[tex]2x + 3y < 45[/tex]
​

Answer:

65

Step-by-step explanation:

45, 50, 52, 58, 62, 68, 72, 78, 81, 95

62 + 68 = 130/2 = 65

The median is 65

Answer:

The median of the data is 65

Step-by-step explanation:

I did it on edge and got it right

Answer:

f(t) = 100,000 ⋅ 0.012 t

Step-by-step explanation:

Hey there! :)

Answer:

x = -1.

Step-by-step explanation:

[tex]\frac{1}{x-4}+ \frac{x}{x-2}= \frac{2}{x^{2}-6x+8 }[/tex]

Make each fraction have a common denominator:

[tex]\frac{1(x-2)}{x^{2}-6x+8}+ \frac{x(x-4)}{x^{2}-6x+8}= \frac{2}{x^{2}-6x+8 }[/tex]

Simplify:

[tex]\frac{x-2}{x^{2}-6x+8}+ \frac{x^{2}-4x }{x^{2}-6x+8}= \frac{2}{x^{2}-6x+8 }[/tex]

Disregard the denominator and solve the numerators:

x - 2 + x² - 4x = 2

Combine like terms:

x² - 3x - 2 = 2

x² - 3x - 4 = 0

Factor:

(x - 4)(x + 1)

***Only one of these solutions works because if x = 4, the denominator of the first fraction would be 0, which is undefined. Therefore, the only possible solution is x = -1.

Answer:

[tex] c = 77.6 [/tex]

Step-by-step explanation:

You may have entered the measure of a side as the measure of an angle.

[tex] \dfrac{\sin A}{a} = \dfrac{\sin C}{c} [/tex]

[tex] \dfrac{\sin 75^\circ}{150} = \dfrac{\sin 30^\circ}{c} [/tex]

[tex] c\sin 75^\circ = 150 \sin 30^\circ [/tex]

[tex] c = \dfrac{150 \sin 30^\circ}{\sin 75^\circ} [/tex]

[tex] c = 77.6 [/tex]

You are correct. Good job!

Answer:

a. The distribution of the sample means is normal with mean 190 mm and standard deviation 1.1031 mm.

b. The probability that the average hand length is less than 189 is P(M<189)=0.1823.

c. The third quartile for the average adult male hand length for this sample size is M_75=190.7440.

d. The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.

Step-by-step explanation:

We have a normal distribution, with mean 190 and standard deviation 7.4.

We take samples of size n=45 from this population.

Then, the sample means will have a distribution with the following parameters:

[tex]\mu_s=\mu=190\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{7.4}{\sqrt{45}}=\dfrac{7.4}{6.7082}=1.1031[/tex]

The probability that the sample mean is less than 189 can be calculated as:

[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{189-190}{7.4/\sqrt{45}}=\dfrac{-1}{1.1031}=-0.9065\\\\\\P(M<189)=P(z<-0.9065)=0.1823[/tex]

The third quartile represents the value of the sample where 75% of the data is to the left of this value. It means that:

[tex]P(M<M^*)=0.75[/tex]

The third quartile corresponds to a z-value of z*=0.6745.

[tex]P(z<z^*)=0.75[/tex]

Then, we can calculate the sample mean for the third quartile as:

[tex]M=\mu_s+z^*\sigma_s=190+0.6745\cdot 1.1031=190+0.7440=190.7440[/tex]

The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.

Answer:

[tex]t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value would be given by:

[tex]p_v =P(t_{(7)}<-0.626)=0.275[/tex]  

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

[tex]\bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

Replacing we got:

[tex]\bar X=58.875[/tex] represent the mean

[tex]s=5.083[/tex] represent the sample standard deviation for the sample  

[tex]n=8[/tex] sample size  

[tex]\mu_o =60[/tex] represent the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 60[/tex]  

Alternative hypothesis:[tex]\mu < 60[/tex]  

The statistic would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value would be given by:

[tex]p_v =P(t_{(7)}<-0.626)=0.275[/tex]  

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Answer:

44

Step-by-step explanation:

11×4

hope it helped!

Answer:

[tex] {1000}^{m} \div {100}^{n} \\ \\ {10}^{3m} \div {10}^{2n} [/tex]

Since they have the same base and are dividing we subtract the exponents

That's

[tex] {10}^{3m - 2n} [/tex]

So

Hope this helps you

Answer:

[tex]\boxed{ z = 3m-2n}[/tex]

Step-by-step explanation:

=> [tex]1000^m / 100^n[/tex]

=> [tex](10)^{3m} / (10)^{2n}[/tex]

Using rule of exponents [tex]a^m/a^n = a^{m-n}[/tex]

=> [tex]10 ^{3m-2n}[/tex]

Comparing it with [tex]10^z[/tex], we get

=> z = 3m-2n

Answer:

Hello There!

`~~~~~~~~~~~~~~~~~~`

26.45 + 4.79 + 120.02 - 3.20 =

148.06

Step-by-step explanation:  Simplify the expression.

Hope this helped you. Brainliet would be nice!

Answer:

Step-by-step explanation:

BODMAS

Align the decimals properly

26.45 + 4.79 + 120.02 = 150.26

26.45

+ 4.79

120.02

______

151.26

______

151.26 - 3.20 = 148.06

Answer:

Blue Triangle.

Step-by-step explanation:

Using the area formula for a triangle, the pink triangle has an area of 0.5×54×33 in² or 891 in². The blue triangle has an area of 0.5×56×39 in² or 1092 in².

Answer:

Step-by-step explanation:

both shapes are triangles so there area is :

A=( b*h) / 2 where h is the height and b the base

A=  (33*54)/2 = 742.5 in²

A= (56*39)/2=  1092 in²

so the blue triangle has a greather area

Answer:

The suitcase originally weighed 44kg.

Step-by-step explanation:

1- 0.25= 0.75 (multiplier)

33÷0.75=44

The suitcase originally weighed 44kg

Answer:

given,

selling price (sp)=rs 5 ×30

=rs 150

now, gain %=20%

cost price (cp)=

[tex] \frac{sp \times 100}{100 + gain\%} [/tex]

[tex] = \frac{150 \times 100}{100 + 20} [/tex]

therefore cp= rs125

now,

again in 2nd case

sp= rs 27×5

therefore sp=rs 135

and cp= rs125

now, sp>cp so,

[tex]gain\% = \frac{sp - cp}{cp} \times 100\%[/tex]

or, gain=

[tex] = \frac{135 - 125}{125} \times 100\%[/tex]

therefore gain %= 8%.... is answer

hope it helps..

Answer:

Xavier's age = 23

Yifei's age = 27

Step-by-step explanation:

Represent Yifei's age with Y and Xavier's age with X;

Given that the sum of their ages is 124;

X + Y = 124

Also, given that Yifei is 4 years older

Y = X + 4

Required

Find their age when they got married

From the parameters above, we've been able to form a simultaneous equation

[tex]X + Y = 124[/tex]

[tex]Y = X + 4[/tex]

Substitute X + 4 for Y in the first equation

[tex]X + X + 4 = 124[/tex]

[tex]2X + 4=124[/tex]

Subtract 4 from both sides

[tex]2X + 4 - 4 = 124 - 4[/tex]

[tex]2X = 120[/tex]

Divide both sides by 2

[tex]\frac{2X}{2} = \frac{120}{2}[/tex]

[tex]X = 60[/tex]

Substitute 60 for X in the second equation

[tex]Y = X + 4[/tex] becomes

[tex]Y = 60 +4[/tex]

[tex]Y = 64[/tex]

To get their ages when they got married; we simply subtract 37 from their current ages

Xavier's age = 60 - 37

Xavier's age = 23

Yifei's age = 64 - 37

Yifei's age = 27

Answer:

8 cm

Step-by-step explanation:

divide 400 by 50 which is 8.

Answer:

x = 2, -3

Step-by-step explanation:

[tex]x^2 + 2x- 6 = 0\\=>x^2 +3x - 2x- 6 = 0\\=>x(x+3) - 2(x +3) = 0\\=> (x-2)(x+3) = 0\\\\[/tex]

(x-2)  = 0     or (x+3) = 0

x = 2  or x = -3

Thus, two values of x are x = 2, -3

Note: The options given are incorrect.

Answer:

a and b.

Step-by-step explanation:

i’m assuming that the 7 is square root of seven.

ap3x verified

Answer:  B) contain the points E and F

Step-by-step explanation:

Dilation of 2 means to multiply both the x- and y-coordinates by 2

see image below

The only option that is true that E'F' contains points E and F

Answer:

  contains the points E and F

Step-by-step explanation:

The center of dilation is an invariant point. It doesn't move, regardless of the dilation factor.

Likewise, any line through the center of dilation will not move. It is not rotated or translated by dilation--it simply is stretched (or compressed) along its length. It is still an infinite line, and it still goes through all of the points it went through before dilation.

The line through the center of dilation that contains points E and F, after dilation, ...

  contains the points E and F.

Answer:

R= sqrt 445

Y = 19

Step-by-step explanation:

Radius is the square root of 445

Find y

So, First step is to substitute what you have

-9^2 + y^2 = 445

 81 + y^2 = 445

-81               -81

y^2 =364

Y is about 19

Let me know if I'm incorrect

Hope this helps :)

Answer:

18 feet

Step-by-step explanation:

Equilateral triangles have 3 equal sides.

If one side is 6 feet, the other two are also 6 feet.

Perimeter is all the sides added.

6 + 6 + 6

= 18

Answer:

a) 95% confidence intervals are

(64.188, 72.652)

b) Mike use  

(t₀.₀₂₅ , ₆)= 2.4469

Step-by-step explanation:

Step(i):-

Given data

    x    :     65    71    74    61    66    70   72

Mean of 'x'

     x⁻ = ∑ x / n

[tex]x^{-} = \frac{65+71+74+61+66+70+72}{7} = 68.42[/tex]

 x       :     65          71        74          61        66         70          72

x - x⁻   :    -3.42     2.58     5.58      -7.42      -2.42    1.58        3.58

(x-x⁻)² :      11.69   6.65     31.13     55.05     5.85      2.49      12.81

∑((x-x⁻)²) =  125.67

Variance

             S² = ∑((x-x⁻)²) / n-1 = [tex]\frac{125.67}{6} = 20.945[/tex]

Standard deviation S = √20.945 =4.576

Step(ii):-

95% confidence intervals are determined by

[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } , x^{-} +t_{\alpha } \frac{S}{\sqrt{n} })[/tex]

Degrees of freedom

ν =n-1 = 7-1 =6

[tex]t_{\frac{\alpha }{2} , n-1 } = t_{(\frac{0.05}{2} , 6)}[/tex]   = (t₀.₀₂₅ , ₆)= 2.4469

[tex](68.42 - 2.4469 \frac{4.576}{\sqrt{7} } , 68.42 +2.4469\frac{4.576}{\sqrt{7} })[/tex]

( 68.42 - 4.232, 68.42 + 4.232)

(64.188, 72.652)

Conclusion:-

95% confidence intervals are

(64.188, 72.652)

Answer:

64.19 to 72.67

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

2/5x40=16

40-16=24

24+9=33

33 marbles

2/5 is .4

Multiply .4 by 40 to get 16

Subtract 16 from 40 to get 24

Add 9 to 24 to get 33

Hope it helps <3

(If it does, please mark brainliest, only need 1 more to get rank up :) )

Answer:

2.4

Step-by-step explanation:

3 3/4 = 3.75

9/3.75 = 2.4

Answer:

T < -25

Step-by-step explanation:

Was correct on TTM

Answer:

The probability that he has exactly 2 hits in his next 7 at-bats is 0.3115.

Step-by-step explanation:

We are given that a baseball player has a batting average of 0.25 and we have to find the probability that he has exactly 2 hits in his next 7 at-bats.

Let X = Number of hits made by a baseball player

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]

where, n = number of trials (samples) taken = 7 at-bats

            r = number of success = exactly 2 hits

            p = probability of success which in our question is batting average

                   of a baseball player, i.e; p = 0.25

SO, X ~ Binom(n = 7, p = 0.25)

Now, the probability that he has exactly 2 hits in his next 7 at-bats is given by = P(X = 2)

          P(X = 2) =  [tex]\binom{7}{2}\times 0.25^{2} \times (1-0.25)^{7-2}[/tex]

                        =  [tex]21 \times 0.25^{2} \times 0.75^{5}[/tex]

                        =  0.3115

Answer:

40x - 16

Step-by-step explanation:

(see attached for reference)

By utilizing the distributive property:

4(10x -4)

= (10x)(4) -4 (4)

= 40x - 16

Answer:

4x10x= 40x           -4x4=-16         40xtimes-4<-----------thats your answer

Step-by-step explanation:

Answer:

10.55% probability

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the CDs are chosen is not important. So we use the combinations formula to solve this question.

1 Bach CD, from a set of 4.

1 Beethoven CD, from a set of 6.

1 Brahms CD, from a set of 3.

1 Handel CD, from a set of 2.

So, D=144

4 CDs from a set of 4+6+3+2 = 15.

So, T= 1365

p= D/T= 144/1365 = 0.1055

10.55% probability that she will choose one by each composer

Answer: G = (19) × (26) × (16)

Step-by-step explanation:

The isomorphism classes of Abelian groups of order 12 are Z₄ ⊕ Z₃ and Z₂ ⊕ Z₂ ⊕ Z₃

SO Let us calculate the orders of some of the elements of G

We have

4² = 16,

4³ = 64

    = 19,

and

4^4 = 19.4

      = 76

      = 31.

furthermore,

4^5 = 31.4

       = 124

       = 34

and

4^6 = 34.4

      = 136

      = 1

Hence, 4 and 34 each have order 6, 16 and 31 each have order 3, and 19 has order 2.

Next, we calculate

11² = 121

    = 31

and

11³ = 11.3

    = 341

    = 26

this is the calculation needed.

26² = 11^6

      = 31³

       = 1

since we already showed that 31 has order 3. This means that 26 has order 2

Since G has two distinct elements of order 2, it cannot be isomorphic to . We conclude

that G = Z₂ ⊕ Z₂ ⊕ Z₃

Finally, we will express as an internal direct product.

The previous calculations show that

(19) = { 1, 19 }

and (26) = { 1, 26 }

are cyclic subgroups of G of order 2 with trivial intersection. We have

(19) × (26) = { 1, 19, 26, 44 }

since

(16) = { 1, 19, 26, 44 }

has trivial intersection with (19) × (26),  conclude that

G = (19) × (26) × (19)

Answer:

[tex]d \approx 2.2[/tex]

Step-by-step explanation:

It is the same process as in previous problems.

Once the origin is the point (0, 0):

[tex]d=\sqrt{(x_{1}-x_{2})^2 + (y_{1}-y_{2})^2}[/tex]

[tex]d=\sqrt{(2-0)^2 + (-1-0)^2}[/tex]

[tex]d=\sqrt{2^2 + (-1)^2}[/tex]

[tex]d=\sqrt{5}[/tex]

[tex]d \approx 2.2[/tex]

Answer:

2.2

Step-by-step explanation:

The distance formula

[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex] with

[tex]x_1=0\\y_1=0\\x_2=2\\y_2=-1[/tex]

[tex]\sqrt{(0-2)^2+(0-(-1))^2}=\sqrt{2^2+1^2}=\sqrt{5}[/tex]

[tex]\sqrt{5} =2.2360...=2.2[/tex]

[tex]\text{We need to find how much the store will sell a GPS navigation system}\\\\\text{We know that the store paid \$56 for it}\\\\\text{We also know that they will mark up the price by 25\%}\\\\\text{We can find 25\% of 56}\\\\56\cdot0.25=14\\\\\text{We can now add that to the original price to get the price the store}\\\text{will sell it for}\\\\56+14=70\\\\\boxed{\$70}[/tex]

Answer:

  B. ∠2 and ∠3 are complementary

Step-by-step explanation:

The substitution property of equality lets you put ∠2 in place of ∠1 in the statement ...

  ∠1 and ∠3 are complementary.

  ∠2 and ∠3 are complementary . . . . using ∠2 for equal ∠1 in the above

Answer: ∠2 and ∠3 are complementary

Step-by-step explanation: