (lower limit + upper limit) / 2

(111.6 +112.4) / 2

= 224 / 2

= 112 Hz

To learn more about confidence interval, please check: https://brainly.com/question/15905477

Answer:

x = -2

y = -5

Step-by-step explanation:

We can solve this algebraically (substitution or elimination) or graphically. I will be using elimination:

Step 1: Add the 2 equations together

-8y = 40

y = -5

Step 2: Plug y into an original equation to find x

-3(-5) + 10x = -5

15 + 10x = -5

10x = -20

x = -2

And we have our final answers!

Answer:

[tex]\boxed{\sf \ \ \ x=-2 \ \ \ and \ \ \ y=-5 \ \ \ }[/tex]

Step-by-step explanation:

let s solve the following system

(1) -5y-10x=45

(2) -3y+10x=-5

let s do (1) + (2) it comes

-5y-10x-3y+10x=45-5=40

<=>

-8y=40

<=>

y = -40/8=-20/4=-5

so y = -5

let s replace y in (1)

25-10x=45

<=>

10x=25-45=-20

<=>

x = -20/10=-2

so x = -2

Answer:  Measure of angle T = 25 degrees and Measure of angle U = 45 degrees

Step-by-step explanation:

Measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.

" Triangles are said to be congruent if the corresponding sides and angles of the one triangle are equals to the other triangles."

According to the question,

In triangle KLM,

KM =27millimeters

LM = 20millimeters

KL = 12 millimeters

∠K= 45degrees

∠M= 25 degrees

∠L = 110degrees

From the given measurements of the triangle we have,

side with measure 27millimeters is opposite to angle 110° .

side with measure 12millimeters is opposite to angle 25° .

side with measure 20millimeters is opposite to angle 45°.

From the conditions in triangle TUV to be congruent to triangle KLM ,

Measure of angle T = 25 degrees and TU = 12  is against the given condition of congruent triangle.

As angle T and side TU are adjacent to each other, which is against the correspondence of the given triangle.

Hence, measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.

Learn more about congruent triangle here

https://brainly.com/question/12413243

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Answer:

D. No, because the differential equation does not have constant coefficients.

Step-by-step explanation:

The undetermined coefficient method cannot be applied to non homogeneous variables. The differential equation does not have constant variables therefore the method of undetermined superposition can not be applied. To complete a solution of non homogeneous equation the particular solution must be added to the homogeneous equation.

Answer:

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

P-value = 0.166.

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\[/tex]

Then, we can perform the hypothesis t-test for the mean.

The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=500\\\\H_a:\mu< 500[/tex]

The significance level is 0.05.

The sample has a size n=5.

The sample mean is M=496.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=5-1=4[/tex]

This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.1)=0.166[/tex]

As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

Answer:

y = 2/3x + 4

Step-by-step explanation:

Step 1: Find slope

m = (4-0)/(0+6)

m = 2/3

Step 2: Write in y-int (0, 4)

y = 2/3x + 4

Answer:

[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.102[/tex]    

[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]    

And the best option would be:

C. (77.1, 78.3)

Step-by-step explanation:

Information given

[tex]\bar X=77.7[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=3.6 represent the sample standard deviation

n=100 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=100-1=99[/tex]

Since the Confidence is 0.90 or 90%, the significance would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value for this case would be [tex]t_{\alpha/2}=1.66[/tex]

And replacing we got:

[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.10[/tex]    

[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]    

And the best option would be:

C. (77.1, 78.3)

Answer:  b) the tiles are not similar because both SP:SR is 5:4 and MJ:ML is 5:2

Step-by-step explanation:

We are given that the tiles are rectangular which implies that they both have a 90° angle.

In order to prove similarity, We need to show that the lengths and widths are proportional.

P Q R S

J  K L M

a) PQ : QR         JK : LM

  w=4  L=5        w=2 w=2

                                  ↓

                                 We need Length (not width)

b) SP : SR         MJ : ML

  L=5  w=4        L=5 w=2

      5 : 4               5 : 2

When comparing length to width they do not have the same ratio so the rectangles are not similar.

c) PQ : QR         JK : KL

  w=4  L=5        w=2 L=5

      4 : 5               2 : 5

When comparing width to length they do not have the same ratio so the rectangles are not similar.

d) SR : ML         PQ : JK

  w=4  w=2        w=4 w=2

           ↓                     ↓

  We need Length (not width)

Answer:

Step-by-step explanation:

1) divide equilateral tri from the middle you will get two 30-60-90 triangles

2) by using pythagorean law & trigimintory, you will get two unknowns (height and side length) and two functions

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

The mean annual tuition and fees for a sample of 15 private colleges was $35,500 with a standard deviation of $6500. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $32,500. State the null and alternate hypotheses. A) H0: 4 = 32,500, H:4=35,500 C) H: 4 = 35,500, H7:35,500 B) H: 4 = 32,500, H : 4 # 32,500 D) H0:41 # 32,500, H : 4 = 32,500

Solution

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 32500

For the alternative hypothesis,

Ha: µ ≠ 32500

This is a two tailed test.

Since the number of samples is small and the population standard deviation is not given, the distribution is a student's t.

Since n = 15,

Degrees of freedom, df = n - 1 = 15 - 1 = 14

t = (x - µ)/(s/√n)

Where

x = sample mean = 35500

µ = population mean = 32500

s = samples standard deviation = 6500

t = (35500 - 32500)/(6500/√15) = 1.79

We would determine the p value using the t test calculator. It becomes

p = 0.095

Assuming alpha = 0.05

Since alpha, 0.05 < than the p value, 0.095, then we would fail to reject the null hypothesis.

Answer:

I'm not completely sure what you mean by a, "single fraction," but I'm pretty sure the answer you are looking for is [tex]\frac{5-4}{a-b}[/tex]

Step-by-step explanation:

Answer:

the step-by-step explanation for height first :

[tex]h=\sqrt{h^{2} } +r^{2} =26[/tex]

[tex]h=\sqrt{h^{2} } +10^{2} =676[/tex]

[tex]h=\sqrt{h^{2} } + 100 = 676[/tex]

[tex]100-100 = 0[/tex]

[tex]676-100=576[/tex]

[tex]\sqrt{576}[/tex]

[tex]height =[/tex] 24 m

________________

step-by-step explanation for the problem :

FORMULA :  [tex]v = \frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]

v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]10^{2}[/tex] · [tex]24[/tex] = [tex]800\pi[/tex] = [tex]2513.27412[/tex] = 2513

Answer:

You didn't state it but you need to find Angle A.

From the Pythagorean Theorem, we calculate side ac

side ac^2 = 5^2 - 3^2  =25 -9 = 16 Side AC = 4

arc tangent angle A = 3 / 4 = .75

angle A =  36.87 Degrees

Step-by-step explanation:

Answer:

3/10

Step-by-step explanation:

Answer:

20gallons

Step-by-step explanation:

Answer:

50 to 60 seconds is the answer

Answer/Step-by-step explanation:

==>Given:

=>Rectangular Pyramid:

L = 5mm

W = 3mm

H = 4mm

=>Rectangular prism:

L = 5mm

W = 3mm

H = 4mm

==>Required:

a. Volume of pyramid:

Formula for calculating volume of a rectangular pyramid us given as L*W*H

V = 5*3*4

V = 60 mm³

b. Volume of prism = ⅓*L*W*H

thus,

Volume of rectangular prism given = ⅓*5*3*4

= ⅓*60

= 20mm³

c. Volume of the prism = ⅓ x volume of the pyramid

Thus, 20 = ⅓ × 60

As we can observe from our calculation of the solid shapes given, the equation written above is true for all rectangular prism and rectangular pyramid of the same length, width and height.

Answer:

34

Step-by-step explanation:

F(x) = 2x^3 - 7x + 1

Let x= 3

F(3) = 2* 3^3 - 7*3 + 1

      = 2 * 27 -21+1

      = 54 -21 + 1

      = 34

Answer: 34

Step-by-step explanation:

Answer:

-0.28

Step-by-step explanation:

(1/5) : (-5/7)=(1*5)/(5*(-5))=-(7/25)=-0.28

Answer:

[tex]-7/25[/tex]

Step-by-step explanation:

[tex]1/5 \div -5/7[/tex]

Do the reciprocal of the second fraction.

[tex]1/5 \times 7/-5[/tex]

Multiply the first fraction by the reciprocal of the second fraction.

[tex]7/-25=-0.28[/tex]

The answer in decimal form is -0.28.

Answer:

Step-by-step explanation:

given a point [tex](x_0,y_0)[/tex] the equation of a line with slope m that passes through the  given point is

[tex]y-y_0 = m(x-x_0)[/tex] or equivalently

[tex] y = mx+(y_0-mx_0)[/tex].

Recall that a line of the form [tex]y=mx+b [/tex], the y intercept is b and the x intercept is [tex]\frac{-b}{m}[/tex].

So, in our case, the y intercept is [tex](y_0-mx_0)[/tex] and the x  intercept is [tex]\frac{mx_0-y_0}{m}[/tex].

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph [tex](x_0,\frac{1}{x_0})[/tex]. Which means that [tex]y_0=\frac{1}{x_0}[/tex]

The slope of the tangent line is given by the derivative of the function evaluated at [tex]x_0[/tex]. Using the properties of derivatives, we get

[tex]y' = \frac{-1}{x^2}[/tex]. So evaluated at [tex]x_0[/tex] we get [tex] m = \frac{-1}{x_0^2}[/tex]

Replacing the values in our previous findings we get that the y intercept is

[tex](y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}[/tex]

The x intercept is

[tex] \frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0[/tex]

The triangle in consideration has height [tex]\frac{2}{x_0}[/tex] and base [tex]2x_0[/tex]. So the area is

[tex] \frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2[/tex]

So regardless of the point we take on the graph, the area of the triangle is always 2.

Answer:

[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]

Step-by-step explanation:

You have the following differential equation:

[tex]3y''+12y=0[/tex]     (1)

In order to find the solution to the equation, you can use the method of the characteristic polynomial.

The characteristic polynomial of the given differential equation is:

[tex]3m^2+12=0\\\\m^2=-\frac{12}{3}=-4\\\\m_{1,2}=\pm2\sqrt{-1}=\pm2i[/tex]

The solution of the differential equation is:

[tex]y(x)=c_1e^{m_1x}+c_2e^{m_2x}[/tex]   (2)

where m1 and m2 are the roots of the characteristic polynomial.

You replace the values obtained for m1 and m2 in the equation (2). Then, the solution to the differential equation is:

[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]