F(x)= (x-2)^2 (x+2)(x+3)

Answer:

The null and alternative hypotheses are:

[tex]H_{0}: p=0.67[/tex]

[tex]H_{a} : p <0.67[/tex]

Under the null hypothesis, the test statistic is:

[tex]z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

Where:

[tex]\hat{p}= \frac{23}{42} = 0.5476[/tex]

[tex]\therefore z = \frac{ 0.5476 -0.67}{\sqrt{\frac{0.67(1-0.67)}{42} }}[/tex]

         [tex]=\frac{-0.1224}{0.072555398}[/tex]

         [tex]=-1.69[/tex]

Now, we have to find the left tailed z critical value at 0.01 significance level using the standard normal table. The z critical value at 0.01 significance level is:

[tex]z_{critical} = -2.33[/tex]

Conclusion: Since the test statistic does not fall in the critical region, therefore, we fail to reject the null hypothesis, and conclude that there is not sufficient evidence to say that the population proportion of women athletes who graduate from the university is now less than 67%.

Answer: No

By considering the given information , the null and the alternative hypotheses will be :-

[tex]H_0: p=0.67\\\\H_a: p<0.67[/tex]

Since the alternative hypotheses is left-tailed , so the test applied here is left-tailed.

Sample size : n= 42

The sample proportion of graduated : [tex]\hat{p}=\dfrac{23}{42}\approx0.55[/tex]

The test statistic for population proportion :-

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

i.e. [tex]z=\dfrac{0.55-0.67}{\sqrt{\dfrac{0.67(1-0.67)}{42}}}\approx-1.65[/tex]

The p-value : [tex]P(z<-1.645)=0.0494715[/tex]

Since the p-value is greater than the significance level, then we do not reject the null hypothesis.

Hence, it does not give enough evidence to indicate that the population proportion of women athletes who graduate from the university is now less than 67%.

Answer:

9,90

Step-by-step explanation:

Since their lack is 90, we can divide 810 by 90 and get 9. So 9 is their common factor. So 9 and 90.

To find two numbers with 90 as their LCM and 810 as their product, prime factorize 810, and choose two numbers from the prime factors that satisfy the conditions.

The question asks to find two numbers that have 90 as their lowest common multiple (LCM) and 810 as their product.

To find these numbers, we need to first prime factorize 810. The prime factorization of 810 is 2 x 3 x 3 x 3 x 3 x 5.

Now, we need to choose two numbers from these prime factors such that their product is 810 and their LCM is 90. Since 90 = 2 x 3 x 3 x 5, we can choose 3 x 3 x 2 = 18 and 5 as the two numbers.

Answer:

$110

Step-by-step explanation:

A = P(1 + r/n)ⁿ⁺

A = 100(1 + .02/1)¹⁽⁵⁾

A =  100(1.10)

A = $110

Using the simple interest formula, you can calculate that after 5 years at an annual interest rate of 2%, an initial deposit of $100 in a savings account would grow to $110.

The subject of this question is simple interest, which is important in Mathematics. To calculate how much money would be in your account after 5 years with an interest rate of 2% per annum, you would utilize the simple interest formula:

Interest = Principal x Rate x Time (I = PRT)

The principal (P) is the initial amount of money, which is $100. The rate (R) is the interest rate per period. The time (T) represents the number of periods.

In our case: The principal is $100, the rate is 2% (or 0.02 in decimal form), and the time is 5 years. Substituting these values into the formula gives. Interest = $100 x 0.02 x 5 = $10. After 5 years, you are entitled to $10 interest. This means the total amount in your account will be your initial principal plus the earned interest: $100 + $10 = $110.

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Answer:

45 and 36

Step-by-step explanation:

The common denominator for the two proper fractions is 45

A proper fraction is a fraction which has its numerator value less than the denominator. For example, ⅔, 6/7, 8/9, etc. are proper fractions.

Given here: The proper fractions 9/15 and 4/9

now LCM(9,15) = 45

Thus, 9×3/45=27/45 , 4×5/45=20/45

Hence, The common denominator for the two proper fractions is 45

Learn more about proper fractions here:

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Answer:

v=2-2root7, v=2+2root7  

Step-by-step explanation:

-2v+8(1+2v)=-90

-2-4v^2+8+16v=-90

6-4v^2+16v=-90

-4v^2+16v=-96

v=2-2root7, v=2+2root7

Answer

-2v+8 (1+2v)=-90 then V = -7

Step-by-step explanation:

-2v + 8 x (1 + 2v) = -90

-2v + 8 + 16v = -90

14v + 8 = -90

14v = -98  

V = -98/14

V= -7

Hope this helps ;)

Answer:

748 trees  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

b + 2c + 3jb + 2c + 3j =

88 + 2(33) + 3(44)(88) + 2(33) + 3(44) =

88 + 66 + 396 + 66 + 132 = 748 trees

After Ben spends 88 hours chopping, Cam spends 33 hours chopping, and Justin spends 44 hours chopping, they chop down a total of 286 trees.

To find the total number of trees chopped down, we'll use the given formula: ( b + 2c + 3j ), where ( b ) is the number of hours Ben spends chopping, ( c ) is the number of hours Cam spends chopping, and ( j ) is the number of hours Justin spends chopping.

Given that Ben spends 88 hours chopping ( b = 88 ), Cam spends 33 hours chopping ( c = 33 ), and Justin spends 44 hours chopping ( j = 44), we can substitute these values into the formula.

Plugging in the values:

[tex]\[ \text{Total trees} = 88 + 2(33) + 3(44) \][/tex]

Now, we calculate each term:

[tex]\[ 2(33) = 66 \][/tex]

[tex]\[ 3(44) = 132 \][/tex]

Then, we add up all the terms:

[tex]\[ \text{Total trees} = 88 + 66 + 132 \][/tex]

[tex]\[ \text{Total trees} = 286 \][/tex]

So, after Ben spends 88 hours chopping, Cam spends 33 hours chopping, and Justin spends 44 hours chopping, they chop down a total of 286 trees.

Answer:

BD= 56units

Step-by-step explanation:

  Since, Diagnols of a parallelogram  bisect each other.

Therefore in parallelogram ABCD where AC and BD are the diagnols wich intersect at Point E, we have, BE=DE

Therefore, x^2-21=4x

x^2-21-4x=0

x^2-4x-21=0

x^2-7x-3x-21=0      [middle term splitting]

x(x-7)+3(x-7)=0

(x+3)(x-7)=0

Hence, x= -3 and x= 7

Since x cannot be negative because no side can have negative values

Therefore, we have x=7

Now, BD= BE+DE      [Since E is the intersecting point of BD]

            = 4x+x^2-21

            = 4(7)+7^2-21

            =28+49-21= 56 units

Answer:

the guinea pig is 21 cm longer

Step-by-step explanation:

fish = 40 mm

guinea pig 25 cm

convert the fish to cm

1 cm = 10 mm

40 mm * 1 cm/10 mm =  4 cm

guinea  pig - fish

25 cm - 4 cm

21 cm

the guinea pig is 21 cm longer

Answer:

y + 1 = 3(x - 5)   Answer

Step-by-step explanation:

Find the slope of the perpendicular line.

m1 * m2 = - 1

m1 = - 1/3

m2 is the slope of the perpendicular

(-1/3) * m2 = - 1             Multiply both sides by -3

-(3)(-1/3) * m2 = -1 * -3  

m2 = 3

The slope of the perpendicular line is 3

Find the equation of the line.

m = (y - y1)/(x -x1)

y - y1 = m(x - x1) is the equation of the line.

y1 =5

x1 = - 1

(y - - 1) = 3(x - 5)

y + 1 = 3(x - 5)   Answer

Answer: 5 gallons

Step-by-step explanation:

There are 3 x's on the graph for 1/4, so 1/4 times 3=3/4

There are 2 x's on the graph for 3/8, so 3/8 times 2=3/4

There are 4 x's on the graph for 5/8, so 5/8 times 4=5/2

There is only 1 x for 1, so it will remain 1.

So if you add these up,

3/4+3/4+5/2+1

6/4+10/4+1

16/4+1

4+1

There is 5 gallons of sap produced that day.

Hope this helped!

Answer:

5 gallons

Step-by-step explanation:

Number of x's on  1/4 = 3

So, amount of sap trees produce that day = 3/4

Number of x's on 3/8 = 2

So, amount of sap trees produce that day = 2 × 3/8 = 3/4

Number of x's on 5/8 = 4

So, amount of sap trees produce that day = 4 ×5/8 = 5/2

Number of x's on 1 = 1

So, amount of sap trees produce that day = 1 × 1 =1

Therefore,

total amount of sap the trees produce =  amount of sap trees produce based on number of x's on 1/4 +  amount of sap trees produce based on number of x's on 3/8 +  amount of sap trees based on number of x's on 5/8 + amount of sap trees based on number of x's on 1 = [tex]\frac{5}{2}+\frac{3}{4}+\frac{3}{4}+1=\frac{10+3+3+4}{4}=\frac{20}{4}=5\,\,gallons[/tex]

Answer:

d ≤ 4

Step-by-step explanation:

4d + 7 ≤ 23

Subtract 7 from both sides:-

4d ≤ 16

d ≤ 4

[tex]Solution, 4d+7\le \:23\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:d\le \:4\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:4]\end{bmatrix}[/tex]

[tex]Steps:[/tex]

[tex]4d+7\le \:23[/tex]

[tex]\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides},\\4d+7-7\le \:23-7[/tex]

[tex]\mathrm{Simplify},\\4d\le \:16[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}4,\\\frac{4d}{4}\le \frac{16}{4}[/tex]

[tex]\mathrm{Simplify},\\d\le \:4[/tex]

[tex]\mathrm{The\:Correct\:Answer\:is\:d\le \:4}[/tex]

[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]

[tex]-Austint1414[/tex]

Answer:

Price in Japan= 17.81

Price in Switzerland = 13.58

Step-by-step explanation:

First set up system of equations

80.59 = 3j +2s

76.36 = 2j + 3s

Make it to where you can eliminate one variable

161.18 = 6j +4 s

-229.08 = -6j - 9s

Reset the problem

-67.9 = -5s

s=13.58

Re plug them in to the original equation to get j = 17.81

By solving a system of linear equations formed from the given information, we found the average cost of a movie ticket in Japan to be $24.60, and in Switzerland to be $6.79.

Let's denote J as the cost of a movie ticket in Japan and S as the cost of a movie ticket in Switzerland. From the problem, we establish two equations: 3J + 2S = $80.59 and 2J + 3S = $76.36. This is a system of linear equations that can be solved by substitution or elimination. If you choose elimination, add these two equations together, which results in 5J + 5S = $156.95, or J + S = $31.39. Now, substitute (J + S) in first equation, we get 3J + 2(31.39 - J) = 80.59. Solving this equation we find J = $24.60. Thus, the price of a movie ticket in Switzerland is S = $31.39 - $24.60 = $6.79. Therefore, a movie ticket in Japan costs $24.60 on average, and in Switzerland, it costs $6.79.

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The complete question is here:

Average movie prices in the United States are, in general, lower than in other countries. It would cost $80.59 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $76.36. How much does an average movie ticket cost in each of these countries?

In Japan the average cost is __.

In Switzerland the average cost is _____.

Answer:

$128,088.54

Step-by-step explanation:

Year Year Deposits Year Interest Total Deposits Total Interest Balance

1  $4,800.00  $72.10  $4,800.00  $72.10  $4,872.10

2  $4,800.00  $207.79  $9,600.00  $279.89  $9,879.89

3  $4,800.00  $347.25  $14,400.00  $627.15  $15,027.15

4  $4,800.00  $490.60  $19,200.00  $1,117.74  $20,317.74

5  $4,800.00  $637.94  $24,000.00  $1,755.68  $25,755.68

6  $4,800.00  $789.38  $28,800.00  $2,545.06  $31,345.06

7  $4,800.00  $945.04  $33,600.00  $3,490.11  $37,090.11

8  $4,800.00  $1,105.04  $38,400.00  $4,595.14  $42,995.14

9  $4,800.00  $1,269.49  $43,200.00  $5,864.63  $49,064.63

10  $4,800.00  $1,438.52  $48,000.00  $7,303.15  $55,303.15

11  $4,800.00  $1,612.26  $52,800.00  $8,915.41  $61,715.41

12  $4,800.00  $1,790.83  $57,600.00  $10,706.24  $68,306.24

13  $4,800.00  $1,974.38  $62,400.00  $12,680.62  $75,080.62

14  $4,800.00  $2,163.05  $67,200.00  $14,843.67  $82,043.67

15  $4,800.00  $2,356.96  $72,000.00  $17,200.63  $89,200.63

16  $4,800.00  $2,556.28  $76,800.00  $19,756.91  $96,556.91

17  $4,800.00  $2,761.14  $81,600.00  $22,518.05  $104,118.05

18  $4,800.00  $2,971.72  $86,400.00  $25,489.77  $111,889.77

19  $4,800.00  $3,188.15  $91,200.00  $28,677.92  $119,877.92

20  $4,800.00  $3,410.62  $96,000.00  $32,088.54  $128,088.54

Answer:

The account after 20 years is $73798.8.

Step-by-step explanation:

Given : James and Terry open a savings account that has a 2.75% annual interest rate, compounded monthly. They despoit $400. Into the account each month.

To find : How much will be in the account after 20 years ?

Solution :

Using monthly payment formula,

[tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]

Discount factor is [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]

Substitute in the formula,

[tex]\text{Amount}=M\times \frac{1-(1+i)^{-n}}{i}[/tex]

Where, M=$400 amount deposited monthly

r= 2.75%=0.0275 is the interest rate

[tex]i=\frac{0.0275}{12} =0.00229[/tex]

t=20 years is the time

[tex]n=12\times 20=240[/tex]

Substitute the value,

[tex]\text{Amount}=400\times \frac{1-(1+0.00229)^{-240}}{0.00229}[/tex]

[tex]\text{Amount}=400\times \frac{1-0.5775}{0.00229}[/tex]

[tex]\text{Amount}=400\times 184.497[/tex]

[tex]\text{Amount}=73798.8[/tex]

Therefore, the account after 20 years is $73798.8.

The formula of a Surface Area of a cylinder:

[tex]S.A.=2\pi r^2+2\pi rH[/tex]

r - radius

H - heihgt

We have r = 3mm and H = 16mm. Substitute:

[tex]S.A.=2\pi(3)^2+2\pi(3)(16)=2\pi(9)+2\pi(48)=18\pi+96\pi=114\pi\ mm^2\\\\\pi\approx3.14\to S.A.\approx114\cdot3.14=357.96\ mm^2[/tex]

Answer:

It's B ) 5.18*108

Step-by-step explanation:

Multiplying these two gives you 518,000,000

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

518, 000, 000

So, it can be written as

[tex]518\times 10^6[/tex]

But we need a scientific notation which means that decimal should be put after first number.

So, scientific notation would be

[tex]5.18\times 10^8[/tex]

Hence, Option 'B' is correct.

Answer: [tex]y=13.5[/tex]

Step-by-step explanation:

1. By definition, if [tex]y=9[/tex] when [tex]x=2[/tex], then:

[tex]\frac{y}{x}=\frac{9}{2}[/tex]

2. Keeping this on mind, to find the value of [tex]y[/tex] when [tex]x=3[/tex], you must apply the following proccedure:

[tex]\frac{y}{3}=\frac{9}{2}[/tex]

3. Now, you must solve for [tex]y[/tex], as following:

[tex]y=3(\frac{9}{2})\\y=\frac{27}{2}\\y=13.5[/tex]

4. Then, the result is:

[tex]y=13.5[/tex]

Answer:

(p-2l)/2 = w

Step-by-step explanation:

p=2l+2w

We want to solve for w.

The first step is to subtract 2l from each side

p-2l=2l-2l+2w

p-2l=2w

Then we will divide each side by 2 to isolate w

(p-2l)/2 = 2w/2

(p-2l)/2 = w

Answer: 7 hours 12 minutes

Step-by-step explanation:

Let he needs x hours to make 1 kg of meat.

Therefore, time taken in making 5 kg of meat = 5 × x = 5x hours.

But, According to the question,

He needs 12 hour to cook 5 kg of meat.

Thus, 5 x = 12

⇒ [tex]x = \frac{12}{5}[/tex] ( By dividing both sides by 5 )

⇒ He needs [tex] \frac{12}{5}[/tex] hours to make 1 kg of meat.

⇒ The time taken to cook 3 kg of meat = [tex]3\times \frac{12}{5}=\frac{36}{5} [/tex]

= [tex]7\frac{1}{5}[/tex]  hours ⇒ 7 hours 12 minutes

Hence, He needs 7 hours 12 minutes time to cook 3 kg of meat.

After calculating, we determined that Myron needs 54 minutes to cook 3 kilograms of meat.

This problem can be solved by setting up a proportion since it involves a direct ratio between the weight of meat and the cooking time.

The given ratio is 1 1⁄2 hours for 5 kilograms of meat (1:5 ratio). To find the time needed for 3 kilograms of meat, use the proportion:

    5 kg      :-      1 1⁄2 hours
    3 kg      :-       x hours

Solving for x yields the following:

    5 kg  /  3 kg  =  1 1⁄2 hours  /  x hours
             x  =  (1 1⁄2 hours × 3 kg)  /  5 kg

Converting 1 1⁄2 hours to minutes (90 minutes) and then performing the multiplication and division:

             x  =  (90 minutes × 3)  /  5
             x  =  270 minutes  /  5
             x  =  54 minutes

Thus, Myron needs to cook 3 kilograms of meat for 54 minutes.

Answer:

-37

Step-by-step explanation:

Well for the multiplication its easy because if it is different signs then all you have to do is multiply it normally the add the negatuve sign.

6×5=30

-6×5=-30

2. For adding negative number to a negative number you just add it on.

Answer:

-37

Step-by-step explanation:

Remember to follow PEMDAS and the left -> right rule.

PEMDAS:

Parenthesis

Exponent (& roots)

Multiplication

Division

Addition

Subtraction

----------------

Also, note the rules of sign:

Multiplying...

Positive number and another positive number will result in a positive answer.

Positive number and a negative number will result in a negative answer.

Negative number and another negative number will result in a positive answer.

--------------------------------------------------------------------------------------------------------

Note the question:

5 x -6 + (-7)

First, change the sign for -6 + -7. Note the rule above and change the sign.

5 x -6 - 7

Next, solve. Remember to follow PEMDAS. Multiply 5 and -6 together

5 x -6 = -30

Then, combine the remaining terms.

-30 - 7 = -37

You're answer:

-37

--------------------------------------------------------------------------------------------------------

~

Answer:17

Step-by-step explanation:8+9 =17

Answer:

51

Step-by-step explanation

Given angles can break like this :

231 = 180 +51

51= 0+51

-129= -180+51

591= 360+180+51

so angles 231, -129 and 591 corresponds to the same terminal while 51 is not related to the particular quadrant . so 51 is not co-terminal with the other three angles .

Answer

The answer is the fourth one or D.

Step-by-step explanation:

Answer:

THE ANSWER IS D

Step-by-step explanation:

I DID TEST GOT 100

Answer:

85

Step-by-step explanation:

Answer:85 would be the correct Answer

Can I have Brainliest?

Step-by-step explanation:

Answer:

x² - 2x - 3

Step-by-step explanation:

P(x) - Q(x)

= x² - x - 6 - (x - 3) ← distribute

= x² - x - 6 - x + 3 ( collect like terms )

= x² - 2x - 3

Answer:

I believe 5 units

Step-by-step explanation: I believe it is five units because the other one Chord AB is also 5 units.  Plz mark brainliest if correct

Answer:

5

Step-by-step explanation:

Because it is at same distance as other one from center so they have same lengths

Answer:

Intercepts at (-1, 0) and (0, 1).

Step-by-step explanation:

The double intercept form for the equation of a line is

ax + by = 1

-1 = -y + x

y = 0

x = -1     Multiply each side by -1

-x = 1

The x-intercept is at (-1, 0).

=====

x = 0

-1 = -y     Multiply each side by -1

y = 1

The y-intercept is at (0, 1).

=====

The graph (see below) is a straight line passing through the points (-1, 0) and (0, 1).

Answer:

Part A) [tex]5\ in=15\ ft[/tex]

Part B) [tex]7\ in=21\ ft[/tex]

Step-by-step explanation:

we know that

The scale factor is [tex]\frac{1}{3}\frac{in}{ft}[/tex]

so

using proportion

Part A)

[tex]\frac{1}{3}\frac{in}{ft}=\frac{5}{x}\frac{in}{ft}\\ \\x=5*3\\ \\x=15\ ft[/tex]

therefore

[tex]5\ in=15\ ft[/tex]

Part B)

[tex]\frac{1}{3}\frac{in}{ft}=\frac{7}{x}\frac{in}{ft}\\ \\x=7*3\\ \\x=21\ ft[/tex]

therefore

[tex]7\ in=21\ ft[/tex]

2x + 5y = 34

x+2y = 14

Multiply the second equation by two to create like terms for one variable.

2(x+2y = 14)

2x + 4y = 28

2x + 5y = 34

2x + 4y = 28 -- Subtract.

y = 34.28 = 6

Solve for x

x + 2(6) = 14

x + 12 = 14

x = 2

Check:

2 + 2(6) = 14

2 + 12 = 14

14 = 14

Answer:

X = 2

Y = 6

Answer:

I need the picture of the pyramid to solve.

Step-by-step explanation:

Answer:

52.4%

Step-by-step explanation:

Simply multiply the value with 100 to find the percentage

thus 0.524× 100 = 52.4%

To convert the decimal 0.524 to a percentage, you multiply it by 100, which results in 52.4%.

To convert 0.524 to a percentage, you multiply the number by 100. This is because when converting a decimal to a percentage, you are essentially calculating how many parts out of 100 it represents. Thus, converting the decimal 0.524 to a percentage involves the calculation:

0.524 × 100 = 52.4%.

So, the decimal 0.524 is equal to 52.4% when expressed as a percentage. This concept is useful in various contexts such as interpreting statistics, understanding the rise in cost of living, or when calculating a rate of growth or decline in a given scenario.