Lisa surveyed 60 students at her school and found that 0.85 of the students she surveyed said their favorite class is math. Another 15% of the students she surveyed reported that their favorite class is science. How many more students in the survey prefer math over science?

Answer:

anything that is not -2+3x or x=2/3 is wrong

Step-by-step explanation:

Answer:

[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]

The expected values for all the categories is :

[tex] E_i =\frac{150}{3}=50[/tex]

And then the statistic would be given by:

[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]

And the best option would be:

b. 4

Step-by-step explanation:

For this problem we have the following observed values:

Yes 40 No 60 No Opinion 50

And we want to test the following hypothesis:

Null hypothesis: All the opinions are uniformly distributed

Alternative hypothesis: Not All the opinions are uniformly distributed

And for this case the statistic would be given by:

[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]

The expected values for all the categories is :

[tex] E_i =\frac{150}{3}=50[/tex]

And then the statistic would be given by:

[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]

And the best option would be:

b. 4

Answer:

2 to the 1/6 th power

Step-by-step explanation:

square root = 1/2

Cube root = 1/3

so 1/3 x 1/2= 1/6

can i please have brainlest

Answer:

2 to the 1/6 th power

Step-by-step explanation:

square root = 1/2

Cube root = 1/3

so 1/3 x 1/2= 1/6

can i please have brainlest

Answer: 3.5 m/s

Step-by-step explanation:

[tex]v=\frac{vf+vi}{2}[/tex]

[tex]v=\frac{5+2}{2}[/tex]

5+2=7

7/2= 3.5

Answer:

Numbers 1,0,8,2 would lie on y-axis.

Step-by-step explanation:

This is because for example, (0,1)

we must prefer 0 as x-axis and 1 as y-axis. That's means left number or side will always be x-axis and right side will always be y-axis.

Answer: (0, 1)

Step-by-step explanation:

When the x is 0 is lies on the y axis.

Answer: (-3, -2)

Step-by-step explanation:

Plug in -2 for y to find x

x - 5(-2) = 7

Multiply -5 and -2

x + 10 = 7

Subtract 10 from both sides

x = -3

The first ordered pair is (-3, -2)

Answer:

A. 2x

Step-by-step explanation:

Step 1: Factor out a 2

2(2x³ - x² + 4x)

Step 2: Factor out an x

2x(2x² - x + 4)

So our answer is B.

Answer: 420 words

Step-by-step explanation:

First find how much he did the first day by doing 1/5*2400=480.

Then find out how much he did the second day by doing 2400-480=1920, then doing 1920*(2/3)=1280.

Then, because he did 220 words the third day, simply do 2400-480-1280-220=420.

Hope it helps <3

Ans420 words per min

Step-by-step explanation:

Answer:

12.5%

Step-by-step explanation:

There is only 1 seven card from the 8 total cards.

1 out of 8.

1/8 = 0.125

P(7) = 12.5%

Answer:

12.5%

Step-by-step explanation:

Total Cards = 8

Number 7 = 1

P(7) = 1/8

In %age:

=> 12.5%

Step-by-step explanation:

It is not specified the compounding period, which in general is a month these days.  So we will assume money is compounded each month, otherwise there is no point depositing monthly.

1. Yolanda:

APR=5% is equivalent to

Monthly interest = 5%/12 = 5/12% = 5/1200 = 1/240 = i

Monthly deposit = 100 = A

Future value after 14 years = 14*12 months = 168 months = n

FV1 =  A((1+i)^n-1)/i

=100*((1+1/240)^168-1)/(1/240)

= $24259.83

2. Zach

He deposits 1200 at the end of the year.  The last payment does not benefit from interest.

Since it is a yearly payment, each amount earns interest over a year, giving an annual interest of

(1+i)^12 -1 = 1.051161897881733 -1 =0.051161897881733 = j

Thus for 13 annual payments with annual interest j gives a compounded amount after 14 years, plus the last payment which does not earn interest

FV2 = A((1+j)^n-1)/j

= 1200((1.051161897881733)^13-1)/(0.051161897881733)+1200

= 22613.34

Summary

Total investments:

Yolanda = 12*100*14 = 16800

Zach = 1200 * 14 = 16800

So both investors have invested $16800 over the 14 year period.

Since Yolanda achieves a higher future value after 14 years ($24259.83) over that of Zach ($22613.34), financially Yolanda has a better strategy.

Note:

If zach had invested annually at the beginning of the year, he would have obtained:

A((1+j)^n-1)/j

= 1200((1.051161897881733)^14-1)/(0.051161897881733)

= 24908.88

which is superior over Yolanda's return.

Answer:

The required sample size increases.

Step-by-step explanation:

The margin of error of a confidence interval is given by:

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which z is related to the confidence level(the higher the confidence level the higher z), [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

The confidence level decreases, so z decreases.

For the margin of error to stay the same, the sample size also has to decrease.

The required sample size increases.

Answer:

a) 6t

b) 6q

c) 8a

d) 2r + 22y

Step-by-step explanation:

a) 6t = 2t +4t

b) 6q = 7q + q-2q

c) 8a = 6-6+8a

d) 2r + 22y = 12r + 10y - 10r +12y

good luck!!

The mass of the lamina is 6 units.

The center of mass of the lamina is (X,Y) = (-3/2, 9/2).

Here,

To find the mass and center of mass of the lamina, we need to integrate the density function ρ(x, y) over the triangular region D.

The mass (M) of the lamina is given by the double integral of the density function over the region D:

M = ∬_D ρ(x, y) dA

where dA represents the differential area element.

The center of mass (X,Y) of the lamina can be calculated using the following formulas:

X = (1/M) ∬_D xρ(x, y) dA

Y = (1/M) ∬_D yρ(x, y) dA

Now, let's proceed with the calculations:

The triangular region D has vertices (0, 0), (2, 1), and (0, 3). We can define the limits of integration for x and y as follows:

0 ≤ x ≤ 2

0 ≤ y ≤ 3 - (3/2)x

Now, let's calculate the mass (M):

M = ∬_D ρ(x, y) dA

M = ∬_D 2(x + y) dA

We need to set up the double integral over the region D:

M = ∫[0 to 2] ∫[0 to 3 - (3/2)x] 2(x + y) dy dx

Now, integrate with respect to y first:

M = ∫[0 to 2] [x(y²/2 + y)] | [0 to 3 - (3/2)x] dx

M = ∫[0 to 2] [x((3 - (3/2)x)²/2 + (3 - (3/2)x))] dx

M = ∫[0 to 2] [(3x - (3/2)x²)²/2 + (3x - (3/2)x²)] dx

Now, integrate with respect to x:

[tex]M = [(x^3 - (1/2)x^4)^2/6 + (3/2)x^2 - (1/4)x^3)] | [0 to 2]\\M = [(2^3 - (1/2)(2^4))^2/6 + (3/2)(2^2) - (1/4)(2^3)] - [(0^3 - (1/2)(0^4))^2/6 + (3/2)(0^2) - (1/4)(0^3)]\\M = [(8 - 8)^2/6 + 6 - 0] - [0]\\M = 6[/tex]

So, the mass of the lamina is 6 units.

Next, let's calculate the center of mass (X,Y):

X = (1/M) ∬_D xρ(x, y) dA

X = (1/6) ∬_D x * 2(x + y) dA

We need to set up the double integral over the region D:

X = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] x * 2(x + y) dy dx

Now, integrate with respect to y first:

X = (1/6) ∫[0 to 2] [x(y² + 2xy)] | [0 to 3 - (3/2)x] dx

X = (1/6) ∫[0 to 2] [x((3 - (3/2)x)² + 2x(3 - (3/2)x))] dx

X = (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x² + 6x - (3/2)x²)] dx

X = (1/6) ∫[0 to 2] [(9/4)x³ - (3/2)x⁴ + 15x - (3/2)x³] dx

Now, integrate with respect to x:

[tex]X = [(9/16)x^4 - (3/8)x^5 + (15/2)x^2 - (3/8)x^4] | [0 to 2]\\X = [(9/16)(2)^4 - (3/8)(2)^5 + (15/2)(2)^2 - (3/8)(2)^4] - [(9/16)(0)^4 - (3/8)(0)^5 + (15/2)(0)^2 - (3/8)(0)^4]\\X = [9/2 - 12 + 15 - 0] - [0]\\X = 15/2 - 12\\X = -3/2[/tex]

Next, let's calculate Y:

Y = (1/M) ∬_D yρ(x, y) dA

Y = (1/6) ∬_D y * 2(x + y) dA

We need to set up the double integral over the region D:

Y = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] y * 2(x + y) dy dx

Now, integrate with respect to y first:

Y = (1/6) ∫[0 to 2] [(xy² + 2y²)] | [0 to 3 - (3/2)x] dx

Y = (1/6) ∫[0 to 2] [x((3 - (3/2)x)²) + 2((3 - (3/2)x)²)] dx

Y= (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x²) + 2(9 - 9x + (9/4)x²)] dx

Y = (1/6) ∫[0 to 2] [(9x - 9x² + (9/4)x³) + (18 - 18x + (9/2)x²)] dx

Now, integrate with respect to x:

[tex]Y= [(9/2)x^2 - 3x^3 + (9/16)x^4) + (18x - 9x^2 + (9/6)x^3)] | [0 to 2]\\Y = [(9/2)(2)^2 - 3(2)^3 + (9/16)(2)^4) + (18(2) - 9(2)^2 + (9/6)(2)^3)] - [(9/2)(0)^2 - 3(0)^3 + (9/16)(0)^4) + (18(0) - 9(0)^2 + (9/6)(0)^3)]\\Y = [18 - 24 + 9/2 + 36 - 36 + 12] - [0]\\Y= 9/2[/tex]

So, the center of mass of the lamina is (X,Y) = (-3/2, 9/2).

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Answer:

-72

Step-by-step explanation:

3*24=72

So he is 72 foot below see level or -72

Martin descended to a depth of 72 feet below sea level.

Ricardo descended to a depth of 24 feet below sea level. His friend Martin descended 3 times as far.

If Ricardo descended to a depth of 24 feet below sea level, and Martin descended three times as far, we can calculate Martin's descent by multiplying Ricardo's depth by 3.

Martin's depth = Ricardo's depth * 3

Martin's depth = 24 feet * 3

Martin's depth = 72 feet

Therefore, Martin descended to a depth of 72 feet below sea level.

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Answer:

A.) NM= x

C.) LM = x√2

E.) tan (45°) = 1

Step-by-step explanation:

If the legs are both x, then the hypotenuse is equal to [tex]x\sqrt{2[/tex]

Therefore, LM= [tex]x\sqrt{2[/tex] is correct and MN= x

Disclaimer: The sum is done according to the picture attached as the question given is wrong.

The true statements regarding the given isosceles right triangle ΔLMN are:

An isosceles triangle is a triangle where two sides and their corresponding angles are equal.

A right triangle is a triangle with one angle = 90°.

An isosceles right triangle is a right-angled triangle with two legs including the right angle are equal. Their corresponding angles are equal and each of them = 45°. So, the three angles of an isosceles right triangle are 45°, 45°, and 90°, always.

In the figure, we can see that we have a ΔLMN, with ∠L = 45°, ∠M = 45°, and ∠N = 90°. Also, we can see that LN = x.

The given angles of ΔLMN determine that it is an isosceles right triangle with a right angle at N.

Since, the two legs involving the right angle, that is N, are equal, we can say that, NM = LN = x.

The hypotenuse of the ΔLMN, that is the side opposite to ∠N, that is LM, can be found using the Pythagoras theorem, by which in a right-angled triangle,

Hypotenuse² = Base² + Perpendicular².

∴ LM² = LN² + NM² = x² + x² = 2x².

or, LM = √(2x²) = x√2.

The tangent of an angle ∅, that is, tan ∅ is computed using the formula,

tan ∅ = Perpendicular/Base.

To calculate tan 45°, that is, tangent to ∠L, we take Perpendicular = NM and Base = LN.

∴ tan 45° = NM/LN = x/x = 1.

Now, we check all the given options:

∴ The true statements regarding the given isosceles right triangle ΔLMN are:

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Answer:

3rd Matrix

Step-by-step explanation:

When you start putting the coefficients in as the matrix, you see that -9 has to be the 1st number, so that eliminates choice B and choice D as answers. You are left with choices A and C. C is the correct choice because when you plug in the second equation, your coefficient is -5, not 0.

Answer:

First Matrix

Step-by-step explanation:

Looking at the first equation, we see that the leading coefficient is -9. This gets rid of choice B and D because the first number in these matrices are not -9. You are left with choices A and C. Looking at the second equation, we see that there is no "w" variable, so we need to add one. The coefficient of this "w" is going to be 0. This means that A is the correct choice. Just to be sure though, evaluate all other coefficients to see if they line up with the matrix. Hope this helps.

As we are not being asked to draw this component form, it makes things a bit more simple. Take the following points that we are given, ( 8, - 2 ) and ( - 2, - 2 ) and consider them in the form ( P1, P2 ) and ( Q1, Q2 ). To determine this component form, you would have to subtract P1 and Q1, P2 and Q2 - or vice versa -

[tex]( 8 - ( - 2 ) ), ( - 2 - ( - 2 ) \\( 10, 0 )\\< 10, 0 >[/tex]

Solution = Option A

Answer:

33%

Step-by-step explanation:

The multiples of 3 are 3,6,9,12

Sum is 6+14+12+1 = 33

The total is 3+6+8+11+14+16+15+12+9+5+1=100

The experimental probability is  number of multiples of 3 over the total

33/100 = 33%

Answer:

Hey!

69/8 as a mixed number is...

8 5/8!

To get this answer, simply divide 69 by 8, then subtract the WHOLE NUMBER from 69 and then the left over number is the numerator over 8

Hope this helps!

Answer:

8 5/8

Step-by-step explanation:

Answer:

  x = 4√5

Step-by-step explanation:

The triangles are all similar, so corresponding lengths are proportional.

  hypotenuse/short side = x/5 = (11+5)/x

  x^2 = 80 . . . . cross multiply

  x = 4√5 ≈ 8.94427

Answer: 0.58

Step-by-step explanation: To write a percent as a decimal, first remember that a percent is a ratio that compares a number to 100.

So we can think of 58% as the ratio 58 to 100 or 58/100.

Dividing by 100 moves the decimal point 2 places to the left so 58/100 would move the decimal point 2 places to the left which would give us .58 or 0.58. So 58% can be written as the decimal 0.58.

Answer:

Pentagon

Step-by-step explanation:

the head is the closest I see

Answer:

3x

Step-by-step explanation:

If Dan is x years old and Olly is 3 times as old, that means that Olly's age is 3 * x or 3x for short.

Answer:

3x

Step-by-step explanation:

If Dan is x years old and Olly is 3 times old as Dan, then the expression is 3x.

Answer:

26.36

Step-by-step explanation:

Hundredths are the second decimal place from the decimal. You would round up to 26.36 because the number before that is up to 5. If it was below 5 you would round down to 26.35.

Answer:

t = d/s

t = 6.4 / 2 miles

t = 3.2 miles

Step-by-step explanation:

follow me plzzz

Answer: 1/35

Step-by-step explanation:

1/5 = 0.2

0.2/7= 1/35

Answer:

Step by step explanation

[tex] \frac{1}{5} \div 7[/tex]

Dividing is equivalent to multiplying with the reciprocal:

[tex] \frac{1}{5} \times \frac{1}{7} [/tex]

Multiply the fraction

[tex] \frac{1 \times 1}{5 \times 7} [/tex]

[tex] = \frac{1}{35} [/tex]

Hope this helps...

Good luck on your assignment.

Step-by-step explanation:

let the larger number be x and smaller number be y

according to this question

x=y+33----------(1)

y+33+5y=129----------(2)

6y+33=129

y=16

x=16+33(takimg equation (1)

x=49

Answer:

Larger number: 49.

Smaller number: 16.

Step-by-step explanation:

Let's say that the larger number is represented by y, and the smaller is represented by x.

y = 33 + x

y + 5 * x = 129

(33 + x) + 5x = 129

6x + 33 = 129

6x = 96

x = 16

y = 33 + 16

y = 49

Check our work...

49 + 5 * 16 = 49 + 80 = 129

49 = 33 + 16 = 49

Since it all works out, the larger number is 49 and the smaller number is 16.

Hope this helps!

Answer:

Amount of money David received = £ 175

Step-by-step explanation:

Both of them share their profit in a ratio of 5:7 . Tina got £70 more than David. Let

the amount David received = a

amount Tina received = 70 + a

the total profit = 70 + 2a

Amount David received = 5/12 × 70 + 2a = a

Therefore,

5/12 × 70 + 2a = a

350 + 10a/12 = a

cross multiply

350 + 10a = 12a

collect like terms

350 = 12a - 10a

350 = 2a

divide both sides by 2

a  = 350/2

a = 175

Amount of money David received = £ 175

Answer:

10% interest.

Step-by-step explanation:

Interest I = PRT/100

If the rate R = x% we have

550 = P*x *1 / 100

and

770 = P*(x + 4) * 1 / 100

so From  first equation

Px = 55000  and from the second

Px + 4P =  77000

So Px = 77000 - 4P

Therefore  77000 - 4P = 55000

4P = 22000

P = 5,500

So x = 55000/5500 = 10%.

And  the rate for the other fund is 10 + 4 = 14%.