17 women and 3 men attend a family reunion. What is the percentage of men with respect to the total number of parents?
1. 3%
2. 15%
3. 16%
4. 17%

Answer:

m∠N = 51°

m∠M = 31°

m∠O = 98°

Step-by-step explanation:

It is given that ΔMNO is an isosceles triangle with base NM.

m∠N = (4x + 7)° and m∠M = (2x + 29)°

By the property of an isosceles triangle,

Two legs of an isosceles triangle are equal in measure.

ON ≅ OM

And angles opposite to these equal sides measure the same.

m∠N = m∠M

(4x + 7) = (2x + 29)

4x - 2x = 29 - 7

2x = 22

x = 11

m∠N = (4x + 7)° = 51°

m∠M = (2x + 9)° = 31°

m∠O = 180° - (m∠N + m∠M)

         = 180° - (51° + 31°)

         = 180° - 82°

         = 98°

Answer:

probability that all of the sprinklers will operate correctly in a fire: 0.0282

Step-by-step explanation:

In order to solve this question we will use Binomial  probability distribution because:

A binomial distribution is a probability of a success or failures outcomes in an  repeated multiple or n times.

Number of outcomes of this distributions are two.

The formula is:

b(x; n, P) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

b = binomial probability  also represented as P(X=x)

x =no of successes

P = probability of a success on a single trial

n = no of trials

[tex]C_{n,x}[/tex] is calculated as:

[tex]C_{n,x}[/tex] = n! / x!(n – x)!

        = 10!  / 10!(10-10)!

        = 1

According to given question:

probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.

number of trials i.e. n = 10 as number of sprinklers are 10

To find: probability that all of the sprinklers will operate correctly in a fire

X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them

So putting these into the formula:

P(X=x) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

           = C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰

           =  1 * 0.0282 * (0.3) ⁰

           = 1 * 0.0282 * 1

  P(X=x)        = 0.0282

Answer:

Step-by-step explanation:

3(−2a - 4)+3a

=-6a - 12 +3a

A: -6a - 12 +3a

[tex]hope \: this \: helps[/tex]

Answer:

the answer is A

Step-by-step explanation:

you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a

Answer:

3.54%

Step-by-step explanation:

This question represents a binomial distribution. A binomial distribution is given by:

[tex]P(x)=\frac{n!}{(n-x)!x!} p^xq^{n-x}[/tex]

Where n is the total number of trials, p is the probability of success, q is the probability of failure and x is the number of success.

Given that:

A basketball player scores 70% of his shots on average, therefore p = 70% = 0.7. Also q = 1 - p = 1 - 0.7 = 0.3.

The total number of trials (n) = 20 shots

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20)

P(x = 18) = [tex]\frac{20!}{(20-18)!18!}*0.7^{18}*0.3^{20-18}=0.0278[/tex]

P(x = 19) = [tex]\frac{20!}{(20-19)!19!}*0.7^{19}*0.3^{20-19}=0.0068[/tex]

P(x = 20) = [tex]\frac{20!}{(20-20)!20!}*0.7^{20}*0.3^{20-20}=0.0008[/tex]

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20) = 0.0278 + 0.0068 + 0.0008 = 0.0354 = 3.54%

Answer:

0

Step-by-step explanation:

Solution:-

We are given two functions as follows:

                      [tex]f ( x ) = x^2 - 15\\\\g ( x ) = 2x[/tex]

We need to determine the composite function defined as ( g - f ) ( x ). To determine this function we need to make sure that both function exist for all real positive value of x.

The function f ( x ) is a quadratic function which has real values for all values of x. Similarly, function g ( x ) is a linear line that starts from the origin. Hence, both functions are defined over the domain ( -∞, ∞ )

We will perform arithmetic operation of subtracting function f ( x ) from g ( x ) as follows:

                       [tex][ g - f ] ( x ) = g ( x ) - f ( x )\\\\\\( g - f ) ( x ) = x^2 - 15 - 2x\\\\[/tex]

Now evaluate the above determined function at x = -3 as follows:

                       [tex]( g - f ) ( -3 ) = ( -3 )^2 - 2 ( -3 ) - 15\\\\( g - f ) ( -3 ) = 9 + 6 - 15\\\\( g - f ) ( -3 ) = 0[/tex]

Answer:

[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]

which agrees with the first answer in the list of possible options.

Step-by-step explanation:

We can use the fact that the addition of all four internal angles of a quadrilateral must render [tex]360^o[/tex]. Then we can create the following equation and solve for the unknown "h":

[tex]2h+2h+h+h = 360^o\\6h=360^o\\h=60^o[/tex]

Therefore the angles of this quadrilateral are:

[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]

Answer:60,60,120,120

Step-by-step explanation:All qualdrilaterals equal to 360, so if you add all of the different numbers you should get 360

Answer:

5:1

Step-by-step explanation:

20/4= 5

1*5 = 5

5:1 ratio

Hope this helps!

The graph shows f(x) to have a y intercept at -1, which is where the diagonal line crosses the y axis. We want the y intercept to move to 3. So we must add 4 to the old y intercept to get the new y intercept.

We do this with every single point on f(x) to get g(x) = f(x)+4. This shifts the graph up 4 units.

Answer:

Option d: The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

The data are continuous if they can take on any value within a range. In this case study, there are different elephants including small/young ones and big ones/old ones.

Thus, their heights will vary and can take on any value within a particular range.

Answer:

Step-by-step explanation:

We assume you are not interested in five infinite sets of translations. Rather, we assume you want to pick 5 translations from the infinite set of possibilities.

The attached graph shows f(x), g(x), and 5 lines (dashed or dotted) that represent possible reflections and shifts of the function f(x).

The function f1 represents a reflection of f(x) about the x-axis, followed by a left-shift of 6 units. To make it match g(x), we need to shift it upward 4 units. Then the set if translations is ...

  g(x) = f(x) ... {reflected over the x-axis, shifted left 6, shifted up 4}

Along the same lines, other possibilities are ...

  g(x) = f(x) ... {reflected over the x-axis, shifted left 3, shifted up 3}

  g(x) = f(x) ... {reflected over the x-axis, shifted left 0, shifted up 2}

  g(x) = f(x) ... {reflected over the x-axis, shifted right 3, shifted up 1}

  g(x) = f(x) ... {reflected over the x-axis, shifted right 9, shifted down 1}

___

Additional comment

All of the transformations listed above use reflection in the x-axis. Reflection could use the y-axis, as well. Reflection of the basic function f(x) in the y-axis will have the identical effect as reflection in the x-axis. The listed translations would apply unchanged.

Explanation:

1. CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC — given

2. ∆CRH ~ ∆HSC — AA similarity theorem

3. ∠SCH ≅ ∠RHC — corresponding angles of similar triangles are congruent

4. CH ≅ HC — reflexive property of congruence

5. ∆CRH ≅ ∆HSC — SAS congruence theorem

6. CR ≅ HS — CPCTC

Answer:

30

Step-by-step explanation:

We can call the number of boys 4x and girls 6x so we can write:

4x + 6x = 50

10x = 50

x = 5, therefore the number of girls is 6x = 6 * 5 = 30.

Answer:

30

Step-by-step explanation:

In the ratio 4:6, we can think of this like 4 boys and 6 girls out of 10 team members.

We can find how many girls play by multiplying 6 by 5, since 50 divided by 10 is 5.

6(5) = 30, so 30 girls play in the soccer league.

Answer:

y=9x

Step-by-step explanation:

rise over run the rise is the y=9 and run is x=1.

9/1=9x

Answer:

Step-by-step explanation:

Let x represent the number of pounds of chocolate in the mix. Then the total price of 10 pounds of mix is ...

  10x +5(10 -x) = 80

  5x +50 = 80

  5x = 30

  x = 6 . . . . . . . . pounds of chocolate

  10 -x = 4 . . . . . pounds of jelly candy

6 pounds of chocolate and 4 pounds of jelly should be used to make the mixture.

Stokes' theorem equates the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation

[tex]x^2+z^2=16[/tex]

Parameterize this circle by

[tex]\mathbf r(t)=4\cos t\,\mathbf i+4\sin t\,\mathbf k[/tex]

with [tex]0\le t\le2\pi[/tex].

The surface is oriented such that its normal vector points in the positive y direction, which corresponds to the curve having counterclockwise orientation. The parameterization we're using here already takes this into account.

Now compute the line integral of F along C :

[tex]\displaystyle\iint_S\mathrm{curl}\mathbf F(x,y,z)\cdot\mathrm d\mathbf S=\int_C\mathbf F(x,y,z)\cdot\mathrm d\mathbf r[/tex]

[tex]=\displaystyle\int_0^{2\pi}\mathbf F(4\cos t,0,4\sin t)\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}(4\sin t\,\mathbf i+4\cos t\,\mathbf j)\cdot(-4\sin t\,\mathbf i+4\cos t\,\mathbf k)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}-16\sin^2t\,\mathrm dt[/tex]

[tex]=-8\displaystyle\int_0^{2\pi}(1-\cos(2t))\,\mathrm dt=\boxed{-16\pi}[/tex]

Line integral of F along C is,

[tex]\rm \int \int_S curl F(x,y,z) dS = -16\pi[/tex]

Step-by-step explanation:

Given :

Hemisphere -   [tex]x^2 +y^2+z^2=16[/tex]

Calculation :

Accordind to Stoke's theorem the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation

[tex]x^2+z^2=16[/tex]

then parameterize the circle,

[tex]\rm r(t) = 4 cos(t) \;\hat{i} + 4 sin(t)\;(\hat{k})[/tex]

with , [tex]0\leq t\leq 2\pi[/tex]

Line integral of F along C is,

[tex]\rm \int \int_S curl F(x,y,z) dS = \int_{C}^{} F(x,y,z) \;dr[/tex]

[tex]= \int_{0}^{2\pi} F(4cos(t),0,4sin(t)) \;\dfrac{dr}{dt}.dt[/tex]

[tex]= \int_{0}^{2\pi}(4sin(t)i+4cos(t) j).(-4sin(t)i+4cos(t)k) \;dt[/tex]

[tex]= \int_{0}^{2\pi} -16sin^2tdt[/tex]

[tex]=-8 \int_{0}^{2\pi} (1-cos(2t))dt[/tex]

[tex]= -16\pi[/tex]

For more information, refer the link given below

https://brainly.com/question/8130922?referrer=searchResults

Answer: 0.045 is the growth rate.

Step-by-step explanation:

A generic exponential growth function can be written as:

f(t) = A*(1 + r)^t

where A is the initial amount.

t is the unit of time.

r is the rate of growth.

For example if we have an increase of 10% per year, with an initial population of 100 we have that:

A = 100, r = 10%/100% = 0.10, t = number of years.

the equation will be:

f(t) = 100*(1 + 0.10)^t

Now, in this case the equation is:

S(t) = 152*(1.045)^t

We can write this as:

S(t) = 152*(1 + 0.045)^t

Then 152 is the initial amount and 0.045 is the growth rate.

hii

Step-by-step explanation:

length-10x

width-x

perimeter-2(l+b)

66=2(10x+x)

66-2=10x+x

64=11x

x=11/64

lenght-11

width-64

Answer: The answer is two

Step-by-step explanation: If you look for opposites of a number its either negative or positive. So when the answer is negative, the opposite is positive and if the answer is positive, the opposite is negative.

Answer:

[tex]\boxed{2}[/tex]

Step-by-step explanation:

The opposite of a number is the number that is the same distance from 0 on the number line.

-2 opposite is 2.

Answer:

54.5 years.

Step-by-step explanation:

From the above question, we are asked to find the time

The formula for Time(t) =

t = log(A/P) / n[log(1 + r/n)]

A = Amount accumulated after a particular interest and period of time = $80,000

P = Principal (Money invested) = $4,000

r = rate = 5.5% = 0.055

n = compounding frequency = compounding continuously

n = number of days in a year × number of hours in a day

= 365 days × 24 hours = 8760

t = log(A/P) / n[log(1 + r/n)]

t = log(80,000/4,000) /8760[log(1 + 0.055/8760)]

t = log(80000 ÷ 4000) ÷ (8760 × [log(1 + 0.0000062785)]

t = 54.468367222 years

Approximately to the nearest tenth of a year, therefore, the length of time it will it take for his money to reach $80,000 is 54.5 years

Answer:

54.5

Step-by-step explanation:

Answer:

Problem 1: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2: We conclude that the volume of Google stock has changed.

Step-by-step explanation:

Problem 1:

We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.

Let p = proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%    {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}

Alternate Hypothesis, [tex]H_A[/tex] : p > 50%     {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}

This is a right-tailed test.

The test statistics that would be used here is One-sample z-test for proportions;

                       T.S.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of adult Americans who were worried about having enough saved for retirement = [tex]\frac{156}{295}[/tex] = 0.53

           n = sample of adult Americans = 295

So, the test statistics =  [tex]\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }[/tex]

                                    =  1.03

The value of z-test statistics is 1.03.

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

              P-value = P(Z > 1.03) = 1 - P(Z [tex]\leq[/tex] 1.03)

                           = 1 - 0.8485 = 0.1515

Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2:

We are given that a random sample of 35 trading days in 2014 resulted in a  sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.

Let [tex]\mu[/tex] = mean daily volume in Google stock

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 5.44 million shares    {means that the volume of Google stock has not changed}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 5.44 million shares     {means that the volume of Google stock has changed}

This is a two-tailed test.

The test statistics that would be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                       T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean volume in Google stock = 3.28 million shares

            s = sample standard deviation = 1.68 million shares

           n = sample of trading days = 35

So, the test statistics =  [tex]\frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }[/tex]  ~ [tex]t_3_4[/tex]

                                    =  -7.606

The value of t-test statistics is -7.606.

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

              P-value = P([tex]t_3_4[/tex] < -7.606) = Less than 0.05%

Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of t, so we sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the volume of Google stock has changed.

Answer:

[tex]\boxed{Area\ of\ sector = 141.4\ cm^2}[/tex]

Step-by-step explanation:

Radius = r = 9 cm

Angle = θ = 200° = 3.5 radians

Now,

[tex]Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]

Area = 1/2 (9)²(3.5)

Area = 1/2 (81)(3.5)

Area = 282.7 / 2

Area of sector = 141.4 cm²

Answer:

45 pi cm^2 or 141.3 cm^2

Step-by-step explanation:

First find the area of the circle

A = pi r^2

A = pi (9)^2

A = 81 pi

A circle has 360 degrees

The shaded part has 200

The fraction that is shaded is

200/360 =5/9

Multiply by the total area

5/9 * 81 pi

45 pi

Using 3.14 for pi

141.3

45 pi cm^2 or 141.3 cm^2

Answer:

x=8

Step-by-step explanation:

[tex]\sqrt{x+8}-\sqrt{x-4}=2\\\sqrt{x+8}=2+\sqrt{x-4}\\\left(\sqrt{x+8}\right)^2=\left(2+\sqrt{x-4}\right)^2\\x+8=x+4\sqrt{x-4}\\8=4\sqrt{x-4}\\8^2=\left(4\sqrt{x-4}\right)^2\\64=16x-64\\x=8[/tex]

The true statement about the given transformation is; B: It is a dilation because the transformation is not isometric.

An isometric transformation is a shape-preserving transformation in the plane or in space. They include reflection, rotation and translation.

Now, from the given attachment showing the two figures, we can see that there is a dilation which means that it can't be isometric as the definition of Isometric transformation does not include Dilation.

Read more about Transformation at; https://brainly.com/question/4289712

#SPJ5

Answer:

b

Step-by-step explanation:

just took the test

Answer:

[tex]\dfrac{21}{10}\text{ km}[/tex].

Step-by-step explanation:

It is given that,

Area of rectangular plot [tex]=\dfrac{7}{10}\text{ km}^2[/tex]

Width of rectangular plot [tex]=\dfrac{1}{3}\text{ km}[/tex]

We need to find the length of the parking lot.

We know that,

[tex]\text{Area of rectangle}=length\times width[/tex]

[tex]\dfrac{7}{10}=length\times \dfrac{1}{3}[/tex]

[tex]\dfrac{7\times 3}{10}=length[/tex]

[tex]length=\dfrac{21}{10}[/tex]

Therefore, length of the parking lot is [tex]\dfrac{21}{10}\text{ km}[/tex].

Answer:

84π mm^2

Step-by-step explanation:

formula for circumference is 2πr where r is the radius of circle

Given,The circumference of the base of a cylinder is 24π mm

Thus,

2πr= 24π mm

=> r = 24π mm/2π = 12 mm

________________________________________

A similar cylinder has a base with circumference of 60π mm.

radius for this cylinder will be

2πr= 60π mm

r =   60π mm/2π = 30mm

______________________________________________

Given

The lateral area of the larger cylinder is 210π mm2

lateral area of cylinder is given by  2πrl

where l is the length of cylinder

thus,

r for larger cylinder = 30mm

2π*30*l  = 210π mm^2

=> l = 210π mm^2/2π*30 = 3.5 mm

___________________________________________

the lateral area of the smaller cylinder

r = 12 mm

l = 3.5 mm as both larger and smaller cylinder are same

2πrl  =  2π*12*3.5 mm^2 = 84π mm^2 answer

Answer:

33.6pi mm2 is the correct answer

edge 2021

Step-by-step explanation:

The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2.

What is the lateral area of the smaller cylinder?

17.1π mm2

33.6π mm2

60π mm2

84π mm2

Answer:

A. 1.812

B. 1.753

C. 2.602

D. 3.747

E. 2.069

F. 2.453

Step-by-step explanation:

A. 95% confidence level, the level of significance = 5% or 0.05

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 10 degrees of freedom = 1.182

B. 95% confidence interval = 0.05 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 15 degrees of freedom = 1.753

C. 99% confidence interval = 0.01 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 15 degrees of freedom = 2.602

D. 99% confidence interval = 0.01 level of significance; DF (n - 1) = 5- 1 = 4

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 4 degrees of freedom = 3.747

E. 98% confidence interval = 0.02 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.02 significance level with 23 degrees of freedom = 2.069

F. 99% confidence interval = 0.01 level of significance; df (n - 1) = 32 - 1 = 31

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 31 degrees of freedom = 2.453

Answer:

[tex]\dfrac{15}{16}[/tex]

Step-by-step explanation:

When a six sided die is rolled, the possible outcomes can be:

{1, 2, 3, 4, 5, 6}

Even numbers are {2, 4, 6}

Odd Numbers are {1, 3, 5}

Probability of even numbers:

[tex]\dfrac{\text{Favorable cases}}{\text{Total cases }} = \dfrac{3}{6} = \dfrac{1}{2}[/tex]

This is binomial distribution.

where probability of even numbers,  [tex]p =\frac{1}{2}[/tex]

Probability of not getting even numbers (Getting odd numbers) [tex]q =\frac{1}{2}[/tex]

Probability of getting r successes out of n trials:

[tex]P(r) = _nC_r\times p^r q^{n-r}[/tex]

Probability of getting even numbers at most 5 times out of 7 is given as:

P(0) + P(1) +P(2) + P(3) +P(4) + P(5)

[tex]\Rightarrow _7C_0\times \frac{1}{2}^0 \frac{1}{2}^{7}+_7C_1\times \frac{1}{2}^1 \frac{1}{2}^{6}+_7C_2\times \frac{1}{2}^2 \frac{1}{2}^{5}+_7C_3\times \frac{1}{2}^3 \frac{1}{2}^{4}+_7C_4\times \frac{1}{2}^4 \frac{1}{2}^{3}+_7C_5\times \frac{1}{2}^5 \frac{1}{2}^{2}[/tex]

[tex]\Rightarrow (\dfrac{1}{2})^7 (_7C_0+_7C_1+_7C_2+_7C_3+_7C_4+_7C_5)\\[/tex]

[tex]\Rightarrow (\dfrac{1}{2})^7 (1+7+\dfrac{7 \times 6}{2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6}{2})\\\Rightarrow \dfrac{120}{128} \\\Rightarrow \dfrac{15}{16}[/tex]

Answer:

Step-by-step explanation:

Assuming the colon between 40 and 8 is a mistype...

PEMDAS(Parenthesis, Exponents, Multiplication + Division, Addition + Subtraction)

[tex]40-8+3^2+(15-7)*2\\\\Parenthesis\\\\40-8+3^2+8*2\\\\Exponents\\\\40-8+9+8*2\\\\Multiplication\\\\40-8+9+16\\\\Subtraction\\\\32+9+16\\\\Addition\\\\41+16\\\\Addition\\\\57[/tex]

Hope it helps <3

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▹ Answer

57

▹ Step-by-Step Explanation

You need to follow PEMDAS:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

40 - 8 + 3² + (15 - 7)* 2

40 - 8 + 9 + (15 - 7) * 2

40 - 8 + 9 + 8 * 2

40 - 8 + 9 + 16

= 57

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Step-by-step explanation:

Given that :

The mean value [tex]\mu[/tex] = 12

The standard deviation [tex]\sigma[/tex] = 3.5

Let Consider Q to be the weight of the parcel that is normally distributed .

Then;

Q [tex]\sim[/tex] Norm(12,3.5)

The objective is to determine thewight  value of c under which there is a surcharge

Also, let's not that 99% of all the parcels are below the surcharge

However ;

From the Percentiles table of Standard Normal Distribution;

At 99th percentile; the value for Z = 2.33

The formula for the Z-score is:

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

[tex]2.33 = \dfrac{X - 12}{3.5}[/tex]

2.33 × 3.5 = X - 12

8.155 = X - 12

- X = - 12 - 8.155

- X = -20.155

 X = 20.155

the weight  value of c under which there is a surcharge = X + 1 (0) since all the  pounds are below the surcharge

c = 20.155 + 1(0)

c = 20.155

Thus ; the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Answer:

72°

Step-by-step explanation:

Given two vectors a and b, The vector i+3j will form a right angled triangle with the x-axis (i.e the horizontal axis).

The opposite side of the triangle on the Cartesian plane will be 3units along the y axis while the adjacent will be 1 unit along the x axis.

The angle between thus two vectors is expressed as tan (theta) = opp/adj

tantheta = 3/1

theta = tan^-1(3)

Theta = 71.57° ≈ 72° to nearest degree