Solve this equation. \large \frac{2}{3}x-\frac{1}{5}x=x-1

Answer:

H0 is rejected and Ha is accepted that the students show a higher population mean math score on the SAT if their parents attained a higher level of education.

Step-by-step explanation:

Part a:

The null and alternate hypothesis can be formulated as

H0 : u1 ≤ u2 the two means ( of students whose parents did or did not attain a higher level of education) are equal .

against the claim

Ha: u1 > u2 the students show a higher population mean math score on the SAT if their parents attained a higher level of education.

Part b:

The point estimate of the difference between the means for the two populations is the difference of sample means

x1`- x2`

525- 487= 38

Student’s Parents

College Grads

x                                            x²

485      487               235,225         237,169

534      533                  285,156        284,089

650     526                 422,500         267,676

554       410                   306,916          168,100

550      515                   302,500        265,225

572      578                      327,184        334,084

497      448                     247,009        200,704

592     469                  350,464         219,961          

∑xi = 8400                      ∑xi ²= 4,462,962          

x1`= ∑ xi/n1= 8400/16= 525

Using statistic calculator Using formula :  σ(n-1)

s1= 59.4205

High School Grads

x                                          x²

442          492                   195,364            242,064

580          478                    336,400            228,484

479           425                      229,441             180,625

486            485                     236,196            235,225

528            390                     278,784           152,100

524             535                     274,576           286,225        

∑xi = 5844                                 ∑xi ²= 2,875,484                

x2`= ∑ xi/n2= 5844/12= 487

Using statistic calculator Using formula :  σ(n-1)

s2= 51.7476

x1`- x2`= 525- 487= 38

The test statistic is

t= (x1`- x2`) / √ s1²/n1+ s2²/n2

t= 38/ √(59.4205)²/16 + (51.7476)²/12

t=38 / √3530.7958/16 + 2677.8141/12

t= 1.804

and the degrees of freedom is

υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1

= [3530.7958/16 + (2677.8141/12) ]²/ (3530.7958/16)²/15 +(2677.8141/12)²/11

≈ 25

The degrees of freedom is always rounded in this calculation

From the table t∝ = 1.708

Hence critical value is t ≥ t∝

Reject H0:

Part C.

The p-value is 0.041647.

The result is less than  0.05.

Result:

H0 is rejected and Ha is accepted that the students show a higher population mean math score on the SAT if their parents attained a higher level of education.

Answer:

foot

Step-by-step explanation:

A stream is like a river, but is usually much smaller.  Whether river or stream, the foot is the best measure of width.

Answer:

612 dollars

Step-by-step explanation:

From the given information:

Amount of the total mixture = 6000 pounds

Also, for each batch, there needs to be at least 25% bluegrass seed.

It implies that:

In 6000 pounds, there are (25×6000)/100 = 1500 pounds of bluegrass seed.

The remaining amount of (6000 - 1500 = 4500)pounds will be for rye and Bermuda.

Suppose the amount of rye seeds = x pounds

while that of Bermuda is (4500 - x) pounds

Then, since the amount of Bermuda contains no more than 2/3 of that of rye.

The equation can be written as:

[tex]( 4500 - x) = \dfrac{2x}{3}[/tex]

13500 - 3x = 2x

13500 = 5x

[tex]x = \dfrac{13500}{5}[/tex]

x = 2700

Now, the amount of rye seed = 2700 pounds

while that of Bermuda seed = 4500 - 2700 = 1800 pounds

However, For Bluegrass, we are told that the cost of 1 pound is 12 cents.

So, the cost of 1500 bluegrass seeds = 12 × 1500 = 18000 cents

For rye seed; cost of 1 pound = 14 cents

the cost of 2700 rye seeds = 14 × 2700 = 37800 cents

For Bermuda seed; cost of 1 pound = 3 cents

the cost of 1800 rye seeds = 3 × 1800 = 5400 cents

The total amount = (18000 + 37800 + 5400) = 61200 cents

Recall that:

100 cents = 1 dollars

61200 cents = x dollars

x = 61200 cents/100 cents

x = 612 dollars

Thus, the minimum cost is 612 dollars.

Answer:

line p matches with the first equation

Step-by-step explanation:

Answer:

[tex]40*a*b[/tex]

Step-by-step explanation:

40ab is 40 multiplied by a multiplied by b

Answer:

[tex] {x}^{2} - 25[/tex]

Step-by-step explanation:

[tex](x + 5)(x – 5) \\ \\ = {(x)}^{2} - {(5)}^{2} \\ \\ = {x}^{2} - 25[/tex]

Answer:

x²-25

Step-by-step explanation:

To do a sum like this, break up the first bracket and multiply by the second (terms from the first bracket is in bold in first few steps for clarity):

(x + 5)(x – 5)

x(x-5)+5(x-5)

x²-5x+5x-25

x²-25

Answer:

(6-2) (3/4-3/20)

4 ((3×20-3×4)/80)

4 48/80

4 3/5

Step-by-step explanation:

1) first eliminate constant(number without variable) you eliminate constant by doing the inverse operation(if constant is being added, then subtract)(if constant is being subtracted, then add it)

ex: if   x+9=32

subtract 9 from both sides to get rid of it

x=23

2) if there is another constant but this constant is being multiplied/divided then do the opposite operation to remove it

you could multiply by 3 on both sides:

x+9=69

x=60

Answer:

1) first eliminate constant(number without variable) you eliminate constant by doing the inverse operation(if constant is being added, then subtract)(if constant is being subtracted, then add it)

ex: if   x+9=32

subtract 9 from both sides to get rid of it

x=23

2) if there is another constant but this constant is being multiplied/divided then do the opposite operation to remove it

you could multiply by 3 on both sides:

x+9=69

x=60

Hope this helps!

Step-by-step explanation:

Answer / Step-by-step explanation:

4 * (2 + 3) - 12

To get our final answer, we need to follow PEMDAS, which is :

Parenthesis

Exponent

Multiply

Divide

Addition

Subtraction

These mean that this is the order you will solve by what is in the question, let us start with the parenthesis.

(2 + 3) fits this description, therefore we add them together :

4 * 5 - 12

There are no more parenthesis and also no more exponents, so move onto multiplying.

4 * 5 - 12

20 - 12

Now subtract :

8

Answer:

[tex]y=\dfrac{3}{4}x+15[/tex]

Step-by-step explanation:

Given that,

A line goes through the point (-8,9), and has a slope of 3/4.

We need to express in the form of Ax+B for this line.

We have, m = 3/4

So,

[tex]y=\dfrac{3}{4}x+B[/tex]

Put y = 9 and x = -8 in the above equation.

[tex]9=\dfrac{3}{4}(-8)+B\\\\9=-6+B\\\\9+6=B\\\\B=15[/tex]

So,

[tex]y=\dfrac{3}{4}x+15[/tex]

It is the required equation of the line.

Answer:

Already answered it

Step-by-step explanation:

Answer:

c)

Step-by-step explanation:

Can't be b) or d) because you have to substract... from c2, so it's not c2 -... And it has to be c) because in a) you don't have twice the sum of a and b, you only have twice a and than you add b.

So it's c)

Answer:

I think the answered is x = 16 hope I right

Answer:

X = 16

Step-by-step explanation:

2.5x+10 = 50

distribute the ten to the other side by substracting

2.5x = 50-10

2.5x = 40

Now divide 2.5 on both sides

2.5x/2.5 = 40/2.5

x = 16

Answer:

(PI x 3/4x square) inches

Step-by-step explanation:

A of a circle = pi times radius squared

A = pi times 3/4x - that is 2x times 3/8

A = 3.14 (or whatever you use for pi) x 3/4 x inches square

Answer:

D

Step-by-step explanation:

For each triangle, you are given two sides and the included angle (the one between those 2 sides). That's side-angle-side, so it is S-A-S.

The SAS Rule for Similar Triangles says that for 2 triangles X and Y, if you have the SAS of one and the SAS of the other, then X and Y are similar (same shape and proportions) if

(a) the angle in X is congruent (same) as the angle in Y

(b) the ratio between the two given sides in X is the same as the ratio between the two given sides in Y

For this particular problem, the ratio PR/PQ = 18/21 = 6/7 if you simplify by dividing both top and bottom by 3.

So we are looking for another triangle where we have the same ratio. (Put the smaller number on top, in the fraction.)

Answer A:  12/15 simplifies to 4/5, wrong answer

Answer B:  9/12 simplifies to 3/4, wrong answer

Answer C:  6/10 simplifies to 3/5, wrong answer

Answer D: 15/17.5 looks harder, because there is a decimal in it. But we know 17.5 is just 17 and a half, so I would first multiply top and bottom by 2

We get 30/35. That looks a lot better. Now it is easier to see we can divide both top and bottom by 5.

We get 6/7! That is the correct answer, so D is the triangle similar to PQR.

Step-by-step explanation:

step 1. what is the question? solve for x? okay.

step 2. 28/54 = (2x+ 8)/(5x - 4)

step 3. 28(5x - 4) = 54(2x + 8) (cross multiplication)

step 4. 14(5x - 4) = 27(2x + 8) (divide both sides by 2)

step 5. 70x - 56 = 54x + 216 (distributive property)

step 6. 16x = 272 (group x's and add 56 to both sides)

step 7. x = 17 (divide both sides by 16).

Answer:

26/7 is 3 remander 7 or 3.71

Step-by-step explanation:

Answer:

Quotient = 3, Remainder = 5.

Step-by-step explanation:

Refer to the attached picture.

Step-by-step explanation:

[tex]f(x) = 2( x - 4) ^{2} + 2 \\ f(x) = 2({x}^{2} - 8x + 16) + 2 \\ f(x) = 2 {x}^{2} - 16x + 32 + 2 \\ f(x) = 2 {x}^{2} - 16x + 34[/tex]

Answer:

103

Step-by-step explanation:

Every straight line's angle measurement is 180 degrees, so if one angle is 77 degrees, the other must be 103 degrees to equal 180. (77+103=180)

Hope this helps!

Answer:

20,00,00

Step-by-step explanation:

Answer:

x = 13

y = 18.38

Step-by-step explanation:

tan 45 = x/13       (tangent = opposite / adjacent)

1 = x/13

multiply both sides by 13

x = 13

cos 45 = 13/y       (cosine = adjacent / hypotenuse

0.7071 = 13/y

multiply both side by y

0.7071y = 13

divide both side by 0.7071

y = 18.38

Answer:

45

Step-by-step explanation:

Let the plane speed be x

Let the wind speed be y

x +y= 500.....equation 1

x -y= 410........equation 2

x + y= 500

-

x- y= 410

2x= 90

x= 90/2

x= 45

From equation 1, substitute 45 for x

x + y= 500

45 + y= 500

y = 500-45

x = 455

Hence the speed of the plane is 45

Answer:

4, it's an isosceles trapezoid, so sides TP and RA should be equivalent

Answer:

B. multiply by

Answer:

2t+5

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

If x equals 5, then you just do 2(5) + 7.

2×5=10 10+7=17