In an examination, 40% of the candidates failed. The number candidates who failed was 160. How many candidates passed the examination?

Answer:

-9p -4q + 69

Step-by-step explanation:

5p +4q + (-9p +69)

=> 5p + 4q -9p +69

=> -4p +4q +69

Now, we need to subtract 5p +8q from -4p + 4q +69

=> -4p +4q +69 - (5p +8q)

=> -4p + 4q +69 - 5p -8q

=> -9p -4q + 69

Answer:

The answer is "[tex]\bold{\frac{1}{4}<k\leq 2+\sqrt{3}}[/tex]"

Step-by-step explanation:

Given:

[tex]\ S_1 = k \\\\ S_{n+1} = \sqrt{4S_n -1}[/tex]   [tex]_{where} \ \ n \geq 1[/tex]

In the above-given value, [tex]S_n[/tex] is required for the monotone decreasing so, [tex]S_2 :[/tex]

[tex]\to \sqrt{4k-1} \leq \ k=S_1\\\\[/tex]

square the above value:

[tex]\to k^2-4k+1 \leq 0\\\\\to k \leq 2+\sqrt{3} \ \ \ \ \ and \ \ 4k+1 >0\\\\[/tex]

[tex]\bold{\boxed{\frac{1}{4}<k\leq 2+\sqrt{3}}}[/tex]

If you know the population standard deviation (sigma), then you use the Z distribution. If sigma is not known, then you use the T distribution.

Side note: Even if sigma is not known, you could use the Z distribution if the sample size n is greater than 30. If n > 30, then the T distribution is approximately about the same as the Z distribution.

Answer:

maximum --> 62

median --> 46.5

upper quartile --> 60

lower quartile --> 37

minimum --> 32

Step-by-step explanation:

Forgive me on the explanation as I'm a bit rusty on these types of problems.

First, we need to put the set of numbers in order -->

from: 34, 37, 39, 32, 48, 45, 53, 62, 58, 61, 60, 41 -->

to: 32, 34, 37, 39, 41, 45, 48, 53, 58, 60, 61, 62

maximum = biggest number => thus, 62

median = middle number in a sense => (45+48)/2 => thus, 46.5

upper quartile = median over the median => thus, 60

lower quartile = median under the median => thus, 37

minimum = lowest number => thus, 32

And there we have our 5 answers.

Hope this helps!

Answer:

x1 = -4

x2 = 6

Step-by-step explanation:

The 2 vertical lines are "absolute values" meaning whatever they contain has to be positive

For Example

|-3| = 3

So we can ignore if the answer we get is positive or negative because it will forced to be a positive

|3 x 4| = 12

|x - 2| = 4

x1 = 6

x2 = -2

Answer:

[tex]D = 42.5\ inch[/tex]

Step-by-step explanation:

Given

[tex]L = Length[/tex] and [tex]W = Width[/tex]

[tex]L:W = 8: 5[/tex]

[tex]Perimeter = 117[/tex]

Required

Determine the Diagonal

First, the dimension of the screen has to be calculated;

Recall that; [tex]L:W = 8: 5[/tex]

Convert to division

[tex]\frac{L}{W} = \frac{8}{5}[/tex]

Multiply both sides by W

[tex]W * \frac{L}{W} = \frac{8}{5} * W[/tex]

[tex]L = \frac{8W}{5}[/tex]

The perimeter of a rectangle:

[tex]Perimeter = 2(L+W)[/tex]

Substitute [tex]L = \frac{8W}{5}[/tex]

[tex]Perimeter = 2(\frac{8W}{5}+W)[/tex]

Take LCM

[tex]Perimeter = 2(\frac{8W + 5W}{5})[/tex]

[tex]Perimeter = 2(\frac{13W}{5})[/tex]

Substitute 117 for Perimeter

[tex]117 = 2(\frac{13W}{5})[/tex]

[tex]117 = \frac{26W}{5}[/tex]

Multiply both sides by [tex]\frac{5}{26}[/tex]

[tex]\frac{5}{26} * 117 = \frac{26W}{5} * \frac{5}{26}[/tex]

[tex]\frac{5 * 117}{26} = W[/tex]

[tex]\frac{585}{26} = W[/tex]

[tex]22.5 = W[/tex]

[tex]W = 22.5[/tex]

Recall that

[tex]L = \frac{8W}{5}[/tex]

[tex]L = \frac{8 * 22.5}{5}[/tex]

[tex]L = \frac{180}{5}[/tex]

[tex]L = 36[/tex]

The diagonal of a rectangle is calculated using Pythagoras theorem as thus;

[tex]D = \sqrt{L^2 + W^2}[/tex]

Substitute values for L and W

[tex]D = \sqrt{36^2 + 22.5^2}[/tex]

[tex]D = \sqrt{1296 + 506.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = 42.4529150943[/tex]

[tex]D = 42.5\ inch[/tex] (Approximated)

Answer5

Step-by-step explanation:

Answer:

D, 49.42

Step-by-step explanation:

ΔVFT=180-90-43=47

formula

a/sin A = b/sin B/ = c/sin C

So,

FV/sin90=53/sin47

FV=72.4684

FT=√(72.4684)^2-(53)^2

FT=49.4234

Ans:D

The length FT in the given right-angle triangle is 49.42.

So option D is the correct answer.

We are given a right-angle triangle and to find the length of any side we can use Pythagoras theorem or trigonometric identities.

In the triangle, we see that TV = 53 and ∠ FVT = 43°

We will find the length FT by using Pythagoras theorem or trigonometric identities.

What are trigonometric functions?

There are some commonly used trigonometric identities:

SinФ = Perpendicular / hypotenuse

Cos Ф = Base / hypotenuse

Tan Ф =  Perpendicular / Base

We will use Tan Ф =  Perpendicular / Base to find the length FT.

Because we need to use trigonometric identities that have TV and FT.

Tan Ф = FT / TV

Tan 43° = FT / 53

FT = Tan 43° x 53

FT = 0.932515 X 53

FT = 49.42

Thus we got FT = 49.42 using the tan function.

Learn more about trigonometric functions here:

https://brainly.com/question/14746686

$SPJ2

Answer:

0.3333

Step-by-step explanation:

Given the following :

Sample mean(m) = 4.001 inch

Standard deviation(sd) = 0.002 inch

Key specification : = 4 ± .003 inches

Upper specification LIMIT ( USL) : (4 + 0.003) = 4.003 inches

Lower specification limit (LSL) : (4 - 0.003) = 3.997 inches

Cpk is found using the relation:

min[(USL - mean) / (3 * sd), (mean-LSL) / (3*sd)]

min[(4.003 - 4.001)/(3*0.002), (4.001 - 3.997)/(3*0.002)]

min[(0.002 / 0.006), (0.004 / 0.006)]

min[(0.33333, 0.66667)

Therefore Cpk = 0.3333

Because 0.33333<0.66667

Answer:

63 cm

Step-by-step explanation:

If Chubby ran his wheel, which has a diameter of 20cm, we want to find its circumference - this will tell us how far Chubby has ran one one full rotation of the wheel.

The formula for the circumference of a circle is [tex]2\pi r[/tex], where r is the radius. We know the diameter is 20, which is double the radius, so the radius is [tex]20\div2=10[/tex] cm.

We can know substitute inside the formula:

[tex]2\cdot \pi \cdot10\\\\2\cdot 3.14 \cdot10\\\\ 6.28\cdot10\\\\62.8[/tex]

62.8 rounded to the nearest cm is 63.

Hope this helped!

Answer:

6280

Step-by-step explanation:

Answer:

what is the amount of money Kim earn per hour of babysitting? Also I need to know how much trip cost to find out how many hours she need to work.

Step-by-step explanation:

Answer:

a = 55°, b = 65°, c = 65°, d = 60°, e = 120°, f = 60°

Step-by-step explanation:

Vertical angles are congruent. Since a and 55° are vertical angles, we know that a = 55°. Since b and 65° are vertical angles, we know that b = 65°. Alternate interior angles are congruent. Since b and c are alternate interior angles and b = 65°, we know that c = 65° as well. Since 60° and d are alternate interior angles, we know that d = 60°. Supplementary angles add up to 180°. Since d and e are supplementary and d = 60°, we know that e = 180 - 60 = 120°. Since vertical angles are congruent, we see that d and f are vertical angles and we know d = 60°, we also know that f = 60°.

Answer:

$6284.4≤μ≤$6313.6

Step-by-step explanation:

Using the formula for calculating confidence interval as shown:

CI = xbar ± Z×S/√n

xbar is the average premium

Z is the z-score at 95% confidence

S is the standard deviation

n is the sample size

Given parameters

xbar = $6600

Z score at 95% CI = 1.96

S = $800

n = 25

Substituting this parameters in the formula we have;

CI = 6600±1.96×800/√25

CI = 6600±(1.96×800/5)

CI = 6600±(1.96×160)

CI = 6600±313.6

CI = (6600-313.6, 6600+313.6)

CI = (6284.4, 6913.6)

Hence the 95% confidence interval for the mean premium amount paid by all workers who have employer provided health insurance is $6284.4≤μ≤$6313.6

Answer: 250 mi

Step-by-step explanation:

Here we can think in a triangle rectangle:

The distance from Birmingham to Atlanta is roughly 150 mi, and this is one of the cathetus.

And the distance from Birmingham to Nashville is roughly 200 mi, this is the other cathetus of the triangle.

Now, the distance from Atlanta to Nashville will be the hypotenuse of this triangle rectangle.

Now we can apply the Pythagorean's theorem:

A^2 + B^2 = H^2

Where A and B are the cathetus, and H is the hypotenuse:

Then:

H = √(A^2 + B^2)

H = √(150^2 + 200^2) mi = √(62,500) mi = 250 mi

Then the estimated distance from Atlanta to Nashville is 250 mi

Answer:

We conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.

Step-by-step explanation:

We are given that the 190 children born to cocaine users had a mean of 7.3 and a standard deviation of 3.0 The 186 children not exposed to cocaine had a mean score of 8.2 with a standard deviation of 3.0.

Let [tex]\mu_1[/tex] = population mean score for children born to cocaine users.

[tex]\mu_2[/tex] = population mean score for children not exposed to cocaine.

So, Null Hypothesis, : = 490      {means that the prenatal cocaine exposure is not associated with lower scores of four-year-old children on the test of object assembly}

Alternate Hypothesis, : 490     {means that the prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly}

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

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

where, [tex]\bar X_1[/tex] = sample mean score of children born to cocaine users = 7.3

[tex]\bar X_2[/tex] = sample mean score of children not exposed to cocaine = 8.2

[tex]s_1[/tex] = sample standard deviation for children born to cocaine users = 3

[tex]s_2[/tex] = sample standard deviation for children not exposed to cocaine = 3

[tex]n_1[/tex] = sample of children born to cocaine users = 190

[tex]n_2[/tex] = sample of children not exposed to cocaine = 186

Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex]  = [tex]\sqrt{\frac{(190-1)\times 3^{2}+(186-1)\times 3^{2} }{190+186-2} }[/tex] = 3

So, the test statistics =   ~

                                     =  -2.908

The value of t-test statistics is -2.908.

Now, at a 0.05 level of significance, the t table gives a critical value of -1.645 at 374 degrees of freedom for the left-tailed test.

Since the value of our test statistics is less than the critical value of t as -2.908 < -1.645, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.

In the null hypothesis, a test always forecasts no effect, while the alternate theory states the research expectation impact, and calculation as follows:

Calculating the pooled estimator of [tex]\sigma^2[/tex], denoted by [tex]S^2_p[/tex], is defined by

[tex]\to \bold{S^2_p= \frac{(n_1 - 1) S^2_1+ (n_2 - 1)S^2_2}{n_1 + n_2 - 2}}[/tex]

Null hypothesis:

[tex]\to H_0 : \mu_1 - \mu_2 = \Delta_0\\[/tex]

Test statistic:

[tex]\to T_0=\frac{\bar{X_1}- \bar{X_2} -\Delta_0}{S_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \\\\[/tex]

Alternative Hypothesis:

[tex]H_1 : \mu_1 -\mu_2 \neq \Delta_0\\\\ H_1 : \mu_1 -\mu_2 > \Delta_0\\\\H_1 : \mu_1 -\mu_2 < \Delta_0\\\\[/tex]

Rejection Criterion

[tex]t_0 > t_{\frac{\alpha}{2} , n_1+n_2 -2}\ \ \ or\ \ \ t_0 < - t_{\frac{\alpha}{2} , n_1+n_2 -2} \\\\t_o > t_{\alpha , n_1+n_2 -2} \\\\t_o > -t_{\alpha , n_1+n_2 -2}[/tex]

Given value:

[tex]\to S_p=9\\\\\to \Delta_0=0\\\\\to t_0=-\frac{0.9}{3(\sqrt{(\frac{1}{190}+\frac{1}{186})})}=-2.9\\\\\to t_{0.05,374}=1.645\\\\[/tex]

here

[tex]\to t_0 < -t_{0.05,374}[/tex]

hence rejecting the [tex]H_0[/tex]

Since there should be enough evidence that prenatal cocaine exposure is linked to inferior item assembly scores in 4-year-olds.

Find out more about the alternative hypothesis here:

brainly.com/question/18831983

Answer:

B y = -1/2x + 7/2

Step-by-step explanation:

We know that it has a negative slope since the points go from the top left to the bottom right

We can eliminate A and D

The y intercept is where it crosses the y axis

It should cross somewhere between 2 and 4

C  has a y intercept of 9 which is too big

Lets verify with a point

x = -4

y = -4(-4)+9 = 16+9 = 25  (-4,25)  not even close to being near the points on the graph

checking B

y = -1/2 (-4) +7/2

  = 2 + 7/2 = 11/2 = 5.5  it seems  reasonable

Answer:

[tex]\Large \boxed{y=-\frac{1}{2} x+\frac{7}{2} }[/tex]

Step-by-step explanation:

Using a graph,

we can see that the line y = -1/2x + 7/2 best fits for the data.

Answer:

Subtraction property

Step-by-step explanation:

Answer:

Subtraction

Step-by-step explanation:I took the test

Answer:

10,9.75,9.5,9.25,9, 8.75 , 8.5, 8.25, 8...

Step-by-step explanation:

Subtract 0.25 from each to find the next number

Answer:

8.25

Step-by-step explanation:

If you substract .25 from each number until you get to a8 you will get 8.25

Answer:

x = 0.09

Step-by-step explanation:

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

Taking Logarith both sides, we get :

Using the properties of Logarithms:

[tex](x + 2) log(3) = 3 log(2) [/tex]

[tex](x + 2) = 1.91[/tex]

(taking log2= 0.3 and log3= 0.47)

x = 0.09

Answer:

Answer=53,800

Step-by-step explanation:

just add the two zero behind the number

Answer:

Step-by-step explanation:

Circumference of a circle = 2πr

where

r is the radius

From the above question

radius = 25 in.

Substitute this value into the above formula

That's

Circumference = 2(25)π

= 50π

= 157.079

We have the final answer as

Hope this helps you

Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 p.m (6: 04 p.m.)

Explanation:

To solve this question, the first step is to calculate how much time does hiking to the lake, go fishing, and go back takes in total. This can be calculated by adding the time of the three activities. This means 1 hour 10 minutes + 3 hours 10 minutes + 1 hour 50 minutes which is equal to 6 hours 10 minutes. The detailed process is shown below.

Add the hours: 1 + 3 + 1 = 5

Add the minutes: 10+50 +10 = 70

Also, because the total of minutes is above 60 (each hour has 60 minutes) it is necessary to subtract 60 minutes and add 1 hour.

5 hours + 1 hour and 70 minutes - 60 minutes = 6 hours and 10 minutes

Now, to solve the question subtract the time of the activities to the time Lila needs to complete all the activities.

6: 05 p.m.  -  6 hours and 10 minutes = 11: 55 a.m

You can get this result by substracting first the hours and then the minutes

6: 05 p.m. - 6 hours = 12: 05 p.m.

12: 05 - 10 minutes = 11: 55 a.m.

According to this, Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 a.m because if she starts at 11: 54 a.m. she will be back at 6:04, which is a minute before 6:05 p.m.

[tex]x-1=\dfrac{6}{x}\qquad(x\not=0)\\\\x^2-x=6\\x^2-x-6=0\\x^2+2x-3x-6=0\\x(x+2)-3(x+2)=0\\(x-3)(x+2)=0\\x=3 \vee x=-2[/tex]

Answer:

[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

A

Step-by-step explanation:

Answer = A

Answer:x ≤ 3

Step-by-step explanation:

Answer:

x ≥ -3

Step-by-step explanation:

x - 6 ≥ 15 + 8x

x - 8x ≥ 15 + 6

-7x ≥ 21

x ≥ 21/-7

x ≥ -3

x greater than equal to -3

check:

-3 - 6 ≥ 15 + 8*-3

-9 ≥ 15 - 24

Answer:

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Step-by-step explanation:

Quadratic function is given as [tex] f(x) = ax^2 + bx + c [/tex]

Let's find a, b and c:

Substituting (0, 6):

[tex] 6 = a(0)^2 + b(0) + c [/tex]

[tex] 6 = 0 + 0 + c [/tex]

[tex] c = 6 [/tex]

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] 16 = a(2)^2 + b(2) + 6 [/tex]

[tex] 16 = 4a + 2b + 6 [/tex]

[tex] 16 - 6 = 4a + 2b + 6 - 6 [/tex]

[tex] 10 = 4a + 2b [/tex]

[tex] 10 = 2(2a + b) [/tex]

[tex] \frac{10}{2} = \frac{2(2a + b)}{2} [/tex]

[tex] 5 = 2a + b [/tex]

[tex] 2a + b = 5 [/tex] => (Equation 1)

Substituting (3, 33), and c = 6

[tex] f(x) = ax^2 + bx + x [/tex]

[tex] 33 = a(3)^2 + b(3) + 6 [/tex]

[tex] 33 = 9a + 3b + 6 [/tex]

[tex] 33 - 6 = 9a + 3b + 6 - 6 [/tex]

[tex] 27 = 9a + 3b [/tex]

[tex] 27 = 3(3a + b) [/tex]

[tex] \frac{27}{3} = \frac{3(3a + b)}{3} [/tex]

[tex] 9 = 3a + b [/tex]

[tex] 3a + b = 9 [/tex] => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

[tex] 3a + b = 9 [/tex]

[tex] 2a + b = 5 [/tex]

[tex] a = 4 [/tex]

Replace a with 4 in equation 2.

[tex] 2a + b = 5 [/tex]

[tex] 2(4) + b = 5 [/tex]

[tex] 8 + b = 5 [/tex]

[tex] 8 + b - 8 = 5 - 8 [/tex]

[tex] b = -3 [/tex]

The quadratic function that represents the given 3 points would be as follows:

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] f(x) = (4)x^2 + (-3)x + 6 [/tex]

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Answer:

(-5, 0) and (0,4)

Step-by-step explanation:

Given equation: -4x + 5y = 20

Sub. in the values

When x = -5 and y = 0 (-5,0),

[tex] - 4( - 5) + 5(0) = 20 [/tex]

When x = 0 and y = 4 (0,4),

[tex] - 4(0) + 5(4) = 20[/tex]

That's how I would do it, not sure if your school has another method. Hope this helps :)

Answer: x = -5 and y = 4

Step-by-step explanation: its the first option do you need me to exlain how cuz its multiple choice  

Answer:

No the sample does not show that the average age  was different in 2010      

Step-by-step explanation:

From the question we are told that

   The sample size is n =  50

    The  sample mean is  [tex]\= x = 38.5[/tex]

    The population mean is  [tex]\mu = 37[/tex]

     The standard deviation is  [tex]\sigma = 16[/tex]

     The level of significance is  [tex]\alpha = 5 \% = 0.05[/tex]

 The null hypothesis is  [tex]H_o : \mu = 37[/tex]

  The alternative hypothesis is  [tex]H_a : \mu \ne 37[/tex]

The critical value of the level of  significance obtained from the normal distribution table is  ([tex]Z_{\alpha } = 1.645[/tex] )

Generally the test statistics is mathematically evaluated as

          [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

          [tex]t = \frac{ 38.5 - 37}{ \frac{16}{\sqrt{50} } }[/tex]        

         [tex]t = 0.663[/tex]

Now looking at the value  t and  [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis.

This mean that there is no sufficient evidence to state that the sample shows that the average age was different in 2010      

Answer:

46

Step-by-step explanation:

(14+x)/4 = 15

14 + x = 60

x = 46

Answer:

46

Step-by-step explanation:

Let a to d be number 1 to 4 respectively.

15 = (a + b + c + d) / 4

(a + b + c + d) = 60 ------> total sum of the 4 numbers

Since the sum of 3 numbers (assuming a to c) is 14,

Fourth number (d) = 60 - 14

= 46

That's how I would do it, hope this helps :)

Answer:

5/3

Step-by-step explanation:

on both sides we can see that the orginal length of 3 increased to five

therfore if we multiply 3 by 3/5 we get five which means the scale factor is 5/3