2/5 × 3/7? please help ​

Answers

Answer 1

Answer:

[tex]\frac{2}{5}[/tex] • [tex]\frac{3}{7}[/tex] = [tex]\frac{6}{35}[/tex]

Answer 2

Answer: 0.171

Step-by-step explanation:

First, do 2/5 which would equal 0.4

Second, so 3/7 which would equal 0.428571428571429

Lastly multiply the two answers together to get 0.171428571428571


Related Questions

2. A 10 Mg truck hauls a 20 Mg trailer. If the unit starts from rest on a level road with a
tractive force of 20 kN between the driving wheels of the truck and the road, calculate the
acceleration of the unit and the tension in the horizontal draw-bar.
Drawbar
20 Mg Trailer
10 Mg Truck
a=0.667 m/s2
T= 13.3 KN
Oro
W​

Answers

Answer:

The acceleration on the unit is 0.667 m/s^2

The tension on the draw-bar is 13.34 kN

Step-by-step explanation:

The mass of the truck = 10 Mg = 10 x 10^3 kg

The mass of the trailer = 20 Mg = 20 x 10^3 kg

Tractive force from the truck = 20 kN = 20 x 10^3 N

The total mass of the unit = 10 Mg + 20 Mg = 30 Mg = 30 x 10^3 kg

The tractive force on the unit will produce an acceleration that is given as

F = ma

where

F is the tractive = 20 x 10^3 N

m is the mass of the unit = 30 x 10^3 kg

a is the acceleration of the unit = ?

substituting into the equation

20 x 10^3 = 30 x 10^3 x a

a = (20 x 10^3)/(30 x 10^3) = 0.667 m/s^2

the tension on the draw-bar T is gotten from considering only the mass that is pulled by the draw-bar which is 20 Mg

The acceleration on the unit = 0.667 m/s^2

The drawn mass = 20 Mg = 20 x 10^3 kg

The tension on the draw bar = ma = 20 x 10^3 x 0.667 = 13340 N

= 13.34 kN

The acceleration is 0.00067m/s^2, while the tension on the horizontal bar is 13.4 N

The given parameters are:

[tex]\mathbf{m = 10Mg}[/tex] -- mass of the truck

[tex]\mathbf{M = 20Mg}[/tex] -- mass of the trailer

[tex]\mathbf{F_T = 20kN}[/tex] --- tractive force

Start by calculating the total mass

[tex]\mathbf{M_T = m + M}[/tex]

So, we have:

[tex]\mathbf{M_T = 10Mg + 20Mg}[/tex]

[tex]\mathbf{M_T = 30Mg}[/tex]

Convert to kilograms

[tex]\mathbf{M_T = 30 \times 10^3kg}[/tex]

[tex]\mathbf{M_T = 30000 kg}[/tex]

Force is calculated as:

[tex]\mathbf{F =ma}[/tex]

So, we have:

[tex]\mathbf{20kN =30000kg \times a}[/tex]

Divide both sides by 30000

[tex]\mathbf{a = 0.00067ms^{-2}}[/tex]

The tension on the horizontal bar (i.e. the 20 Mg trailer) is:

[tex]\mathbf{T=ma}[/tex]

So, we have:

[tex]\mathbf{T=20Mg \times 0.00067ms^{-2}}[/tex]

Rewrite as:

[tex]\mathbf{T=20 \times 10^3 kg \times 0.00067m/s}[/tex]

[tex]\mathbf{T=13.4N}[/tex]

Hence, the acceleration is 0.00067m/s^2, while the tension on the horizontal bar is 13.4 N

Read more about force and acceleration at:

https://brainly.com/question/20511022

Step 1: Subtract 3 from both sides of the inequality
Step 2
Step 3: Divide both sides of the inequality by the
coefficient of x.
What is the missing step in solving the inequality 5 -
8x < 2x + 3?
O Add 2x to both sides of the inequality
O Subtract 8x from both sides of the inequality
O Subtract 2x from both sides of the inequality
Add 8x to both sides of the inequality.
Mark this and return
Save and Exit
Intext
Submit

Answers

Answer:

add 8x to both sides

Step-by-step explanation:

5-8x<2x+3

first step, subtract 3 from both sides:

2-8x<2x

second step,?

2<?x

so you need to add 8x first

x power 8 + x power 4 + 1
factorize

Answers

Answer:

[tex]1(x {}^{8} + x {}^{4} + 1)[/tex]

Step-by-step explanation:

[tex]x {}^{8} + {x}^{4} + 1 =1( x {}^{8} + x {}^{2} + 1)[/tex]

Hope this helps ;) ❤❤❤

Let me know if there is an error in my answer.

Answer: See below

Explanation:

x^8 + x^4 + 1 = 0
(x^8 + x^4) + 1 = 0
x^4(x^4 + 1) + 1 = 0
(x^4 + 1)(x^4 + 1) = 0

A sample of a radioactive substance decayed 11% over the course of 3 weeks. How many grams were in the sample originally if 30.26 grams of the substance were remaining after the 3 weeks?

Answers

Answer:

34 grams

Step-by-step explanation:

If the remaining sample has 30.26 grams of radioactive substance, and 11% of it decayed, that means that 30.26 grams is 89% of the original. Let the original be x.

30.26=0.89x

Multiply both by one hundred

3026=89x

Divide both by 89

34=x

x=original, so the original was 34 grams.

Given these four points: A(3, 3), B(−5, 7), C(2, 11), and D(9, −2), find the coordinates of the midpoint of line segments AB and CD.

Answers

Midpoint formula: (x1 + x2)/2 , (y1 + y2)/2

Midpoint AB = (3 +-5)/2, (3 + 7)/2 = -2/2 , 10/2 = (-1,5)

Midpoint CD = (2 +9)/2, (11 + -2)/2 = (11/2,9/2)

A population of bacteria P is changing at a rate of dP/dt = 3000/1+0.25t where t is the time in days. The initial population (when t=0) is 1000. Write an equation that gives the population at any time t. Then find the population when t = 3 days.

Answers

Answer:

- At any time t, the population is:

P = 375t² + 3000t + 1000

- At time t = 3 days, the population is:

P = 13,375

Step-by-step explanation:

Given the rate of change of the population of bacteria as:

dP/dt = 3000/(1 + 0.25t)

we need to rewrite the given differential equation, and solve.

Rewriting, we have:

dP/3000 = (1 + 0.25t)dt

Integrating both sides, we have

P/3000 = t + (0.25/2)t² + C

P/3000 = t + 0.125t² + C

When t = 0, P = 1000

So,

1000/3000 = C

C = 1/3

Therefore, at any time t, the population is:

P/3000 = 0.125t² + t + 1/3

P = 375t² + 3000t + 1000

At time t = 3 days, the population is :

P = 375(3²) + 3000(3) + 1000

= 3375 + 9000 + 1000

P = 13,375

Given the graph, find an equation for the parabola.

Answers

Answer:

[tex]\Large \boxed{\sf \bf \ \ y=\dfrac{1}{16}(a-3)^2-2 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

When the parabola equation is like

[tex]y=a(x-h)^2+k[/tex]

The vertex is the point (h,k) and the focus is the point (h, k+1/(4a))

As the vertex is (3,-2) we can say that h = 3 and k = -2.

We need to find a.

The focus  is (3,2) so we can say.

[tex]2=-2+\dfrac{1}{4a}\\\\\text{*** We add 2. ***}\\\\\dfrac{1}{4a}=2+2=4\\\\\text{*** We multiply by 4a. ***}\\\\16a=1\\\\\text{*** We divide by 16. ***}\\\\a=\dfrac{1}{16}[/tex]

So an equation for the parabola is.

[tex]\large \boxed{\sf y=\dfrac{1}{16}(a-3)^2-2 }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

A sample of 36 observations is selected from one population with a population standard deviation of 4.2. The sample mean is 101.5. A sample of 50 observations is selected from a second population with a population standard deviation of 5.0. The sample mean is 100.1. Conduct the following test of hypothesis using the 0.10 significance level.H0 : μ1 = μ2H1 : μ1 ≠ μ2a. This is a_________tailed test.b. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)The decision rule is to reject H0 if z is ___________the interval.c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0?e. What is the p-value? (Round your answer to 4 decimal places.)

Answers

Answer:

Step-by-step explanation:

Given that :

the null and the alternative hypothesis are computed as :

[tex]H_o: \mu_1 = \mu_2[/tex]

[tex]H_a : \mu _1 \neq \mu_2[/tex]

This is a two tailed test

This is because of the ≠ sign in the alternative hypothesis which signifies that the rejection region in the alternative hypothesis are at the both sides of the hypothesized mean difference .

Decision Rule: at the level of significance ∝ = 0 . 10

The decision rule is to reject the null hypothesis if z < - 1 . 64 and z > 1 . 64

NOTE: DURING THE MOMENT OF TYPING THIS ANSWER THERE IS A TECHNICAL ISSUE WHICH MAKES ME TO BE UNABLE TO SUBMIT THE FULL ANSWER BUT I'VE MADE SCREENSHOTS OF THEM AND THEY CAN BE FOUND IN THE ATTACHED FILE BELOW

200,000=2x10 to the power of 6

Answers

False.

2x10^6 you move the decimal point 6 places to the right. ( add 6 zeros after the 2)

2x 10^6 = 2,000,000

the production of a printer consists of the cost of raw material at 100 dollars the cost of overheads at 80$ and wages at 120$ if the cost of raw materials and overheads are increased by 11% and 20% respectively while wages are decreased by 15% find the percentage increase or decrease in the production cost of the printer

Answers

Answer:

The percentage increase in the production cost of the printer is 3%.

Step-by-step explanation:

We are given that the production of a printer consists of the cost of raw material at 100 dollars the cost of overheads at 80$ and wages at 120$.

Also, the cost of raw materials and overheads are increased by 11% and 20% respectively while wages are decreased by 15%.

Cost of raw material = $100

Cost of overheads = $80

Cost of wages = $120

So, the total cost of the printer = $100 + $80 + $120

                                                   = $300

Now, the increase in the cost of raw material = $100 + 11% of $100

                                                                           = [tex]\$100 + (\frac{11}{100} \times \$100)[/tex]

                                                                           = $100 + $11 = $111

The increase in the cost of overheads = $80 + 20% of $80

                                                                = [tex]\$80 + (\frac{20}{100} \times \$80)[/tex]

                                                                = $80 + $16 = $96

The decrease in the cost of wages = $120 - 15% of $120

                                                          = [tex]\$120 - (\frac{15}{100} \times \$120)[/tex]

                                                          = $120 - $18 = $102

So, the new cost of a printer = $111 + $96 + $102 = $309

Now, the percentage increase in the production cost of the printer is given by;

      % increase =  [tex]\frac{\text{Net increase in the cost of printer}}{\text{Original cost of printer}} \times 100[/tex]

                         =  [tex]\frac{\$309- \$300}{\$300} \times 100[/tex]

                         =  3%

Hence, the percentage increase in the production cost of the printer is 3%.

1/3 of a shipment of books weights 28 pounds

Answers

Answer:

84 pounds

Step-by-step explanation:

If 1/3 of a book is equal to 28 pounds then 28*3 will give you your answer

Find the work W done by a force of 7pounds acting in the direction 30 degreesto the horizontal in moving an object 7feet from (0 comma 0 )to (7 comma 0 ).

Answers

Answer:

The work done by the force is 42.4 Joules

Step-by-step explanation:

The force F = 7 pounds

angle to the horizontal that the force acts ∅ = 30°

The object is moved a distance d = 7 feet

The coordinate  (0 comma 0 )to (7 comma 0 ), indicates that the movement started from the origin, and is along the x-axis.

The work done by this force = F cos ∅ x d

==> 7 cos 30° x 7

==> 7 x 0.866 x 7 = 42.4 Joules

Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 16 of 42 at one school and 18 of 34 at the other have ear infections. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools? Group of answer choices

Answers

Answer:

Step-by-step explanation:

The summary of the given data includes;

sample size for the first school [tex]n_1[/tex] = 42

sample size for the second school [tex]n_2[/tex]  = 34

so 16 out of 42 i.e [tex]x_1[/tex] = 16 and 18 out of 34 i.e [tex]x_2[/tex] = 18 have ear infection.

the proportion of students with ear infection Is as follows:

[tex]\hat p_1 = \dfrac{16}{42}[/tex] = 0.38095

[tex]\hat p_2 = \dfrac{18}{34}[/tex]  =  0.5294

Since this is a two tailed test , the null and the alternative hypothesis can be computed as :

[tex]H_0 :p_1 -p_2 = 0 \\ \\ H_1 : p_1 - p_2 \neq 0[/tex]

level of significance ∝ = 0.05,

Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.

The test statistics for the difference in proportion can be achieved by using a pooled sample proportion.

[tex]\bar p = \dfrac{x_1 +x_2}{n_1 +n_2}[/tex]

[tex]\bar p = \dfrac{16 +18}{42 +34}[/tex]

[tex]\bar p = \dfrac{34}{76}[/tex]

[tex]\bar p = 0.447368[/tex]

[tex]\bar p + \bar q = 1 \\ \\ \bar q = 1 -\bar p \\ \\\bar q = 1 - 0.447368 \\ \\\bar q = 0.552632[/tex]

The pooled standard error can be computed by using the formula:

[tex]S.E = \sqrt{ \dfrac{ \bar p \bar q}{ n_1} + \dfrac{\bar p \bar p}{n_2} }[/tex]

[tex]S.E = \sqrt{ \dfrac{ 0.447368 * 0.552632}{ 42} + \dfrac{ 0.447368 * 0.447368}{34} }[/tex]

[tex]S.E = \sqrt{ \dfrac{ 0.2472298726}{ 42} + \dfrac{ 0.2001381274}{34} }[/tex]

[tex]S.E = \sqrt{ 0.01177284105}[/tex]

[tex]S.E = 0.1085[/tex]

The test statistics is ;

[tex]z = \dfrac{\hat p_1 - \hat p_2}{S.E}[/tex]

[tex]z = \dfrac{0.38095- 0.5294}{0.1085}[/tex]

[tex]z = \dfrac{-0.14845}{0.1085}[/tex]

z = - 1.368

Decision Rule: Since the test statistics is greater than the rejection region - 1.96 , we fail to reject the null hypothesis.

Conclusion: There is insufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools

The image of (-2, 7) reflected across the x-axis is
2
(-2,-7)
b)
(2,7)
(2, -7)
d)
(-2, 7)

Answers

Answer:

(-2,-7)

Step-by-step explanation:

because it's reflected across the x-axis, only the y-intercept will change

Answer:

(-2,-7)

Step-by-step explanation:

All you have to do is draw a graph and draw the point across the x axis in the same row and same distance from the x axis.The distance is 7 so you just change it to -7.

Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = (x - 6)2 Shift the graph of y = x2 down 6 units. Shift the graph of y = x2 right 6 units. Shift the graph of y = x2 up 6 units. Shift the graph of y = x2 left 6 units.

Answers

Answer:

Shift the graph of y = x2 right 6 units.

According to the Census Bureau, 3.34 people reside in the typical American household. A sample of 26 households in Arizona retirement communities showed the mean number of residents per household was 2.70 residents. The standard deviation of this sample was 1.17 residents. At the .10 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.34 persons?



(a) State the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.)


H0: ? ?
H1: ? <


(b)
State the decision rule for .10 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)



Reject H0 if t <

(c)
Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)



Value of the test statistic

(d)
Is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.34 persons?



H0. Mean number of residents less than 3.34 persons.

Answers

Answer:

Step-by-step explanation:

Given that:

Mean = 3.34

sample size = 26

sample mean = 2.7

standard deviation = 1.17

level of significance = 0.10

The null hypothesis and the alternative hypothesis can be computed as follows:

[tex]\mathtt{H_o: \mu \geq 3.34} \\ \\ \mathtt{H_1: \mu < 3.34}[/tex]

degree of freedom = n - 1

degree of freedom = 26 -1

degree of freedom =  25

level of significance = 0.10

Since the alternative hypothesis contains <, then the test is left tailed

[tex]\mathtt{t_{\alpha, df} = t_{0.10, 25}}[/tex]

[tex]\mathtt{t_{0.10, 25}}[/tex] = - 1.316

The rejection region therefore consist of all values smaller than - 1.316, therefore ; reject [tex]H_o[/tex] if t < -1.316

The test statistics can be computed as follows:

[tex]t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \dfrac{2.7 - 3.34}{\dfrac{1.17}{\sqrt{26}}}[/tex]

[tex]t = \dfrac{-0.64}{\dfrac{1.17}{5.099}}[/tex]

t = - 2.789

Decision Rule:  To reject the null hypothesis if the t test lies in the rejection region or less than the rejection region.

Conclusion: We  reject the null hypothesis since t = (- 2.789) < -1.316. Then we conclude that  the mean number of residents in the retirement community household is less than 3.34 persons.

A schoolteacher would like to know whether or not toothpaste brands are used differentially in her classroom (in other words, is one brand preferred over the others?). She asks her students to report which of three brands they use: Crest, Colgate, or Aquafresh. Below are the numbers of students who use each type of toothpaste (notice there are 45 students total in her class). Test her hypothesis using an alpha level of .05.
Crest Colgate Aquafresh
24 13 8
a. What test is appropriate for this analysis?
b. State the null hypothesis:
c. State the alternative hypothesis:
d. Find the critical value:
e. Calculate the test statistic:
f. Make a decision:

Answers

Answer:

Step-by-step explanation:

a. What test is appropriate for this analysis?

A Chi-square  test of independence is appropriate for this analysis because it is used to compare two variables or testing relationship on categorical variables.  

b. State the null hypothesis:

The null hypothesis is the default hypothesis

[tex]\mathtt{H_o:}[/tex] There is no particular preference for any brand of toothpaste among students.

c. State the alternative hypothesis:

The alternative hypothesis is the research hypothesis which comes in place to challenge the validity of the null hypothesis.

[tex]\mathtt{H_a:}[/tex] There is particular preference for brands of toothpaste among students.

d. Find the critical value:

degree of freedom = n-1

degree of freedom = 3 - 1

degree of freedom = 2

At the level of significance ∝ = 0.05

The confidence interval = 0.95 and degree of freedom = 2, the critical value from the chi-square distribution table = 5.991

e. Calculate the test statistic:

Using the chi square test statistics; we have the following:

Crest             Colgate            Aquafresh            Total

24                        13                     8                      45

Since we have three brands. Then, for each brand, the expected value

= Total /3

= 45/3

=15

Thus:

Chi -square [tex]\mathtt{X^2 = \dfrac{(observed \ value - expected \ value)^2}{expected \ value}}[/tex]

[tex]\mathtt{X^2 = \dfrac{(24 - 15)^2}{15} + \dfrac{(13 - 15)^2}{15} + \dfrac{(8 - 15)^2}{15} }[/tex]

[tex]\mathtt{X^2 = \dfrac{81}{15} + \dfrac{4}{15} + \dfrac{49}{15} }[/tex]

[tex]\mathtt{X^2 = \dfrac{81+4+49}{15}}[/tex]

[tex]\mathtt{X^2 = \dfrac{134}{15}}[/tex]

[tex]\mathtt{X^2 =8.93 }[/tex]

f. Make a decision:

Since the chi-square value is greater than the critical value , we reject the null hypothesis and conclude that the students have  particular preference for brands of toothpaste.

What are the solutions of the equation x4 + 6x2 + 5 = 0? Use u substitution to solve.
x = i and x = i5
x=+ i and x
x= +115
O x=V-1 and x = = -5
x=+ -1 and x = = -5​

Answers

Answer:

A; The first choice.

Step-by-step explanation:

We have the equation [tex]x^4+6x^2+5=0[/tex] and we want to solve using u-substitution.

When solving by u-substitution, we essentially want to turn our equation into quadratic form.

So, let [tex]u=x^2[/tex]. We can rewrite our equation as:

[tex](x^2)^2+6(x^2)+5=0[/tex]

Substitute:

[tex]u^2+6u+5=0[/tex]

Solve. We can factor:

[tex](u+5)(u+1)=0[/tex]

Zero Product Property:

[tex]u+5=0\text{ and } u+1=0[/tex]

Solve for each case:

[tex]u=-5\text{ and } u=-1[/tex]

Substitute back u:

[tex]x^2=-5\text{ and } x^2=-1[/tex]

Take the square root of both sides for each case. Since we are taking an even root, we need plus-minus. Thus:

[tex]x=\pm\sqrt{-5}\text{ and } x=\pm\sqrt{-1}[/tex]

Simplify:

[tex]x=\pm i\sqrt{5}\text{ and } x=\pm i[/tex]

Our answer is A.

Lydia drives from city a to city b to transport goods. her return speed is 3 times her departure speed and she takes 40 minutes less on her return trip. how long did her departure trip take?

Answers

Answer:

1 hour

Step-by-step explanation:

Hello, let's say that her departure trip takes t in minutes, as her return speed is 3 times her departure speed, she took t/3 for the return and we know that this 40 minutes less, so we can write.

t/3=t-40

We can multiply by 3

t = 3t -40*3 = 3t - 120

This is equivalent to

3t -120 = t

We subtract t

2t-120 = 0

2t = 120

We divide by 2

t = 120/2 = 60

So this is 60 minutes = 1 hour.

Thank you.

A type of related samples design in which participants are observed more than once is called a
A. repeated measures design
B. matched pairs design
C. matched samples design
D. both matched pairs design and matched samples design

Answers

Answer:

Option A (repeated measures design) is the correct option.

Step-by-step explanation:

Researchers as well as statisticians vary in terms of methods used mostly for repetitive measurements. Besides illustration, repeated models of measurements are however recognized as repeated analyzes of variance measurements, standardized considerations of measurements, or layouts of objects throughout them.

The other three options are not related to the given instance. So that alternative A would be the correct choice.

Evaluate the expression: -(31 + 2) +7² - (-5²)
A) -9
B) -5
C) 41
OD -40​

Answers

Answer: C. 41

Step-by-step explanation:

[tex]-\left(31+2\right)+7^2-\left(-5^2\right)[/tex]

[tex]=-33+7^2-\left(-5^2\right)[/tex]

[tex]\left(-5^2\right)=-25[/tex]

[tex]=-33+7^2-\left(-25\right)[/tex]

[tex]7^2=49[/tex]

[tex]=-33+49-\left(-25\right)[/tex]

[tex]-33+49=16[/tex]

[tex]=16-\left(-25\right)[/tex]

[tex]\mathrm{Apply\:rule\:}-\left(-a\right)\:=\:+a[/tex]

[tex]16+25=41[/tex]

The answer should be 41

A study of 25 graduates of four-year public colleges revealed the mean amount owed by a student in student loans was $55,051. The standard deviation of the sample was $7,568.

Required:
a. Construct a 90% confidence interval for the population mean.
b. Confidence interval for the population men between _______ up to_______________

Answers

Answer:

a

   The  90%  confidence interval is  [tex]52561.13 < \mu < 57540.8[/tex]

b

Confidence interval for the population men between $52561.13  up to $57540.8

Step-by-step explanation:

From the question we are told that

   The sample size is  [tex]n = 25[/tex]

     The  sample mean is  [tex]\= x = \$ 55,051[/tex]

     The standard deviation is  [tex]\sigma = \$ 7,568[/tex]

Given that the confidence level is  90% then the level of confidence is mathematically represented as

             [tex]\alpha = 100 -90[/tex]

              [tex]\alpha = 10\%[/tex]

             [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table the values 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{ 7568}{ \sqrt{ 25} }[/tex]

             [tex]E = 2489.9[/tex]

The 90% confidence interval is mathematically evaluated as

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

substituting values

     [tex]55051 - 2489.8 < \mu < 55051 + 2489.8[/tex]

     [tex]52561.13 < \mu < 57540.8[/tex]

Which expression is equal to (1+6i)−(7+3i) ?

Answers

Answer:

- 6+3i

Step-by-step explanation:

[tex](1+6i)-(7+3i) ?\\Group\:the\:real\:part\:and\:the\:imaginary\\\:part\:of\:the\:complex\:number\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\=\left(1-7\right)+\left(6-3\right)i\\1-7=-6\\6-3=3\\=-6+3i[/tex]

Compute (3/4)*(8/9)*(15/16)*(24/25)*(35/36)*(48/49)*(63/64)*(80/81)*(99/100) Express your answer in the simplest way possible. (Suggestion: First, try computing 3/4*8/9 then 3/4*8/9*15/16 and so on. Look for patterns.

Answers

Answer:

[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]

Step-by-step explanation:

Given

[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100})[/tex]

Required

Simplify

For clarity, group the expression in threes

[tex]((\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Evaluate the first group [Divide 8 by 4]

[tex]((\frac{3}{1})*(\frac{2}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 9 by 3]

[tex]((\frac{1}{1})*(\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex]((\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 15 by 3]

[tex]((\frac{2}{1})*(\frac{5}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 16 by 2]

[tex]((\frac{1}{1})*(\frac{5}{8}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](\frac{5}{8})*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Evaluate the second group [Divide 35 and 25 by 5]

[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{7}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 49 by 7]

[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{1}{3})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 24 by 3]

[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{1}{1})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Merge the first and second group

[tex]((\frac{5}{8})*(\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](1*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Evaluate the last group [Divide 99 by 9]

[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{9})*(\frac{11}{100}))[/tex]

[Divide 63 by 9]

[tex](\frac{4}{7})*((\frac{7}{64})*(\frac{80}{1})*(\frac{11}{100}))[/tex]

[Divide 64 and 80 by 8]

[tex](\frac{4}{7})*((\frac{7}{8})*(\frac{10}{1})*(\frac{11}{100}))[/tex]

[Divide 10 and 4 by 2]

[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{5}{1})*(\frac{11}{100}))[/tex]

[Divide 100 by 5]

[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{1}{1})*(\frac{11}{20}))[/tex]

[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{11}{20}))[/tex]

[tex](\frac{4}{7})*(\frac{7}{4})*(\frac{11}{20})[/tex]

[tex]1*(\frac{11}{20})[/tex]

[tex]\frac{11}{20}[/tex]

Hence;

[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]

Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x)=-2cos^(2)x

Answers

Answer:

Increasing

0°≤x≤180°

Decreasing

180°≤x≤360°

Hi I cannot seem to get this question correct

Answers

Answer:

150000 doctoral degrees

Step-by-step explanation:

From the graph attached,

At t = 0 represents the year 2005 and each unit of y-axis represents 10000 degrees.

Number of approximate number of degrees awarded to women in 2008,

f'(3) = 2.25

Similarly, number of doctoral degrees awarded from 2009 to 2013 are,

f'(4) = 2.5

f'(5) = 2.5

f'(6) = 2.5

f'(7) = 2.5

f'(8) = 2.75

Total number of degrees awarded to women from the start of 2008 to the start of 2014 = (2.25 + 2.5 + 2.5 + 2.5 + 2.5 + 2.75 ) × 10000

= 15 × 10000

= 150000

Please answer asap this person made a mistake what is the error and correct solution to this problem

Answers

Answer:

6

Step-by-step explanation:

Hello, please consider the following.

[tex](4+x)^2=4^2+2\cdot 4\cdot x+x^2=16+\boxed{8}x+x^2\\\\\text{ ... and not ...}\\\\16+\boxed{4}x+x^2[/tex]

So the correct equation becomes.

[tex]x^2+64=16+8x+x^2\\\\8x=64-16=48\\\\\text{ we divide by 8 both sides of the equation.}\\\\x=\dfrac{45}{8}=6[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Error : The expression ( 4 + x )² was expanded incorrectly.

Correct Solution : x = 6

Step-by-step explanation:

The planning of the solution is correct, by Pythagorean Theorem you can say that PQ² + QO² = PO², and hence through substitution x² + 8² = ( 4 + x )². Let's look into the calculations.

PQ² + QO² = PO²,

x² + 8² = ( 4 + x )²,

x² + 8² = 16 + 8x + x²,

64 = 16 + 8x,

48 = 8x,

x = 48 / 8 = 6, x = 6

As you can see, the only error in the calculations was expanding the expression ( 4 + x )². ( 4 + x )² = 4² + 2 [tex]*[/tex] 4 [tex]*[/tex] x + x² = 4² + 8x + x² = 16 + 8x + x², not 16 + 4x + x².

) A random sample of size 36 is selected from a normally distributed population with a mean of 16 and a standard deviation of 3. What is the probability that the sample mean is somewhere between 15.8 and 16.2

Answers

Answer:

The probability is 0.31084

Step-by-step explanation:

We can calculate this probability using the z-score route.

Mathematically;

z = (x-mean)/SD/√n

Where the mean = 16, SD = 3 and n = 36

For 15.8, we have;

z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4

For 16.2, we have

z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4

So the probability we want to calculate is;

P(-0.4<z<0.4)

We can get this using the standard normal distribution table;

So we have;

P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)

= 0.31084

The base of a triangle is 4 cm greater than the
height. The area is 30 cm. Find the height and
the length of the base
h
The height of the triangle is
The base of the triangle is​

Answers

Answer:

Step-by-step explanation:

Formula for area of a triangle:

Height x Base /2

Base (b) = h +4

Height = h

h + 4 x h /2 = 30cm

=> h +4 x h = 60

=> h+4h =60

=> 5h = 60

=> h = 12

Height = 12

Base = 12 +4 = 16

Sarah had a balance of $155 in her bank account at the start of the week. She withdrew $65.50 on Monday, $23.25 on Wednesday, and $26.45 on Thursday. On Friday she deposited $165.30. Write an expression that represents Sarah's spending.

Answers

Answer:

155 + 165.3 - 65.5 - 23.25 - 26.45

Step-by-step explanation:

She had $155 dollars in the starting = +155

She withdrew $65.5 = -65.5

She withdrew another $23.25 = -23.25

She withdrew another $26.45 = -26.45

The deposited $165.3 = +165.3

The expression looks like:

155 + 165.3 - 65.5 - 23.25 - 26.45

We could simplify the expression:

155 + 165.3 - 65.5 - 23.25 - 26.45

=> 320.3 - 88.75 - 26.45

=> 320.3 -115.2

=> 205.1

At the end of the week, she had a total of $205.10.

Other Questions
The number of fish in the lake can be modeled by exponential regression equation y equals 14.08 * 2.08 X where X represents the year which is the best prediction for the number of fish in your 6 round your answer to the nearest whole number The ______ rate of interest is the actual rate charged by the supplier and paid by the demander of fund You pack sandwiches for a hike with your friends. Each sandwich takes 2 slices of bread, and each hiker eats one sandwich. How many slices of bread are used for n hikers? Is this statement true or false?A hypothesis is a lucky guess. Which correlation coefficient could represent the relationship in the scatter plot The specifications for the diameter of a molded part are 10 mm 0.5 mm. The actual average and standard deviation from 250 parts sampled is 10.1 mm and 0.1 mm, respectively. The process can be characterized as: The Federal Open Market Committee is comprised of A. the seven members of the Board of Governors plus five of the twelve Federal Reserve Bank presidents. B. the five members of the Board of Governors plus the twelve Federal Reserve Bank presidents. C. the seven members of the Board of Governors plus the twelve Federal Reserve Bank presidents. D. the five members of the Board of Governors plus seven of the twelve Federal Reserve Bank presidents. Which statements are true about "evidence"? select all that appy observations which answer questions proof that an idea is true information for or against an idea data to help draw a conclusion Most U.S. territories and protectorates are located in A. North Africa B. the Pacific Ocean C. North America D. the Caribbean Sea Public health ethics is a field of study that can enrich and support real-world public health decision-making and management of ethical conflict.A. TrueB. False The intensity at a certain distance from a bright light source is 7.20 W/m2 . A. Find the radiation pressures (in pascals) on a totally absorbing surface and a totally reflecting surface.B. Find the radiation pressures (in atmospheres) on a totally absorbing surface and a totally reflecting surface. According to the Constitution, how many people represent each state in the Senate? According to the Constitution, how many people represent each state in the House of Representatives? Who could vote for representatives in the lower house? Who would elect the Senators? Who would elect the President? What does the fugitive clause say in the Constitution? What was the three-fifths compromise? If a company uses straight-line depreciation, the annual average investment can be calculated as: (Check all that apply.) When the legislative and executive powers are united in the same person, or in the same body of magistrates, there can be no liberty; because apprehensions may arise, lest the same monarch or senate should enact tyrannical laws, to execute them in a tyrannical manner. Baron de Montesquieu, The Spirit of the Laws, 1748 According to Montesquieu, what would happen in an absolute monarchy? Laws could not be enacted. Citizens could lose their freedom. Tyranny would be avoided. Powers would be limited. Why were astronomers often considered magicians in ancient civilizations? What is the value of (7 + 3i) + (2 6i)? a. 9 3i b. 9 + 9i c. 5 + 9i d. 5 3i Select the correct answer.Which subordinating conjunction correctly completes this sentence?Mandy failed to beat her final opponent,she practiced karate every dayA.B.c.thoughthatifOD. whereResetNext A Carnot air conditioner takes energy from the thermal energy of a room at 61F and transfers it as heat to the outdoors, which is at 98F. For each joule of electric energy required to operate the air conditioner, how many joules are removed from the room? Profits from a sole proprietorship are reported as taxable income and Question 5 options: can be reported as a deduction. are subject to a self-employment tax of approximately 15%. can be deferred to the next tax year. can't be taxed again in a future tax year. The following are two independent situations. 1. Conchita Cosmetics acquired 10% of the 210,100 shares of common stock of Martinez Fashion at a total cost of $15 per share on March 18, 2014. On June 30, Martinez declared and paid a $77,700 cash dividend. On December 31, Martinez reported net income of $122,500 for the year. At December 31, the market price of Martinez Fashion was $17 per share. The securities are classified as available-for-sale. 2. Monica, Inc. obtained significant influence over Seles Corporation by buying 33% of Seles's 33,500 outstanding shares of common stock at a total cost of $11 per share on January 1, 2014. On June 15, Seles declared and paid a cash dividend of $45,800. On December 31, Seles reported a net income of $94,600 for the year. Prepare all necessary journal entries in 2014 for both situations.