If one number is five more than another number, and the smaller number is half of the larger number, what are the two numbers?

Answer:

Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19

Step-by-step explanation:

Given:

Number of balls = 1 to 19

Find:

Probability ball is an even numbered ball or a 4

Computation:

Total even number = 2, 4, 6, 8, 10, 12, 14, 16, 18

Probability to get even number P(A) = 9 / 19

Probability to get 4 number P(B) = 1 / 19

P(A and B) = 1 / 19 (4 common)

Probability ball is an even numbered ball or a 4 [P(A or B)]

P(A or B) = P(A) + P(B) -P(A and B)

P(A or B) = [9 / 19] + [1 / 19] - [1 / 19]

Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19

Answer:

Slope = -2

Step-by-step explanation:

You want to get it to the slope intercept form first.

2y = -4x + 3

Divide by 2

y = -2x + 3/2

Parallel means in the new slope intercept form there will still be -2x.

y = -2x + b (enter in points ( 0, 1.5 ) )

1.5 = 0 + b

b = 1.5

y = -2x + 1.5 ( just an example of a line parallel to 4x + 2y = 3 )

Answer:

(A) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \geq \mu_2[/tex]    

     Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex]  

(B) The value of t-test statistics is -18.48.

(C) The P-value is Less than 0.005%.

(D) Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

Step-by-step explanation:

We are given that the Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right;

Diet Regular

μ μ1 μ2

n 20 20

x 0.78062lb 0.81645 lb

s 0.00444 lb 0.00745 lb

Let [tex]\mu_1[/tex] = mean weight of contents of cans of diet soda.

[tex]\mu_2[/tex] = mean weight of contents of cans of regular soda.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \geq \mu_2[/tex]      {means that the contents of cans of diet soda have weights with a mean that is more than or equal to the mean for the regular soda}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex]     {means that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda}

The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;

                    T.S.  =  [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]  ~  [tex]t__n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean weight of cans of diet soda = 0.78062 lb

[tex]\bar X_2[/tex] = sample mean weight of cans of regular soda = 0.81645 lb

[tex]s_1[/tex] = sample standard deviation of cans of diet soda = 0.00444 lb

[tex]s_2[/tex] = sample standard deviation of cans of regular soda = 0.00745 lb

[tex]n_1[/tex] = sample of cans of diet soda = 20

[tex]n_2[/tex] = sample of cans of diet soda = 20

Also,  [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(20-1)\times 0.00444^{2}+ (20-1)\times 0.00745^{2}}{20+20-2} }[/tex] = 0.00613

So, the test statistics =  [tex]\frac{(0.78062-0.81645)-(0)}{0.00613 \times \sqrt{\frac{1}{20}+\frac{1}{20} } }[/tex]  ~  [tex]t_3_8[/tex]

                                    =  -18.48

The value of t-test statistics is -18.48.

Also, the P-value of the test statistics is given by;

              P-value = P( [tex]t_3_8[/tex] < -18.48) = Less than 0.005%

Now, at a 0.01 level of significance, the t table gives a critical value of -2.429 at 38 degrees of freedom for the left-tailed test.

Since the value of our test statistics is less than the critical value of t as -18.48 < -2.429, so we have sufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.

Answer:

$12.10

Step-by-step explanation:

First, you have to set up a proportion to find what 20% of $60.50, or 60.5, is. On one side of the proportion you have 20/100 to represent the percent, anytime you have a percent it will always go over 100. On the other side you'll have x/60.5 because you are trying to find a value out of 60.5. This gives you the proportion 20/100=x/60.5. In order to solve this you have to cross multiply using the equation 20(60.5)=100x. First, you multiply to get 1210=100x, then divide both sides by 100 to get 12.1=x. In order for this to represent money, we add a zero on the end. This means that 20% of $60.50 is $12.10, so $12.10 is the tip.

Answer:

The "formula" for an exponential function is f(x) = a * bˣ where a is the initial value / y-intercept. Therefore, a = 4 so f(x) = 4 * bˣ. To solve for b, we can plug in the values x = 3 and f(x) = 500 which becomes:

500 = 4 * b³

125 = b³

b = 5 so the answer is f(x) = 4 · 5ˣ.

Answer:

f(x)=4(5)x

Step-by-step explanation:

An exponential equation in the form y=a(b)x has initial value a and common ratio b. The initial value is the same as the y-intercept, 4, so the equation is in the form y=4(b)x. Substituting the point (3,500) gives 500=4(b)3. Solve for b to find that the common ratio is 5.

Step-by-step explanation:

I'm not sure what your answers are, but you can only square 3 and -3 to get 9.

Answer:

3, -3

Step-by-step explanation:

3*3 = 9

-3 * -3 = 9

These are the only two numbers that square to 9

Answer:

The variable n represents the number of times in a year in which we compound the interest rate

Step-by-step explanation:

The periodic compound interest formula is given as;

A = P( 1 + r/n)^nt

The variable n represents the number of times in a year in which the interest rate is compounded

Answer: $2.95

Step-by-step explanation:

Given: Probability of losing the $7 = [tex]\dfrac{20}{38}[/tex]

Probability of winning $14  = [tex]\dfrac{18}{38}[/tex]

Then, the expected value = (- $7)  x ( Probability of losing the $7) + $14 x(Probability of winning $14)

= [tex](-\$ 7)\times\dfrac{20}{38}+(\$14)\times\dfrac{18}{38}[/tex]

= [tex]-\dfrac{70}{19}+\dfrac{126}{19}[/tex]

= [tex]\dfrac{56}{19}\times\approx\$2.95[/tex]

∴ If a doctor pays $7 that the outcome is an odd number, the doctor's

expected value is $2.95.

Answer:

There are two or zero positive solutions and zero negative roots (zeros).

Step-by-step explanation:

Use Descartes' Rule of Signs to determine the number of real zeros of [tex]f(x)=2x^6-3x^3+1-2x^5[/tex]

[tex]f(x)=2x^6-2x^5-3x^3+1\\[/tex]

Answer: 0.4255

Step-by-step explanation:

Given:  IQ scores of adults, and those scores are normally distributed

Mean: [tex]\mu=100[/tex]

Standard deviation: [tex]\sigma= 15[/tex]

Let X denotes the IQ of a random adults.

The area between 102 and 130 = [tex]P(102<X<130)=P(\dfrac{102-100}{15}<\dfrac{X-\mu}{\sigma}<\dfrac{130-100}{15})[/tex]

[tex]=P(0.13<Z<2)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<2)-P(Z<0.13)\\\\=0.9772- 0.5517\ [\text{By z-table}]\\\\=0.4255[/tex]

Hence, area between 102 and 130 = 0.4255

Answer:

[tex]\boxed{Option \ 4}[/tex]

Step-by-step explanation:

∠YVZ = 180 - 52 - 43 - 38   (Angles on a straight line add up to 180 degrees so if we try to find an unknown angle on the straight line, we need too subtract all the other angles from 180 degrees)

=> ∠YUZ = 47 degrees

Step-by-step explanation: In the figure shown, <UVW is a straight angle.

This means it measures 180 degrees.

So to find <YVZ, we add up all the angles and subtract the sum

from 180 to get the answer to this problem.

43 + 52 + 38 gives us a sum of 133.

Now we take 180 - 133 yo get 47.

So m<YVZ is 47 degrees.

Answer:

C. 510 cm^2

Step-by-step explanation:

Well to find TSA or Total Surface Area,

We need to find the area of al the triangles and rectangles.

Let's start with the 2 rectangles facing forwards.

They both have dimensions of 5*15 and 12*15,

75 + 180

= 255 cm ^2

Now let's do the back rectangle which has dimensions of 15 and 13.

15*13 = 195 cm^2

Now we can do the top and bottom triangles,

Since we don't have height we can use the following formula,

[tex]A = \sqrt{S(S-a)(S-b)(S-c)}[/tex]

S is [tex]S = \frac{1}{2} (A+B+C)[/tex]

S= 15

Now with s we can plug that in,

[tex]A = \sqrt{15(15-5)(15-13)(15-12)}[/tex]

The a b and c are the sides of the triangle.

So let's solve,

15 - 5 = 10

15 - 13 = 2

15 - 12 = 3

10*2*3 = 60

60*15 = 900

[tex]\sqrt{900}[/tex] = 30 cm^2

Since there is 2 triangles with the same dimensions their areas combined is 60 cm^2

60 + 255 + 195 = 510 cm^2

Thus,

the TSA of the right triangular prism is C. 510 cm^2.

Hope this helps :)

Answer:

C) 510 square centimetres

Step-by-step explanation:

The surface area of a prism is given as:

A = bh * pL

where b = base length of the prism = 12 cm

h = base width = 5 cm

p = b + h + c

where c = slant height = 13 cm

L = height of the prism = 15 cm

Therefore, the surface area of the prism is:

A = (12 * 5) + (12 + 5 + 13) * 15

A = 60 + (30 * 15)

A = 60 + 450

A = 510 square centimetres

That is the surface area of the prism.

Answer:

D. 4x − 6

Step-by-step explanation:

f(x) = 4x − 2

f(x−1) = 4(x−1) − 2

f(x−1) = 4x − 4 − 2

f(x−1) = 4x − 6

Answer:

5u+8

Step-by-step explanation:

Both of the 4's will cancel out with each other.

5u+8. it works actuallly by taking common nunbers and cancelling them. in this case. 4. leaving it with just 5u+8 :)

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question

Slope / m = 5

Equation of the line passing through point (2 , 10) is

y - 10 = 5(x - 2)

y - 10 = 5x - 10

y = 5x - 10 + 10

Hope this helps you

Answer:

x = -1

y =2

Step-by-step explanation:

3x+ 5y = 7

9x+ 11y = 13

Multiply the first equation by -3 so we can eliminate x

-3 (3x+ 5y = 7)

-9x -15y = -21

Add this to the second equation

-9x -15y = -21

9x+ 11y = 13

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

   - 4y = -8

Divide by -4

-4y/-4 = -8/-4

y=2

Now solve for x

3x+5y = 7

3x+5(2) = 7

3x+10 = 7

Subtract 10

3x = 7-10

3x = -3

Divide by 3

3x/3 = -3/3

x = -1

Answer:

-1, 2

Step-by-step explanation:

Although you already have the answer, here's another method of doing it that may or may not help you someday. First, we solve the top equation for x. We get:

[tex]x = \frac{7}{3} - \frac{5}{3}y\\9x + 11y = 13[/tex]

Now that we know what x is, we can plug it into the bottom equation to solve for y.

[tex]9(\frac{7}{3} - \frac{5}{3}y) + 11y = 13[/tex]

Simplify everything out, and you'll see that y = 2. We can now plug it into our equation to solve for x.

x = 7/3 - 5/3 x 2; x = -1

Answer:

-1

Step-by-step explanation:

Anything raised to  0 is 1

Multiply i 1 by  1

Simplify.

Rewrite i2 as −1

Move −1  to the left of i

Rewrite −1 i as −i

Factor out i2

Rewrite i2 as −1

Rewrite i2 as  −1

Rewrite i4 as 1

Multiply −1 by  1

Answer:

A. 0.89.

Step-by-step explanation:

The value of correlation coefficient ranges from -1 to 1. Any value outside this range cannot possibly be correlation coefficient of a scatter plot representing relationship between two variables.

The scatter plot given shows a positive correlation between average daily temperatures and number of visitors, as the trend shows the two variables are moving in the same direction. As daily temperature increases, visitors also increases.

From the options given, the only plausible correlation that can represent this positive relationship is A. 0.89.

Answer:

[tex]\boxed{D = 69}[/tex]

Step-by-step explanation:

The given quadratic equation is:

[tex]3x^2-9x+1 = 0[/tex]

Comparing it with the standard form of Quadratic Equation [tex]ax^2+bx+c = 0[/tex] , we get:

a = 3, b = -9 and c = 1

Discriminant = b² - 4ac

D = (-9)²-4(3)(1)

D = 81 - 12

D = 69

Answer:

The first statement is incorrect. They have to be complementary.

Step-by-step explanation:

You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.

You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.

The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.

Answer:

[tex]\boxed{\sf A}[/tex]

Step-by-step explanation:

The first statement is incorrect. The angle B is not equal to theta θ. The two acute angles in the right triangle can be different, if the triangle was an isosceles right triangle then angle B would be equal to theta θ.

Answer:

2 meters

Step-by-step explanation:

The volume is 4.5

​

⋅1.5⋅h⋅3

=2.25h

=h

​

The height of the tent is 2 meters.

Hope this helps :)

Answer:

2 meters

Step-by-step explanation:

Answer:

range of the function F(x) is  (-infinity, 3)

Step-by-step explanation:

I do not see the graph function F(x), so will assume that it is a graph of the function F(x) over the complete domain (-inf,inf).

As you can see from the attached graph, the function reaches a maximum at y=+3, and extends all the way to -infinity.

So the range of the function F(x) is  (-infinity, 3)

Answer:

a) y = 25495 - 2707x

b) y = 25495 - 2707(4) = 14,667

c) $2,707 per year

Step-by-step explanation:

Value now: $25,495

Value in 2 years: $20,081

Loss of value in 2 years: $25,495 - $20,081 = $5,414

Loss of value per year: $5,414/2 = $2,707

a) y = 25495 - 2707x

b) y = 25495 - 2707(4) = 14,667

c) $2,707 per year

Answer:

1.5

Step-by-step explanation:

average rate of change = (f(x2) - f(x1))/(x2 - x1)

f(x) = -2/x^2

f(x2) = f(2) = -2/(-2)^2 = -2/4 = -0.5

f(x1) = f(1) = -2/1^2 = -2

average rate of change = (-0.5 - (-2))/(2 - 1)

average rate of change = (-0.5 + 2)/1

average rate of change = 1.5

Answer:

  10%

Step-by-step explanation:

Using the given formula with the given data, we have ...

  efficiency = output work / input work

  = (10 J)/(100 J) = 0.10 = 10%

Answer:

A) 10%

Step-by-step explanation:

10/100=10

Answer:

4 boys

Step-by-step explanation:

Let x represent boys and y represent girls

Hence, x : y = 3 : 2

x/y = 3/2  

2x = 3y ------ (1)

x/y + 4 = 3/3

3x = 3(y + 4)

3x = 3y + 12 --------- (2)

From (1): x = 3y/2

Substitute x into (2) we have:

9y/2 = 3y + 12

9y = 6y + 24

9y - 6y = 24

3y = 24

∴ y = 8

From (2) : 3x = 24 - 12 = 12

∴ x = 4

Hence there Four boys

Answer:

Time taken by Stephen = 162 seconds

Step-by-step explanation:

Stephan gathered data which fits in the line of best fit,

y = -2.1x + 565.6

Where x represents the age (in months)

And y represents the time (in seconds) taken by Stephen to run two laps on the track.

Time taken to run 2 laps at the age of 192 months,

By substituting x = 192 months,

y = -2.1(192) + 565.6

  = -403.2 + 565.6

  = 162.4 seconds

  ≈ 162 seconds

Therefore, time taken by Stephen to cover 2 laps was 162 seconds when he was 192 months old.

Answer:

4.1

Step-by-step explanation:

1.8 x 0.5 = 0.9

0.5 x 0.5 = 0.25

2(0.9 + 0.9 + 0.25) = 2(1.8 + 0.25) = 2(2.05)

2 x 2.05 = 4.1

Therefore the answer is 4.1

I hope that was helpful!

Answer:

Vertical asymptote: [tex]x=3[/tex]

Horizontal asymptote: [tex]f(x) =2[/tex]

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

[tex]f (x) = -\dfrac{1 }{ x-3} +2[/tex]

One root, [tex]x = 3.5[/tex]

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

Roots of f(x) means the value of x where f(x) = 0

[tex]0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5[/tex]

One root, [tex]x = 3.5[/tex]

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) [tex]\rightarrow \infty[/tex]

For all, other values of [tex]x[/tex] , [tex]f(x)[/tex] is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is [tex]\frac{1}{x-3}[/tex].

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) [tex]\rightarrow \infty[/tex].

[tex]-\dfrac{1 }{ x-3} +2 \rightarrow \infty[/tex]

It is possible only when

[tex]x-3=0\\\Rightarrow x=3[/tex]

[tex]\therefore[/tex] vertical asymptote: [tex]x=3[/tex]

Horizontal Asymptote is the value of f(x) , where value of x [tex]\rightarrow \infty[/tex].

[tex]x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2[/tex]

[tex]\therefore[/tex] Horizontal asymptote: [tex]f(x) =2[/tex]

Please refer to the graph of given function as shown in the attached image.

Answer:

A : A1 = -7, an = an-1 + 3

Step-by-step explanation:

a1=-7, a2=-7+(1)3=-4

a3=-7+(2)3=-1