in the diagram, POS and UOR are straight lines. OQ is the bisector of angle POR . angle POU and angle UOT are complementary angles.Find the values ofx abd y.​

Answer:

48 soldiers

Step-by-step explanation:

60 soldiers                    20 days

x soldiers                       100 days

60 x 20 = 1200 = 100x

Therefore x = 1200/100 = 12

60 - 12 = 48

Hope that helped!!! k

Answer:

30 Soldiers

Step-by-step explanation:

Given:

1) No of soldiers=60

No of days=20

2) No of days=100

No of soldiers=?

No of soldiers to leave=?

Solution:

Let us use the cross multiplication method.

Let x be the no of soldiers.

No of days                                     No of  soldiers

1) 20                                                     60

2) 100                                                    x

by cross multiplying,

20x=100 x 60

20x=600

x=600/20

x=30 soldiers

Therefore, No of soldiers to leave =60-30=30 soldiers

Answer:

i am having issues using the math editor and my time is almost running out. i added an attachment.

Step-by-step explanation:

Step-by-step explanation:

When θ is very small, θ ≈ sin θ ≈ tan θ.

θ (sin θ)² / (2 tan θ)

θ³ / (2θ)

θ² / 2

Answer:

29 years of experience.

Step-by-step explanation:

So let's take the expression step by step.  Remember that you need to follow the order of precedence here for the operations.  Parentheses, exponentials, multiplication, and addition.

-5 + { 4 * 6 + 3 + 1 + [ 3 - ( 4 - 8 ) + ( 3 - 2 ) ] }

-5 + { 4 * 6 + 3 + 1 + [ 3 - ( -4 ) + ( 1 ) ] }

-5 + { 4 * 6 + 3 + 1 + [ 3 + 4 + 1 ] }

-5 + { 4 * 6 + 3 + 1 + [ 8 ] }

-5 + { 24 + 3 + 1 + 8 }

-5 + { 36 }

29

So the teacher has 29 years of experience.

Cheers.

Answer:

Sample size n [tex]\simeq[/tex] 1269.15

Step-by-step explanation:

From the information given ,

At 99% of confidence interval,

the level of significance ∝ = 1 - 0.99

the level of significance ∝ =  0.01

the critical value for 99% of confidence interval is:

[tex]\mathtt{\dfrac{\alpha }{2} = \dfrac{0.01}{2}}[/tex]

= 0.005

[tex]\mathtt {z_{\alpha/2} = z_{0.005/2} }[/tex]

The value for z from the standard normal tables

= 2.58

The Margin of error E= 3% = 0.03

The formula to  determine the sample size n used can be expressed as follows:

[tex]\mathtt { n = (\dfrac{z_{\alpha/2}}{E})^2 \ \hat p (1 - \hat p) }[/tex]

where;

[tex]\mathtt{\hat p }[/tex] = 22% = 0.22

Then:

[tex]\mathtt { n = (\dfrac{2.58}{0.03})^2 \ \times 0.22 \times (1 - 0.22) }[/tex]

[tex]\mathtt { n = (86)^2 \ \times 0.22 \times (0.78) }[/tex]

[tex]\mathtt { n = 7396 \ \times 0.22 \times (0.78) }[/tex]

n = 1269.1536

Sample size n [tex]\simeq[/tex] 1269.15

Answer:

-5 ≤x ≤6

Step-by-step explanation:

The domain is the values that x can take

X goes from -5 and includes -5 to x =6 and includes 6

-5 ≤x ≤6

Answer:

See attached!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Two events A and B are said to be independent if the occurrence of one of the events does not affect the other occurring. For example, the event of tossing two coins is an independent event since they occur simultaneously. Two events are therefore independent if the following are true.

P(A|B) = P(A)

P(B|A) = P(B)

P(A and B) = P(A)P(B)

If A and B are independent events with P( A) = 0.35 and P( B) = 0.55,

then P( A| B) is a probability of A occurring provided that B has occurred. This is known as conditional probability for an independent event.

From the condition above for independent events, P(A|B) = P(A) and since P(A) =  0.35, hence P(A|B) =0.35

Answer:

it is clear that at 95% confidence that the bonus plan has increased the sales significantly, because if we observe you will notice that sales after is greater than sales before in all six cases.

Step-by-step explanation:

A 95% confidence interval as we have above is the range of values that we can say with utmost certainty and confidence that 95% chance it contains the true mean of the population. in other words we can say that a  95% confidence interval defines a range of values that you can be 95% certain contains the population mean.

Answer:

C) A only

Step-by-step explanation:

In statistics, the null hypothesis is the default hypothesis and the alternative hypothesis is  the research hypothesis. The alternative hypothesis usually comes in place to challenge the null hypothesis in order to determine if the test is statistically significant or not.

Similarly,

In hypothesis testing, the confidence interval consist of all reasonable value of the population mean. Values for which the null hypothesis will be rejected [tex]H_o[/tex] .

Given that:

At 95% confidence interval for the  difference between the population means is (1.4, 8.7).

The level of significance = 1 - 0.95 = 0.05  = 5%

So , If the hypothesis test is based on the same samples, The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.

Answer:

27.5

Step-by-step explanation:

3 = 7.5

4 = 10

5*7.5=37.5-10=27.5

Seriously. 2=5 contradicts.

the answer is 667.

100/x = 15/100

it’s a proportion so you cross multiply. after cross multiplying you get 15x = 10,000. divided both sides by 15 and you get x = 66.6 (continuation of the 6). since it’s repeating, round it and you get 667.

by the way this is actually one of my homework questions for today ;)

The predicted number of butterflies that starts from Kansas and Missouri and migrate to Mexico is 667.

The Aim of the experiment is to measure the Monarch butterfly migration

Predicting the number of butterflies

= [tex]\frac{100}{x} = \frac{15}{100}[/tex]

= [tex]15x = ( 100 * 100)[/tex]

∴ x( predicted value ) = [tex]\frac{10000}{15 } = 667[/tex]

hence the approximate value of the number of butterflies that migrate to Mexico from Kansas and Missouri is  667

learn more about migration : https://brainly.com/question/23903333

Answer:

14M

Step-by-step explanation:

7*2*M

14*M

14M

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

        ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                       PEACE!

Answer:

Null hypothesis: μ = 407

Alternative hypothesis: μ < 407.

Step-by-step explanation:

In this case, the machine is SUPPOSED to fill the bag so that the bag weighs 407 grams. So, the null hypothesis will be that the machine is doing what it is supposed to be doing. And so, μ = 407 grams would be the null.

The worker thinks the machine is filling the bags to LESS THAN what it is supposed to. So, the alternative hypothesis is that the machine is NOT doing what it is supposed to and μ < 407 grams.

Hope this helps!

Answer:

8.66 years

Step-by-step explanation:

Given that:

Interest rate = 8%

Using the exponential growth function:

A = Ao * e^(rt)

Where A = final amount

Ao = Initial amount

r = growth rate

t = time

Here we are to calculate the time it takes an investment earning 8% interest to double;

rate (r) = 8% = 0.08

2A = A * e^(rt)

Divide both sides by A

2 = e^(rt)

2 = e^(0.08 * t)

2 = e^(0.08t)

In(2) = 0.08t

0.6931471 = 0.08t

Divide both sides by 0.08

0.6931471 / 0.08 = 0.08t / 0.08

8.6643397 = t

t = 8.66 years

Answer:

symbolically, the answer would be t= ln(2)/(.08)

Step-by-step explanation:

start by writing out your variables:

rate= .08

*dont forget the investment doubles too, thats where 2P is in the bottom equation

equation should look like:

[tex]2P=Pe^{.08t}[/tex]

then you solve, so divide P on the right and left:

[tex]\frac{2p}{p} = \frac{Pe^{.08t}}{p}[/tex]

now it looks like: [tex]2=e^{.08t}[/tex]

you can take the natural log (ln) of 2 to get the exponent by itself .08t

ln(2)=.08t

then divide .08 to get t by itself

[tex]\frac{ln(2)}{.08} =\frac{.08t}{.08}[/tex]

so symbolically, your equation should be:

[tex]t=\frac{ln(2)}{.08}[/tex]

to get t as your answer you can plug this equation into your calculator to get:

t=8.66 years so approximently 8 years

Answer:

126°

Step-by-step explanation:

If that angle is 27, so is angle a.

180-27-27=126

Answer:

x^6 y^3

Step-by-step explanation:

(x²y)³

We know that (ab) ^c = a^c * b^c

(x²y)³ = x^2 ^3  * y^3

We know that a^b^c = a^(b*c)

(x²y)³ = x^2 ^3  * y^3 = x^( 2*3) y^3 = x^6 y^3

Answer:

Diameter of wheel in millimetres is 660.4

Step-by-step explanation:

Diameter of wheel in inches = 26

given

1 inch = 25.4 millimeters

multiplying RHS and LHS by 26

26*1 inch = 26*25.4 millimeters

=>26 inch = 660.4 mm.

Thus, diameter of wheel in millimetres is 660.4

Answer:

Step-by-step explanation:

Hello, I assume that you mean

[tex]x^2-5x-36[/tex]

The product is -36.

[tex]x_1 \text{ and } x_2 \text{ are the two roots, we can write}\\\\(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2[/tex]

So in this example, it means that the sum is 5 and the product is -36.

Thank you

Answer:

88 if a rectangular prism, 64 based on the net.

Step-by-step explanation:

A = 4 * 2

B = 6 * 2

C = 4 * 2

D = 6 * 2

E = 6 * 4

A/C= 8

B/D= 12

E = 24

2(8) + 2(12) + 24 = 64

Surface Area: 64

However, a rectangular prism must have 6 faces, so unless this is a box, the answer would be 88, and E = F, the last face.

Answer:

Step-by-step explanation:

If there are 30 students in a class with natasha in the class and natasha is to select four leaders in the class of which she is already part of the selection, this means there are 3 more leaders needed to be selected among the remaining 29 students (natasha being an exception).

Using the combination formula since we are selecting and combination has to do with selection, If r object are to selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

Sinca natasha is to select 3 more leaders from the remaining 29students, this can be done in 29C3 number of ways.

29C3 = 29!/(29-3)!3!

29C3 = 29!/(26!)!3!

29C3 = 29*28*27*26!/26!3*2

29C3 = 29*28*27/6

29C3 = 3,654 different ways.

This means that there are 3,654 different ways to select the 4 leaders so that natasha is one of the leaders

Answer:

This list of all the outcome of  [tex]E^c[/tex] is  [tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]

 [tex]P(E^c ) = 0.5[/tex]

Step-by-step explanation:

From the question we are told that

      The sample sample space is  [tex]S = \{ 1,2,3,4,5,6,7,8,9,10,11,12 \}[/tex]

       The number of elements in the sample space is [tex]n = 12[/tex]

        The event is  [tex]E = \{ 3,4,5,6,7,8 \}[/tex]

        The  number of outcomes in the Event is  [tex]n_e = 6[/tex]

The objective in to obtain [tex]P(E^c)[/tex]

 Now  [tex]E^c[/tex]  is the compliment of  E  and number of elements in [tex]E^c[/tex] ican be mathematically evaluated as

            [tex]nE^c = n - n_e[/tex]

substituting values

            [tex]E^c = 12-6[/tex]

             [tex]E^c = 6[/tex]

This list of all the outcomes of [tex]E^c[/tex] is

        [tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]

Generally  [tex]P(E^c )[/tex]  which is the probability of  [tex]E^c[/tex] is mathematically evaluated  as

      [tex]P(E^c ) = \frac{nE^c}{n}[/tex]

substituting values

         [tex]P(E^c ) = \frac{6}{12}[/tex]

         [tex]P(E^c ) = 0.5[/tex]

Answer:

i [tex]\to[/tex] a

    [tex]n = 96040000[/tex]

i [tex]\to[/tex] b

    [tex]n_1 =24010000[/tex]

i [tex]\to[/tex] c

    [tex]n_2 =41602500[/tex]

ii[tex]\to[/tex]a

     [tex]E = 58.16[/tex]

ii[tex]\to[/tex]b

    [tex]291.84 < \mu < 408.16[/tex]\

ii[tex]\to[/tex]c

    There is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval

Step-by-step explanation:

From the question we are told that

     The sample size is [tex]n = 8[/tex]

      The sample mean is  [tex]\= x = \$ 350[/tex]    

      The sample standard deviation is  [tex]\$ 100[/tex]

Considering question i

    i [tex]\to[/tex] a

         At   [tex]E = 0.02[/tex]  

given that the confidence level is 95%  =  0.95

         the level of significance would be  [tex]\alpha =1-0.95 = 0.05[/tex]

The critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

        [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

So  the sample size is mathematically evaluated as

            [tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]

=>        [tex]n =[ \frac{ 1.96 * 100}{ 0.02} ]^2[/tex]

=>         [tex]n = 96040000[/tex]

 i [tex]\to[/tex] b

  At  [tex]E_1 = 0.04[/tex]    and  confidence level  = 95%  =>  [tex]\alpha_1 = 0.05[/tex]   =>  [tex]Z_{\frac{\alpha_1 }{2} } = 1.96[/tex]

             [tex]n_1 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_1} ]^2[/tex]

=>           [tex]n_1 =[ \frac{ 1.96 * 100}{ 0.04} ]^2[/tex]

=>           [tex]n_1 =24010000[/tex]

 i [tex]\to[/tex] c

       At   [tex]E_2 = 0.04[/tex]     confidence level  = 99%  =>    [tex]\alpha_2 = 0.01[/tex]

The critical value of  [tex]\frac{\alpha_2 }{2}[/tex] from the normal distribution table is  

        [tex]Z_{\frac{ \alpha_2 }{2} } = 2.58[/tex]

=>    [tex]n_2 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_2} ]^2[/tex]

=>    [tex]n_2 =[ \frac{ 2.58 * 100}{ 0.04} ]^2[/tex]

=>    [tex]n_2 =41602500[/tex]

Considering ii

Given that the level of significance is  [tex]\alpha = 0.10[/tex]

Then the critical value  of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

           [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

Generally the margin of error is mathematically represented as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]E = 1.645 * \frac{100 }{\sqrt{8} }[/tex]

         [tex]E = 58.16[/tex]

Generally the 90% confidence interval is mathematically evaluated as

         [tex]\= x - E < \mu < \= x + E[/tex]

=>      [tex]350 - 58.16 < \mu < 350 + 58.16[/tex]

=>     [tex]291.84 < \mu < 408.16[/tex]

So the interpretation is that there is 90% confidence that the mean  fee charged to H&R Block customers last year is in the interval .So there is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval.

Answer:

False.

Step-by-step explanation:

Probability distribution is the function which describes the likelihood of possible values assuming a random variable. The variance distribution is the squared value of each the difference by the mean. values of probability are squared and then their sum is taken to calculate variance deviation. The number of motorcycles greater than 1 has probability of 0.35 so the probability of x = 1 must also be 0.35.

Answer:

Step-by-step explanation:

Whenever you add two number x and -x and it becomes 0 . IT is the identity property.

Ex:

-1/3 + 1/3 = 0

-1 + 1 = 0

-58 + 58 = 0

Answer:

f(x) = -0.5x

Step-by-step explanation:

.25*8 = 2 which is really a slope of 2/1

place a negative in front flips it over the y axis and flipping the slope flips it over the x axis.

Answer:

Apllying cos on the triangle

cos(angle)= Base/ Hyp

cos(34)= 29/ AB

AB= 29/0.8290

AB=34.98

Step-by-step explanation:

The length of AB is 34.98 units which the correct answer would be an option (D).

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

Given that ΔABC

∠C = 90°

Here base = BC = 29 units and hypotenuse = AB

To determine the length of AB

Apply the cosine on the given right triangle

⇒ cos(θ) = Base/hypotenuse

⇒ cos(34) = 29/ AB

∴ cos(34°) = 0.8290

⇒ 0.8290 = 29/ AB

⇒ AB= 29/0.8290

⇒ AB = 34.98 units

Hence, the length of AB is  34.98 units

Learn more about Trigonometric functions here:

https://brainly.com/question/6904750

#SPJ2

Answer:

A

  [tex]t = 10.1[/tex]

B

  [tex]p-value = p(t > 10.1)= 0.000[/tex]

C

  [tex]0.4714 < p_1 - p_2 <0.6988[/tex]

D

  The  oxygen treatment  is effective because

1 the is no 0 in the interval telling us that the treatments are different

 2 the upper and the lower limit are positive tell us that the proportion of those treated by the oxygen treatment is greater

Step-by-step explanation:

From the question we are told that

    The  first sample size is  [tex]n_1 = 140[/tex]

     The  number of patient which the oxygen cured is k = 113  

     The second sample size is  [tex]n_2 = 158[/tex]

     The number of patient that  placebo cured is  l =  35

The first sample proportion is

           [tex]\r p_1 = \frac{ 113}{140 }[/tex]

           [tex]\r p_1 = 0.8071[/tex]

The second sample proportion is  

           [tex]\r p_2 = \frac{ 35}{ 158 }[/tex]

          [tex]\r p_2 = 0.222[/tex]

The null hypothesis is  [tex]H_o : p_1 = p_2[/tex]

 The  alternative hypothesis is  [tex]H_a : p_1 > p_2[/tex]

Let assume the level of significance be[tex]\alpha = 0.05[/tex]

Generally the pooled proportion is mathematically evaluated as

    [tex]p = \frac{p1 * n1 + p2 * n2}{n1 + n2}[/tex]

substituting values

     [tex]p = \frac{0.8071 * 140 + 0.222 * 158}{140 + 158}[/tex]

      [tex]p = 0.4969[/tex]

Generally the standard error is mathematically represented

      [tex]SE = \sqrt{ p(1- p ) * [ \frac{1}{n_1} + \frac{1}{n_1}] }[/tex]

      substituting values

     [tex]SE = \sqrt{ 0.4969(1- 0.4969 ) * [ \frac{1}{140} + \frac{1}{158}] }[/tex]

     [tex]SE = 0.0580[/tex]

Generally the test statistics is mathematically represented as

       [tex]t = \frac{ \r p_1 - \r p_2}{ SE}[/tex]

       [tex]t = \frac{ 0.8071 -0.222}{ 0.0580}[/tex]

       [tex]t = 10.1[/tex]

The  p-value is from the normal distribution table as  

      [tex]p-value = p(t > 10.1)= 0.000[/tex]

given that [tex]t< \alpha[/tex] the null hypothesis is rejected

From the normal distribution table the critical value of  [tex]\frac{\alpha }{2}[/tex]  is  

     [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically the represented as

         [tex]E = Z_{\frac{\alpha }{2} } * SE[/tex]      

         [tex]E = 1.96 * 0.0580[/tex]      

          [tex]E = 0.1137[/tex]

The 95% confidence interval is mathematically  represented as

           [tex](\r p_1 - \r p_2) - E < p_1 - p_2 < (\r p_1 - \r p_2) + E[/tex]

substituting value

             [tex](0.8071 - 0.222) - 0.1137 < p_1 - p_2 < (0.8071 - 0.222) + 0.1137[/tex]

             [tex]0.4714 < p_1 - p_2 <0.6988[/tex]

The  oxygen treatment  is effective because

1 the is no 0 in the interval telling us that the treatments are different

 2 the upper and the lower limit are positive tell us that the proportion of those treated by the oxygen treatment is greater

Answer:

See below.

Step-by-step explanation:

The degree is simply the number of the exponent (or the sum) and the coefficient is simply the number in front of the term.

First Term: -7; Deg=0, Co=-7.

-7 is the same as saying -7x^0. Thus, the degree is 0.

Second Term: -x^4; Deg=4, Co=-1

-x^4 is the same as saying -1(x^4). Thus, the degree is 4 while the coefficient is -1.

Third Term: -5x^3; Deg=3, Co=-5

Again, this is the same as saying -5(x^3). Thus, the degree is 3 while the coefficient is -1.

Fourth Term: 7x; Deg=1, Co=7

7x is the same as saying 7x^1. Thus, the degree is 1 while the coefficient is 7.

Fifth Term: x^2; Deg=2, Co=2

x^2 is the same as 1(x^2). Thus, the degree is 2 while the coefficient is 1.

The leading coefficient is the first coefficient when the polynomial is placed in descending order based on degree number. First, arrange the polynomial into descending order based on the degree:

[tex]-x^4-5x^3+x^2+7x-7[/tex]

Thus, the leading coefficient is -1 (belonging to the x^4).

The degree of the leading term will always be the highest. In this case, it is 4.

The degree of the polynomial is the highest degree. In this case, it is 4.

Answer:

C. 50 degrees

Step-by-step explanation:

Because 6x + 5x = 110° and x = 10

5×10 = FEG 50°

Step-by-step explanation:

Putting values

A = - 7(15 + 9)

A = - 7(24)

A = - 168