A boy has 10 cookies. His sister has 2.5 times as many. How many does the sister have?
Make a Selection:
A.
12.5
B.
20.5
C. 25
D. 25.5
NE

Answer:

OD. 45,45,90

Step-by-step explanation:

The particular identity you want to use is

[tex]\cos^2x=\dfrac{1+\cos(2x)}2[/tex]

Then

[tex]3\cos^4x=3(\cos^2x)^2=3\left(\dfrac{1+\cos(2x)}2\right)^2=\dfrac34(1+\cos(2x))^2[/tex]

Expand the binomial to get

[tex]3\cos^4x=\dfrac34\left(1+2\cos(2x)+\cos^2(2x)\right)[/tex]

Use the identity again to write

[tex]\cos^2(2x)=\dfrac{1+\cos(4x)}2[/tex]

and so

[tex]3\cos^4x=\dfrac34\left(1+2\cos(2x)+\dfrac{1+\cos(4x)}2\right)[/tex]

[tex]3\cos^4x=\dfrac38\left(3+4\cos(2x)+\cos(4x)\right)[/tex]

Answer:

For this case we know that the random variable of interest would be X and the distribution for X is given by:

[tex] X \sim Bin (n,p)[/tex]

And by properties of this distribution the expected value for this case is:

[tex] E(X)= np[/tex]

And the variance :

[tex] Var(X)= np(1-p)[/tex]

Step-by-step explanation:

For this case we know that the random variable of interest would be X and the distribution for X is given by:

[tex] X \sim Bin (n,p)[/tex]

And by properties of this the expected value for this case is:

[tex] E(X)= np[/tex]

And the variance :

[tex] Var(X)= np(1-p)[/tex]

The set of numbers that can represent the lengths of the sides of a triangle are 3,5,7. That is option B.

Triangle is defined as a type of polygon that has three sides in which the sum of both sides is greater than the third side.

That is to say, 3+5 = 8 is greater than the third side which is 7.

Therefore, the set of numbers the would represent a triangle are 3,5,7.

Learn more about triangle here:

https://brainly.com/question/17335144

#SPJ1

Answer:

1024/59049

Step-by-step explanation:

P( clear hurdle) = 2/3

There are 10 hurdles

P ( clear all hurdles) = P( clear hurdle) * P( clear hurdle)...... 10 times

                                 = 2/3 * 2/3 *....... 10 times

                                  = (2/3) ^ 10

                                  =1024/59049

Answer:

1024/59049, 1.7%

Step-by-step explanation:

One way to do it would to be simply multiply 2/3 by itself 10 times

2/3 x 2/3 x 2/3 x 2/3 and so on

That would be a really long equation so instead we can use exponents to shorten it. We can simply just do 2^10/3^10

2^10=1024

3^10=59049

1024/59049, 1.7%

Answer:

a

Step-by-step explanation:

that is the only thing there

16, think of 4 plus 4 plus 4 plus 4.

Answer:

99% confidence interval for the mean of college students

A) 112.48 < μ < 117.52

Step-by-step explanation:

step(i):-

Given sample size 'n' =150

mean of the sample = 115

Standard deviation of the sample = 10

99% confidence interval for the mean of college students are determined by

[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom

ν = n-1 = 150-1 =149

t₁₄₉,₀.₀₁ =  2.8494

99% confidence interval for the mean of college students are determined by

[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]

on calculation , we get

(115 - 2.326 , 115 +2.326 )

(112.67 , 117.326)  

[tex]\text{Find the distance from one corner to the other}\\\\\text{In this question, we would use the Pythagorean theorem to find the length}\\\text{between corners}\\\\\text{Pythagorean theorem:}\\\\a^2+b^2=c^2\\\\\text{We are trying to find c}\\\\\text{Plug in and solve:}\\\\7^2+6^2=c^2\\\\49+36=c^2\\\\85=c^2\\\\\text{Square root}\\\\\sqrt{85}=\sqrt{c^2}\\\\\sqrt{85}=c\\\\\text{In decimal form, it's: 9.219544}\\\\\text{Round to the nearest tenths place}\\\\\boxed{9.2\,\, feet}[/tex]

Answer:

-2/3

Step-by-step explanation:

2/3-4x+7/2 = -9x+5/6

Bring the x to one side and the numbers to the other:

5x = -2/3-7/2+5/6

5x = -20/6

x = -4/6

x = -2/3

Answer:

C

Step-by-step explanation:

write an equation for the costs:

if x is the number of sodas

and y is the number of waters

2.75x + 2y <= 15

(<= is less than or equal to)

if we substitute 3 for y

we get 2.75x + 2(3) <= 15

2.75x + 6 <= 15

2.75x <= 9

9 / 2.75 = 3.2727

however, you cannot buy part of a soda

so, round to 3

you also cannot buy negative sodas

so, the answer is C

Answer:

c. 0.40

Step-by-step explanation:

The probability that a student has an A or B in the class can be found by simply adding up the probabilities of both. Since 0.30 + 0.30 =0.60, the probability a student has an A or B is 0.60. Now to find the probability that they don't have a A or B is represented by 1-0.60, which equals 0.40, which is our answer.

The probability of receiving grade other than A or B is 0.60.

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

The probability of receiving A grade in class = 0.30

And probability of receiving B grade in class = 0.30

Probability of receiving grade A or B = 0.30 + 0.30 = 0.60

Let total probability is equal to 1.

The probability of receiving grade other than A or B = 1 - 0.60 = 0.40

The required probability is 0.40.

To know more about Probability on:

https://brainly.com/question/12478394

#SPJ5

Answer:

(a) 1.645

(b) 2.5758

Step-by-step explanation:

The complete question is: Find Z([tex]\alpha[/tex]/2) for the confidence level 90% and for the confidence level 99%.

Firstly, as we know that [tex]\alpha[/tex] represent the level of significance, i.e;

Level of significance = 1 - confidence level

(a) We are given the confidence level of 90%, so;

     Level of significance = 1 - 90%

                                         = 1 - 0.90 = 0.10 or 10%

Now, [tex]Z_(_\frac{\alpha}{2}_)[/tex] = [tex]Z_(_\frac{0.10}{2}_)[/tex] = [tex]Z_(_0_._0_5_)[/tex]

This means that we have to look for a critical value in the z table at a 5% level of significance which gives us a value of 1.645.

(a) We are given the confidence level of 99%, so;

     Level of significance = 1 - 99%

                                         = 1 - 0.99 = 0.01 or 1%

Now, [tex]Z_(_\frac{\alpha}{2}_)[/tex] = [tex]Z_(_\frac{0.01}{2}_)[/tex] = [tex]Z_(_0_._0_0_5_)[/tex]

This means that we have to look for a critical value in the z table at a 0.5% level of significance which gives us a value of 2.5758.

Answer: 35.0 units long.

Step-by-step explanation:

You can treat a rhombus as four right triangles, where there is a short side, a long side, and a hypotenuse.

The hypotenuse of a right triangle inside a rhombus will always be on the exterior.

To find the hypotenuse of one of the right triangles, use the Pythagorean theorem:

[tex]a^2 + b^2 = c^2[/tex]

We are given that a = 9 and b = 15, but in order to get the values needed for the theorem, we must divide them by 2 in order to get the sides for the triangles.

9 / 2 = 4.5, 15 / 2 = 7.5

Then, you can substitute your values into the Pythagorean theorem:

[tex]4.5^2 + 7.5^2 = c^2\\\\20.25 + 56.25 = 76.5\\\\c^2 = 76.5\\c = 8.7464[/tex]

Knowing that one of the external sides is 8.7464 units long, you can then multiply that value by 4 to get your perimeter, as there are four identical sides forming the perimeter:

8.7464 * 4 = 34.9856. Rounded: 35.0

Answer:

Step-by-step explanation:

Since there are  2 red and 5 white balls in the box, the total number of balls in the bag = 2+5 = 7balls.

Probability that at least 1 ball was​ red, given that the first ball was replaced before the second can be calculated as shown;

Since at least 1 ball picked at random, was red, this means the selection can either be a red ball first then a white ball or two red balls.

Probability of selecting a red ball first then a white ball with replacement = (2/7*5/7) = 10/49

Probability of selecting two red balls with replacement = 2/7*2/7 = 4/49

The probability that at least 1 ball was​ red given that the first ball was replaced before the second draw= 10/49+4/49 = 14/49

If the balls were not replaced before the second draw

Probability of selecting a red ball first then a white ball without replacement = (2/7*5/6) = 10/42 = 5/21

Probability of selecting two red balls without replacement = 2/7*2/6 = 4/42 = 2/21

The probability that at least 1 ball was​ red given that the first ball was not replaced before the second draw = 5/21+4/21 = 9/21 = 3/7

The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Since two balls are drawn in succession out of a box containing 2 red and 5 white balls, to find the probability that at least 1 ball was red, given that the first ball was A) replaced before the second draw; and B) not replaced before the second draw; the following calculations must be performed:

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Learn more about probability in https://brainly.com/question/14393430

Answer:

[tex]\chi^2 =\frac{15-1}{25} 16 =8.96[/tex]

The degrees of freedom are given by:

[tex] df = n-1 = 15-1=14[/tex]

The p value for this case would be given by:

[tex]p_v =P(\chi^2 <8.96)=0.166[/tex]

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes

Step-by-step explanation:

Information given

[tex]n=15[/tex] represent the sample size

[tex]\alpha=0.05[/tex] represent the confidence level  

[tex]s^2 =16 [/tex] represent the sample variance

[tex]\sigma^2_0 =25[/tex] represent the value that we want to  verify

System of hypothesis

We want to test if the true deviation for this case is lesss than 5minutes, so the system of hypothesis would be:

Null Hypothesis: [tex]\sigma^2 \geq 25[/tex]

Alternative hypothesis: [tex]\sigma^2 <25[/tex]

The statistic is given by:

[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]

And replacing we got:

[tex]\chi^2 =\frac{15-1}{25} 16 =8.96[/tex]

The degrees of freedom are given by:

[tex] df = n-1 = 15-1=14[/tex]

The p value for this case would be given by:

[tex]p_v =P(\chi^2 <8.96)=0.166[/tex]

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes

Answer:

270 centimeters

Step-by-step explanation:

A = wl

A = 15 cm x 18 cm

A = 270 centimeters

Answer: The point (-10,-20) becomes (-8,-16) & point (15,25) becomes (12,20).

Step-by-step explanation:

When a point (x,y) is dilated by a scale factor k from the origin, then the new points become

[tex](kx,ky).[/tex]

The given rule of dilation : (x,y) →(0.8x, 0.8y)

The first point is (-10,-20), so its image will be

[tex](-10,-20)\to (0.8\times-10,0.8\times-20)=(-8,-16)[/tex]

So, the point (-10,-20)  becomes (-8,-16).

The second point is (15,25), so its image will be

[tex](15,25)\to (0.8\times15,0.8\times25)=(12,20)[/tex]

So, the point (15,25) becomes (12,20).

Hence, the point (-10,-20) becomes (-8,-16) & point (15,25) becomes (12,20).

Answer:

DF and CG

Step-by-step explanation:

Two or more segments are said to be parallel is the angle between them is [tex]180^{0}[/tex]. While two segments are said to be perpendicular when the angle between them is [tex]90^{0}[/tex].

The given figure is a parallelogram. A parallelogram is a quadrilateral with a pair of parallel opposite sides.

In the given question if ∠ADH ≅ ∠ECK , then the parallel segment would be DF and CG.

Answer:

The series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Step-by-step explanation:

We are given with the following series options below;

a. 3, 5, 7, 9

b. 2, 4, 5, 8

c. 4, 6, 8,10

d. 2, 3, 4, 5

And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].

For this, we will put the values of n in the above expression and then will see which series is obtained as a result.

So, the given expression is ; [tex]X_n=2n+1[/tex]

If we put n = 1, then;

[tex]X_1=(2\times 1)+1[/tex]

[tex]X_1 = 2+1 = 3[/tex]

If we put n = 2, then;

[tex]X_2=(2\times 2)+1[/tex]

[tex]X_2 = 4+1 = 5[/tex]

If we put n = 3, then;

[tex]X_3=(2\times 3)+1[/tex]

[tex]X_3 = 6+1 = 7[/tex]

If we put n = 4, then;

[tex]X_4=(2\times 4)+1[/tex]

[tex]X_4 = 8+1 = 9[/tex]

Hence, the series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Answer:

3×^2+2

The product of three times a number is multiplied with the same product and added with 2.

Answer:

Option A

Step-by-step explanation:

Equation of the given quadratic function is,

y = 2x² + 8x + 3

y = 2(x² + 4x) + 3

  = 2(x² + 4x + 4 - 4) + 3

  = 2(x + 2)² - 8 + 3

  = 2(x + 2)² - 5

By comparing this equation with the equation of a quadratic function in vertex form,

y = a(x - h)² + k

Here (h, k) is the vertex of the parabola

Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)

Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.

Option (A). Graph A will be the answer.

Answer:

A.

Step-by-step explanation:

Multiply straight across:

[tex]\frac{2}{x+1}\cdot \frac{5}{3x}=\frac{10}{3x(x+1)}[/tex]

Simplify:

[tex]=\frac{10}{3x^2+3x}[/tex]

This cannot be simplified further.

Answer:

[tex] \boxed{\sf \frac{10}{3 {x}^{2} + 3x}} [/tex]

Step-by-step explanation:

[tex] \sf Expand \: the \: following: \\ \sf \implies \frac{2}{x + 1} \times \frac{5}{3x} \\ \\ \sf \implies \frac{2 \times 5}{3x(x + 1)} \\ \\ \sf 2 \times 5 = 10 : \\ \sf \implies \frac{ \boxed{ \sf 10}}{3x(x + 1)} \\ \\ \sf 3x(x + 1) = (3x)(x) + (3x)(1) : \\ \sf \implies \frac{10}{ \boxed{ \sf (3x)(x) + (3x)(1)}} \\ \\ \sf (3x)(x) = 3 {x}^{2} : \\ \sf \implies \frac{10}{ \boxed{ \sf 3 {x}^{2}} + (3x)(1) } \\ \\ \sf (3x)(1) = 3x : \\ \sf \implies \frac{10}{3 {x}^{2} + 3x} [/tex]

Answer:

14.  C   41

15. k = 72

Step-by-step explanation:

14.

For parallel lines, alternate exterior angles must be congruent.

3x - 43 = 80

3x = 123

x = 41

15.

The sum of the measures of the angles of a triangle is 180 deg.

k + 33 + 75 = 180

k + 108 = 180

k = 72

Answer:

1. 32

2. 41

3. 72

Step-by-step explanation:

Answer:

The expected number of bowerbirds in the sample that will have bower featuring reflective color is E(X)=0.9

Step-by-step explanation:

We can model this with a binomial random variable, with sample size n=3 and probability of success p=0.3.

[tex]p=X/n=6/20=0.3[/tex]

The expected number of bowerbirds in the sample that will have bower featuring reflective color can be calculated as:

[tex]E(X)=np=3\cdot 0.3=0.9[/tex]

Answer:

3/20

Step-by-step explanation:

15%

15/100

/5  /5

3/20

Step-by-step explanation:

the average change H = Δy/ Δx

so H = ( f(4) - f(2) )/ (4 -2) = ( 0 -1 ) / 2 = -1/2

Answer:

a) k=2.08 1/hour

b) The exponential growth model can be written as:

[tex]P(t)=Ce^{kt}[/tex]

c) 977,435,644 cells

d) 2.033 billions cells per hour.

e) 2.81 hours.

Step-by-step explanation:

We have a model of exponential growth.

We know that the population duplicates every 20 minutes (t=0.33).

The initial population is P(t=0)=58.

The exponential growth model can be written as:

[tex]P(t)=Ce^{kt}[/tex]

For t=0, we have:

[tex]P(0)=Ce^0=C=58[/tex]

If we use the duplication time, we have:

[tex]P(t+0.33)=2P(t)\\\\58e^{k(t+0.33)}=2\cdot58e^{kt}\\\\e^{0.33k}=2\\\\0.33k=ln(2)\\\\k=ln(2)/0.33=2.08[/tex]

Then, we have the model as:

[tex]P(t)=58e^{2.08t}[/tex]

The relative growth rate (RGR) is defined, if P is the population and t the time, as:

[tex]RGR=\dfrac{1}{P}\dfrac{dP}{dt}=k[/tex]

In this case, the RGR is k=2.08 1/h.

After 8 hours, we will have:

[tex]P(8)=58e^{2.08\cdot8}=58e^{16.64}=58\cdot 16,852,338= 977,435,644[/tex]

The rate of growth can be calculated as dP/dt and is:

[tex]dP/dt=58[2.08\cdot e^{2.08t}]=120.64e^2.08t=2.08P(t)[/tex]

For t=8, the rate of growth is:

[tex]dP/dt(8)=2.08P(8)=2.08\cdot 977,435,644 = 2,033,066,140[/tex]

(2.033 billions cells per hour).

We can calculate when the population will reach 20,000 cells as:

[tex]P(t)=20,000\\\\58e^{2.08t}=20,000\\\\e^{2.08t}=20,000/58\approx344.827\\\\2.08t=ln(344.827)\approx5.843\\\\t=5.843/2.08\approx2.81[/tex]

Answer:

The answer is below

Step-by-step explanation:

We have the following information:

Number of songs you like = 2

Total number of songs = 12

a) P(you like both of them) = 2/12 x 1/11 = 0.015

This is unusual because the probability of the event is less than 0.05

b) P(you like neither of them) = 10/12 x 9/11  = 0.68

c) P(you like exactly one of them) = 2 x 2/12 x 10/11 = 0.30

d) If  a song can be replayed before all 12,

P(you like both of them) = 2/12 x 2/12  =0.027

This is unusual because the probability of the event is less than 0.05

P(you like neither of them) = 9/12 x 9/12  = 0.5625

P(you like exactly one of them) = 2 x 2/12 x 9/12 = 0.25