Out of a sample of 1,450 people, 1,000 said they prefer to drive themselves to work rather than carpool. Construct a 95% confidence interval for the population mean of people who would rather drive themselves than carpool.

CI = (65.84%, 72.09%)
CI = (66.58%, 71.35%)
CI = (65.27%, 72. 13%)
CI = (66.97%, 70.96%)

The total money that student saves after paying tax and other expenses is $9600

It is given that

Total earning = $15000

Tax = 1%

Spendings on living expenses = 25%

The percentage is the value per hundred.

Total saving = Total earning- Tax-spendings on living expenses

Total saving  = 15000-(11% of 15000 -(25%of 15000)

Total saving = 15000-11*15000/100 - 15000*25/100

Total saviing  = 15000-1650-3750

Total saving = $9600

Therefore, The total money that student saves after paying tax and other expenses is $9600.

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Answer:

D) 7.1 units³

Step-by-step explanation:

V = (3.14)(1.5)²(3/3)

= (3.14)2.25 = 7.1

Answer:

96.2

Step-by-step explanation:

The material Nabil need in order to make the second prism is 87.5

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.

So area of first figure = k² × area of second figure

Similarly,

Volume of first figure = k³ × volume of second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

We are given that;

Volume of material= 1000 cm³

Volume of prism= 8.7 cm³

Now,

Find the volume of the first prism using the formula: V = (1/2)bhℓ1, where b is the base, h is the height of the triangle, and ℓ is the length of the prism. Plug in the given values: V = (1/2)(8.7)(8.7)(10) = 378.45 cm³

Find the volume of the second prism using the same formula, but multiply each dimension by 5 since it is a dilation with a scale factor of 5: V = (1/2)(5b)(5h)(5ℓ) = (1/2)(43.5)(43.5)(50) = 46593.75 cm³

Subtract the volume of material he has from the volume of material he needs for both prisms: 1000 - (378.45 + 46593.75) = -45972.2 cm³

Since he needs more material than he has, he needs to get more material with a volume equal to | -45972.2 | cm³ or 45972.2 cm³.

Therefore, by dilation the answer will be 87.5

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Answer:

   x = 8

Step-by-step explanation:

The halves of a bisected segment are congruent, so we have ...

  YZ = YX

  3x -5 = 2x +3

  x = 8 . . . . . . . . add 5-2x

__

Additional comment

The right triangles are congruent, so ...

  WZ = WX

  2y +7 = 5y -8

  15 = 3y

  5 = y

Answer:

A.   x = 0, 14

B.   x = 12, -2

Step-by-step explanation:

A.

2x - 3       x + 6

    /      =      /

 x + 1        x - 2

 2x^2 - 7x + 6  =  x^2 + 7x + 6

-  x^2 - 7x - 6   -  x^2 - 7x - 6    

x^2 - 14x = 0        

( x + 0 ) = 0     ( x - 14 ) =  0

x = 0,                    +14     +14

                                x = 14

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

B.

2               x

/     =         /

x          5x + 12

x^2 = 2( 5x + 12 )

x^2                   = 10x + 24

     - 10x - 24    - 10x - 24

x^2 - 10x - 24 = 0

( x - 12 ) = 0      ( x + 2) = 0

    +12     +12         -2     -2

x = 12,               x = -2

I hope this helps!

The correct  null and the alternative hypotheses are:

[tex]h_0: \mu = 2.7\\\\ h_a: \mu < 2.7[/tex]

A hypothesis is an untested statement in mathematics that is supported by all available data and numerous weaker results.

A "conjecture" is a mathematical statement that has not been proven.

The given data in the problem is;

n is the sample size = 40

μ is the population mean = 2.7

[tex]\rm \sigma[/tex] is the standard deviation= 0.2

[tex]\bar x[/tex] is the sample mean:= 2.3

It is found that the null hypothesis always shows the equality sign.

So for the null hypothesis;

[tex]h_0: \mu = 2.7[/tex]

It is observed that the sample mean is less than the population mean in that case, the alternate hypothesis will be;

[tex]h_a: \mu < 2.7[/tex]

Hence the correct  null and the alternative hypotheses are:

[tex]h_0: \mu = 2.7\\\\ h_a: \mu < 2.7[/tex]

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Step-by-step explanation:

y = -50x -100

When x= 0, plug in 0 to x.

y = -50(0) -100

= 0 - 100

= -100

So in the first y box, you would put -100

I can't tell what the number is in bottom right box so i don't know what x is going to be

Answer:

Omar would get 2267.25 Russian rubles

Step-by-step explanation:

it's simple:

if one dollar equals 30.23 Russian rubles than you would do 75x30.23 and get the answer 2267.25 Russian rubles

hope that helps ;)

have a wonderful day!

Answer:

U is Union

Step-by-step explanation:

In math, the symbol U represents the union of two sets.

Answer:

3,848 feet.

Step-by-step explanation:

1) Square 70

2) Multiply 4,900 (the square of 70) by pi

3) Divide 15,393.804 (4,900 times pi) by 4 (to find a quarter of the tank)

4) Round 3,848.451 (15,393.804 divided by 4) to the nearest whole number and you get 3,848 feet.

I hope this helps.

Answer:

35.3

explanation:

breakdown:

total:

[tex]\\ \rm{:}\dashrightarrow 7.06(5)[/tex]

[tex]\\ \rm{:}\dashrightarrow (7+0.06)(5)[/tex]

[tex]\\ \rm{:}\dashrightarrow 7(5)+0.06(5)[/tex]

[tex]\\ \rm{:}\dashrightarrow 35+0.3[/tex]

[tex]\\ \rm{:}\dashrightarrow 35.3[/tex]

Step-by-step explanation:

integral of log(log x)+1 /(log x)² is equal tointegral of log(log x)+1 /(log x)² is equal to

Answer:

-37

Step-by-step explanation:

for the first equation to equal 4 the x must equal -6.

because something plus 7 had to equal 4. and we know that -3 + 7 equals 4. Now, -6 ÷ 2 equals -3 and that gives us the right answer.

So now plug -6 into the new problem so now it is

5 × (-6) - 7 so according the PEMDAS, we do 5 × -6 first which is -30. and -30 - 7 equals -37!!

hope this helps :)

76 / 325 = 23.38% so 23.4% so round down to 23% is used for rent

Answer:

Step-by-step explanation:

=> 1/6 as a decimal

=> by dividing we get 0.1666....

=> rounded to 3 decimal places = 0.167

Answer:

y=-2x

Step-by-step explanation:

if x<-5

x+5<0

x-5 also<0

so

|x-5|=-(x-5)=-x+5

|x+5|=-(x+5)=-x-5

Hence

y=-x+5-x-5

or

y=-2x,if x<-5

Answer:

[tex]=10\sqrt{10}+10\sqrt{2}-10\sqrt{5}-10[/tex]

Step-by-step explanation:

  [tex](2\sqrt{5} -\sqrt{10})(5\sqrt{2}+\sqrt{10})[/tex]

[tex]=2\sqrt{5}\cdot5\sqrt{2}+2\sqrt{5}\sqrt{10}-5\sqrt{2}\sqrt{10}-\sqrt{10}\sqrt{10}[/tex]

[tex]=10\sqrt{10}+2\sqrt{50}-5\sqrt{20}-10[/tex]

[tex]=10\sqrt{10}+2\sqrt{25 \cdot 2}-5\sqrt{4 \cdot5}-10[/tex]

[tex]=10\sqrt{10}+2\sqrt{25}\sqrt{2}-5\sqrt{4}\sqrt{5}-10[/tex]

[tex]=10\sqrt{10}+2\cdot5\sqrt{2}-5\cdot2\sqrt{5}-10[/tex]

[tex]=10\sqrt{10}+10\sqrt{2}-10\sqrt{5}-10[/tex]

Answer:

x= -5

Step-by-step explanation:

f(x)  =  [ x^2  -  25 ] / [ x + 5 ]  =  [ (x + 5) ( x- 5)]  / [ x + 5 ]  =  x - 5

This will be the graph of  f(x) =   x - 5  with a  "hole"  at   x  =  - 5

The graph of the rational function f(x) = (x² - 25)/(x + 5) is represented by the graph second option (B) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The equation of the rational function:

f(x) = (x² - 25)/(x + 5)

As we know, in the rational function the denominator cannot be zero.

x + 5 ≠ 0

x ≠ -5 (there will be a hole at x = -5)

f(x) = (x - 5)(x + 5)/(x + 5)

Because: a² - b² = (a - b)(a + b)

f(x) = (x - 5)

The above function represents the linear function.

The slope of the linear function is positive.

m = 1

The y-intercept of the linear function is c = -5

Thus, the graph of the rational function f(x) = (x² - 25)/(x + 5) is represented by the graph second option (B) is correct.

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Solution:

Facts about absolute values:

We know that:

This question is asking to find the absolute value of a negative integer. As said above, the result will be the negative integer's opposite.

The absolute value of -12 is 12.

Answer:

reflection, rotation, and translation would be correct

Step-by-step explanation:

dilation/enlargement changes size

Answer:

-4

Step-by-step explanation:

First step, plug 1 in for X

Second step, -5(1)+1

= -4

Answer:

c .40

Step-by-step explanation:

Answer:

c .40

Step-by-step explanation:

because we all now that 20+20 is the same as 20×2 which gives us 40

[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]

The Length of PQ such that Triangle JKL is similar to Triangle PQR ~

To make the given triangles similar, we have to get the ratios of each of their corresponding side to be equal to one another.

That is :

[tex]\qquad \sf  \dashrightarrow \: \dfrac{PQ}{12} = \dfrac{9}{6} [/tex]

[tex]\qquad \sf  \dashrightarrow \: PQ = \dfrac{9}{6} \times 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: PQ = {9}{} \times 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: PQ = 18 \: units[/tex]

hence, the option C is correct