A teacher bought some bookmarks for her students. if she gave each students 3 bookmarks, she would have 21 bookmarks left. if she gave each students 5 bookmarks, she would be short of 53 bookmarks . How many students does the Teacher have?​

Answer:

A

Step-by-step explanation:

We can use the trigonometric ratios. Recall that sine is the ratio of the opposite side to the hypotenuse:

[tex]\displaystyle \sin(C)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

The opposite side with respect to ∠C is 24 and the hypotenuse is 26.

Hence:

[tex]\displaystyle \sin(C)=\frac{24}{26}=\frac{12}{13}[/tex]

Our answer is A.

Answer:

0.0174 = 1.74% probability that the sample mean hardness for a random sample of 10 pins is at least 51

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 50, \sigma = 1.5, n = 10, s = \frac{1.5}{\sqrt{10}} = 0.4743[/tex]

What is the probability that the sample mean hardness for a random sample of 10 pins is at least 51

This is 1 subtracted by the pvalue of Z when X = 51. So

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

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{51 - 50}{0.4743}[/tex]

[tex]Z = 2.11[/tex]

[tex]Z = 2.11[/tex] has a pvalue of 0.9826

1 - 0.9826 = 0.0174

0.0174 = 1.74% probability that the sample mean hardness for a random sample of 10 pins is at least 51

Answer:

96 degrees

Step-by-step explanation:

Since x is half of 168, its angle measure is 84 degrees. Since x and y are a linear pair, their angle measures must add to 180 degrees, meaning that:

y+84=180

y=180-84=96

Hope this helps!

[tex]\displaystyle\bf\\\textbf{At any translation of a quadrilateral the sides remain the same,}\\\\\textbf{the angles remain the same.}\\\\\textbf{It turns out that the quadrilateral remains the same.}\\\\P_{A'B'C'D'}=P_{ABCD}=AB+BC+CD+DA=\\\\~~~~~~~~~~~~~~=2.2+4.5+6.1+1.4=\boxed{\bf14.2}[/tex]

Answer:

44.93% probability that the person will need to wait at least 7 minutes total

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and conditional probability.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Conditional probability:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 5 minutes

This means that [tex]m = 5, \mu = \frac{1}{5} = 0.2[/tex]

Assume a person has waited for at least 3 minutes to be served. What is the probability that the person will need to wait at least 7 minutes total

Event A: Waits at least 3 minutes.

Event B: Waits at least 7 minutes.

Probability of waiting at least 3 minutes:

[tex]P(A) = P(X > 3) = e^{-0.2*3} = 0.5488[/tex]

Intersection:

The intersection between waiting at least 3 minutes and at least 7 minutes is waiting at least 7 minutes. So

[tex]P(A \cap B) = P(X > 7) = e^{-0.2*7} = 0.2466[/tex]

What is the probability that the person will need to wait at least 7 minutes total

[tex]P(B|A) = \frac{0.2466}{0.5488} = 0.4493[/tex]

44.93% probability that the person will need to wait at least 7 minutes total

Answer:

(a) The first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.

The second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.

The third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.

(b) The 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.

Step-by-step explanation:

The first, second the third quartile are the values that let a probability of 0.25, 0.5 and 0.75 on the left tail respectively.

So, to find the first quartile, we need to find the z-score for which:

P(Z<z) = 0.25

using the normal table, z is equal to: -0.67

So, the value x equal to the first quartile is:

[tex]z=\frac{x-m}{s}\\ x=z*s +m\\x =-0.67*119 + 462\\x=382.27[/tex]

Then, the first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.

At the same way, the z-score for the second quartile is 0, so:

[tex]x=0*119+462\\x=462[/tex]

So, the second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.

Finally, the z-score for the third quartile is 0.67, so:

[tex]x=z*s +m\\x =0.67*119 + 462\\x=541.73[/tex]

So, the third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.

Additionally, the z-score for the 99th percentile is the z-score for which:

P(Z<z) = 0.99

z = 2.33

So, the 99th percentile is calculated as:

[tex]x=z*s +m\\x =2.33*119 + 462\\x=739.27[/tex]

So, the 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.

Answer: 18 cm

Step-by-step explanation:

We know the circumference formula is C=2πr. Since our circumference is given in terms of π, we can easily figure out what the radius is.

36π=2πr                   [divide both sides by π to cancel out]

36=2r                        [divide both sides by 2]

r=18 cm

Answer:

18cm

Step-by-step explanation:

because i found it lol

Answer:

20 4/5

Step-by-step explanation:

13/5 times 8/1

104/5

which is simplify

to 20 4/5\

hope this helps

Answer:

225º or 3.926991 radians

Step-by-step explanation:

The area of the complete circle would be π×radius²: 3.14×8²=200.96

The fraction of the circle that is still left will be a direct ratio of the angle of the sector of the circle.

[tex]\frac{125.6}{200.96}[/tex]=.625. This is the ratio of the circe that is in the sector. In order to find the measure we must multiply it by either the number of degrees in the circle or by the number of radians in the circle (depending on the form in which you want your answer).

There are 360º in a circle, so .625×360=225 meaning that the measure of the angle of the sector is 225º.

We can do the same thing for radians, if necessary. There are 2π radians in a circle, so .625×2π=3.926991 radians.

Answer:

225º

Step-by-step explanation:

Answer:

The 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two means is:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

It is provided that:

[tex]\bar x_{1}=45\\\bar x_{2}=33.7\\SE_{\text{diff}} =4.14\\\text{Confidence Level}=90\%[/tex]

The critical value of z for 90% confidence level is,

z = 1.645

*Use a z-table.

Compute the 90% confidence interval for the difference in mean number of days meeting the goal as follows:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

    [tex]=45-33.7\pm 1.645\times 4.14\\\\=11.3\pm 6.8103\\\\=(4.4897, 18.1103)\\\\\approx (4.49, 18.11)[/tex]

Thus, the 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Answer:

infinite solutions

Step-by-step explanation:

it means that all x are solution of this equation as 6=6 is always true

Answer:

41

Step-by-step explanation:

[tex]24*2-7=\\48-7=\\41[/tex]

Answer:

The total number of houses are "9". The further explanation is given below.

Step-by-step explanation:

The given values are:

height,

h =  28h - h²

Housing profit of developers will be:

⇒  [tex]\pi^h=28h-h^2-hf[/tex]

If airport won't pay any cost for the damage,

⇒  [tex]\pi^A=20f-f^2[/tex]

then,

⇒  [tex]\frac{\partial \pi^A}{\partial f}[/tex] = [tex]20-2f =0[/tex]

                      [tex]20=2f[/tex]  

                       [tex]f=\frac{20}{2}[/tex]

                       [tex]f=10[/tex]

On putting the value of "f", we get

⇒  [tex]\pi^h=28h-h^2-10h[/tex]

         [tex]=18h-h^2[/tex]

⇒  [tex]\frac{\partial \pi h}{\partial h}=18-2h=0[/tex]

                      [tex]2h=18[/tex]

                        [tex]h=\frac{18}{2}[/tex]

                        [tex]h=9[/tex]

So that the total number of house built by the developers will be "9".

Answer:

C)  µ = 8000.

Step-by-step explanation:

Explanation:-

Given data A grocery store has an average sales of $8000 per day

mean of the Population μ = $ 8000

sample size 'n' = 64

mean of the sample x⁻ = $ 8300

Null Hypothesis : H₀ : μ = $ 8000

Alternative Hypothesis : H₁: μ > $ 8000

Test statistic

[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z = \frac{8300 -8000}{\frac{1200}{\sqrt{64} } }[/tex]

Z = 2

Level of significance : ∝ = 0.05

Z₀.₀₅ = 1.96

The calculated value Z = 2 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted at 0.05 level of significance

Conclusion :-

The advertising campaigns have been effective in increasing sales

Answer:

[tex]X \sim Exp (\mu = 49)[/tex]

But also we can define the variable in terms of [tex]\lambda[/tex] like this:

[tex]X \sim Exp(\lambda= \frac{1}{\lambda} = \frac{1}{49})[/tex]

And usually this notation is better since the probability density function is defined as:

[tex] P(X) =\lambda e^{-\lambda x}[/tex]

Step-by-step explanation:

We know that the random variable X who represents the waiting time to see a shooting star during a meteor shower follows an exponential distribution and for this case we can write this as:

[tex]X \sim Exp (\mu = 49)[/tex]

But also we can define the variable in terms of [tex]\lambda[/tex] like this:

[tex]X \sim Exp(\lambda= \frac{1}{\lambda} = \frac{1}{49})[/tex]

And usually this notation is better since the probability density function is defined as:

[tex] P(X) =\lambda e^{-\lambda x}[/tex]

Answer:

It is vertically stretched by a factor of 200 and shifted 10 units right

Step-by-step explanation:

Suppose we have a function f(x).

a*f(x), a > 1, is vertically stretching f(x) a units. Otherwise, if a < 1, we are vertically compressing f(x) by a units.

f(x - a) is shifting f(x) a units to the right.

f(x + a) is shifting f(x) a units to the left.

In this question:

Initially: [tex]f(x) = \frac{1}{x}[/tex]

Then, first we shift, end up with:

[tex]f(x+10) = \frac{1}{x + 10}[/tex]

f was shifted 10 units to the left.

Finally,

[tex]200f(x+10) = \frac{200}{x + 100}[/tex]

It was vertically stretched by a factor of 200.

So the correct answer is:

It is vertically stretched by a factor of 200 and shifted 10 units right

Answer:

the answer is D

Step-by-step explanation:

Answer:

100 possible extensions

Step-by-step explanation:

we can calculated how many possible extensions they have to try using the rule of multiplication as:

___1_____*___10_____*___10_____*____1____ = 100

1st digit        2nd digit        3rd digit         4th digit

You know that the 1st and 4th digits of the extension are 5. it means that you just have 1 option for these places. On the other hand, you don't remember nothing about the 2nd and 3rd digit, it means that there are 10 possibles digits (from 0 to 9) for each digit.

So, There are 100 possibles extensions in which the 5 is the first and last digit.

Answer:

  [tex]\dfrac{x^2+8x+16}{x-1}[/tex]

Step-by-step explanation:

In general, "over" and "divided by" are used to mean the same thing. Parentheses are helpful when you want to show fractions divided by fractions. Here, we will assume you intend ...

  [tex]\dfrac{\left(\dfrac{x^2+7x+12}{x+3}\right)}{\left(\dfrac{x-1}{x+4}\right)}=\dfrac{(x+3)(x+4)}{x+3}\cdot\dfrac{x+4}{x-1}=\dfrac{(x+4)^2}{x-1}\\\\=\boxed{\dfrac{x^2+8x+16}{x-1}}[/tex]

Answer:

727 adults

Step-by-step explanation:

In a survey of 1914 adults, 38% responded "yes" to the survey question.

=> The number of adults who answered "yes":

N = 1914 x 38/100 = 727.32 = ~ 727

Answer:

727 adults

Step-by-step explanation:

Number of adults = 38% of 1914

                             = 0.38 * 1914

                             = 727.32

                            ≈ 727 adults

Answer:

-10

Step-by-step explanation:

Use the Order of Operations - PEMDAS

Do what is in parentheses first - (4-2) = 2

Next multiply 3 and 4 = 12

Last, perform 2 - 12; which equals -10

Answer:

[tex]f(x)=3x^2+2[/tex] and the limit is 12

Step-by-step explanation:

we know that the derivative of the function f in x=a is the limit of this

[tex]\dfrac{f(a+h)-f(a)}{a+h-a}=\dfrac{f(a+h)-f(a)}{h}[/tex]

as the expression is

[tex][3(a+h)^2+2 ]-14[/tex]

we can say that

     [tex]f(a+h)=3(2+h)^2+2 \\\\f(a)=14[/tex]

from the first equation we can identify a = 2 and then

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

to verify that we are correct, we can compute f(2)=3*4+2=14

f'(x)=6x

so f'(2)=12

we can estimate it from the fraction as well

so the limit is 12

Answer:

Center, radius, chord, diameter... are Words related to circle

Answer:

(a)[tex]D(t)=\dfrac{50000}{1.9t+9}[/tex]

(b)[tex]D'(115)=-1.8355[/tex]

Step-by-step explanation:

The demand function for a product is given by :

[tex]D(p)=\dfrac{50000}{p}[/tex]

Price, p is a function of time given by [tex]p=1.9t+9[/tex], where t is in days.

(a)We want to find the demand as a function of time t.

[tex]\text{If } D(p)=\dfrac{50000}{p},$ and p=1.9t+9\\Then:\\D(t)=\dfrac{50000}{1.9t+9}[/tex]

(b)Rate of change of the quantity demanded when t=115 days.

[tex]\text{If } D(t)=\dfrac{50000}{1.9t+9}[/tex]

[tex]\dfrac{\mathrm{d}}{\mathrm{d}t}\left[\dfrac{50000}{\frac{19t}{10}+9}\right]}}=50000\cdot \dfrac{\mathrm{d}}{\mathrm{d}t}\left[\dfrac{1}{\frac{19t}{10}+9}\right]}[/tex]

[tex]=-50000\cdot\dfrac{d}{dt} \dfrac{\left[\frac{19t}{10}+9\right]}{\left(\frac{19t}{10}+9\right)^2}}}[/tex]

[tex]=\dfrac{-50000(1.9\frac{d}{dt}t+\frac{d}{dt}9)}{\left(\frac{19t}{10}+9\right)^2}}}[/tex]

[tex]=-\dfrac{95000}{\left(\frac{19t}{10}+9\right)^2}\\$Simplify/rewrite to obtain:$\\\\D'(t)=-\dfrac{9500000}{\left(19t+90\right)^2}[/tex]

Therefore, when t=115 days

[tex]D'(115)=-\dfrac{9500000}{\left(19(115)+90\right)^2}\\D'(115)=-1.8355[/tex]

Answer:

Volume of liquid which freezes to ice is 1620. 37 .

Expression to find this is 108x/100 = 1750

Step-by-step explanation:

Let the volume of liquid be x cubic inches

It is  given that volume of liquid increases by 8% when it freezes to ice

increase in volume of x  x cubic inches liquid = 8% of x = 8/100 * x = 8x/100

Total volume of ice = initial volume of liquid + increase in volume when it freezes to ice  = x + 8x/100 = (100x + 8x)/100 = 108x/100

Given that total volume of liquid which freezes is 1750

Thus,

108x/100 = 1750

108x = 1750*100

x = 1750*100/108 = 1620. 37

Volume of liquid which freezes to ice is 1620. 37 .

Expression to find this is 108x/100 = 1750

Answer:

The approximate p-value for the suitable test

0.05 < p < 0.1

|t| = |-1.5806| = 1.5806

t = 1.5806 < 2.009 at 0.05 level of significance

Carisoprodol, a generic muscle relaxer, claims to have, on average, is equal to 120 milligrams of active ingredient.

Step-by-step explanation:

Step(i):-

Given mean of the Population 'μ' = 120 milligrams

Given random sample size  'n' = 50

Given mean of the sample x⁻ = 116.2 milligrams

Standard deviation of the sample 'S' = 17 milligrams

Null hypothesis :  'μ' = 120

Alternative hypothesis : 'μ' < 120

Step(ii):-

Test statistic

[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]

[tex]t = \frac{116.2 - 120}{\frac{17}{\sqrt{50} } } = \frac{-3.8}{2.404} = -1.5806[/tex]

Degrees of freedom

ν = n-1 = 50 -1 =49

t₀.₀₅ = 2.009

|t| = |-1.5806| = 1.5806

t = 1.5806 < 2.009 at 0.05 level of significance

Null hypothesis is accepted

Carisoprodol, a generic muscle relaxer, claims to have, on average, is equal to 120 milligrams of active ingredient.

P- value:-

The test statistic |t| = 1.5806 at 49 degrees of freedom

The test statistic value is lies between 0.05 to 0.1

0.05 < p < 0.1

Answer:

0.0602

Step-by-step explanation:

jus took the test

Answer:

d) [tex]8.97*10^{-3}[/tex]

Step-by-step explanation:

Move the decimal 3 spaces to the right so that way the decimal can be between the first two numbers. When you move the decimal to the right, it makes the exponent negative, when it moves to the left, it makes it positive

Answer:

  15 minutes

Step-by-step explanation:

Betty mows at 3 times the speed that Bullwinkle does, so is equivalent to having 3 Bullwinkles in her place. That makes the lawn get mowed as though 4 Bullwinkles were working, so it will take 1/4 the time it takes Bullwinkle to mow the whole yard. 1/4 of 60 minutes is 15 minutes.

Working together, Betty and Bullwinkle will take 15 minutes to mow the lawn.

Answer:

the math problem is incomplete