Find the probability that z lies between 0 and 1.56.

Answer:

Step-by-step explanation:

Given f(x)=40-1.25x, where x=pounds of birdseed and 40=her saved amount, and birdseed costs 1.25/lb.

f(3)=40-1.25(3)

f(3)40-3.75

f(3)=36.25

If she buys (3 pounds) of birdseed, she saves ($36.25).

f(18)=40-1.25(18)

f(18)=40-22.5

f(18)=17.5

If she buys (18 pounds) of birdseed, she saves ($17.5)

f(36)=40-1.25(36)

f(36)=40-45

f(36)=-5

If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.

If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given function f(x)=40-1.25x,

where x=pounds of birdseed and 40 is her saved amount, and birdseed costs is 1.25/lb.

f(3)=40-1.25(3)

f(3)40-3.75

f(3)=36.25

If she buys (3 pounds) of birdseed, she saves ($36.25) then;

f(18)=40-1.25(18)

f(18)=40-22.5

f(18)=17.5

If she buys (18 pounds) of birdseed, she saves ($17.5) then;

f(36)=40-1.25(36)

f(36)=40-45

f(36)=-5

If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.

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Answer:

x= 4/5 or x = -2

Step-by-step explanation:

Step 1: Subtract -6x from both sides.

5x^2 -8 - -6x = -6x -6x

5x^2 + 6x - 8 = 0

Step 2: Factor left side of equation.

(5x - 4) (x + 2) = 0

Step 3: Set factors equal to 0.

5x - 4 = 0 or x + 2 = 0

Hense the Answer is x= 4/5 or x = -2

Answer:

16/5=7

Step-by-step explanation:

Root x= 3 of multiplicity 2, it means we can factor it with : (x-3)²

Root x = 1, of multiplicity 1, it means we can factor this polynomial with : (x-1)

Root x = -3, of multiplicity 2, it means we can factor this polynomial with : (x+3)²

Finally we get this expression : (x-3)²(x+3)²(x-1)

This expression is a polynomial of degree 5 but what is the y intercept of it ?

Basically, we need to replace x by zero and the value of the expression will be the y intercept :

let x = 0

then ,

(0-3)²(0+3)²(0-1) = 9*9*(-1) = -81 #-162

We need an y intercept of value = -162

Thus we simply need to multiply by 2, and finally f(x) = 2(x-3)²(x+3)²(x-1)

satisfies all the required condition

Good Luck

Answer:

$17.12

Step-by-step explanation:

2.14 · 8 = 17.12

Answer:

9

Step-by-step explanation:

12÷1 [tex]\frac{1}{3}[/tex]=9

Answer:

  d) 16x² -56x +49

Step-by-step explanation:

The square of a binomial difference will have the form ...

  (ax -b)² = a²x² -2abx +b²

__

The sign of the linear term will be negative, which eliminates choices A and C.

The linear term will be double the product of the roots of the other two terms.

In choice B, the linear term has a factor of 5 that appears nowhere else, so that cannot be a perfect square.

Choice D factors as ...

  16x² -56x +49 = (4x -7)² . . . . the square of a difference

The amount Howie will pay back at the end of one year is $26000.00

The given parameters are:

[tex]P =25000[/tex] -- the principal amount

[tex]R = 4\%[/tex] -- the interest rate

[tex]T=1[/tex] --- the duration

The amount to pay back in this duration is then calculated using:

[tex]A = P(1 + RT)[/tex]

So, we have:

[tex]A = 25000(1 + 4\% \times 1)[/tex]

[tex]A = 25000(1 + 4\% )[/tex]

Express percentage as decimal

[tex]A = 25000(1 + 0.04)[/tex]

[tex]A = 25000(1 .04)\\[/tex]

Multiply

[tex]A = 26000[/tex]

Hence, the amount to pay back is $26000.00

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Answer:

x = 3π/4, 5π/4

Step-by-step explanation:

cos(x+2π) = -√2/2, [0,2π]

cos(x)cos(2π)-sin(x)sin(2π) = -√2/2

cos(x) = -√2/2

x = 3π/4, 5π/4

Remember that the cosine function is periodic, so cos(θ+2π)=cos(θ).

Answer: 40 mg

Unitary method:

For 3kg --> 8mg

For 1kg --> 8/3 mg

For 15kg--> (8/3) * 15

              --> 40 mg

The number of milligrams of the fever reducer the pediatrician will prescribe is 40 mg.

Given that, for every 3 kg of a child's weight, pediatricians prescribe 8 mg of fever reducer.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here, for 1 kg of child's weight pediatricians prescribe [tex]\frac{8}{3}[/tex] mg of fever reducer.

If Nidhi weighs 15 kg, then the fever reducer = [tex]\frac{8}{3}\times15[/tex]

[tex]=8\times5[/tex]

[tex]=40[/tex] mg

Therefore, the number of milligrams of the fever reducer the pediatrician will prescribe is 40 mg.

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Answer:

5.67

Step-by-step explanation:

The scale factor of the height of the image is 7.89.

The scale factor is defined as the proportion of the new image's size to that of the previous image.  The scale factor is the ratio of the actual size to the scaled size of the object.

Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

Given that In an old photograph, the height of grandma's table is 3.8 cm. The table doesn't exist anymore; grandma doesn't know what happened to it. She does still have the vase in the photograph which is 0.8cm tall in the photograph and 30 cm tall in real life.

The scale factor will be calculated as,

Scale factor = ( 30 / 3.8)

Scale factor = 7.89

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Answer:

a. 587

b. 543

Step-by-step explanation:

a. Mean = sum / number of numbers

To find the sum, we can add the numbers up.

432 + 543 + 348 + 788 + 823 = 2934

There are 5 numbers. Our mean is thus

2934/5 = 586.8, or 587 when rounding up. We round up because we have a .8 at the end, and 8 ≥ 5

b. To find the median, we first must order the numbers. The numbers ordered are this:

348 ,  432 , 543 , 788 , 823

To find the median, we can cross off one number on each side until we are left with one or two numbers.

348 ,  432 , 543 , 788 , 823

cross out one number from each endpoint

432 , 543 , 788

cross out one number from each endpoint

543

Answer:

90.25π

Step-by-step explanation:

The formula for solving the area of a circle is πr².

r is the radius. We can find the radius by splitting the diameter in half: 19/2 = 9.5.

We can apply the area formula and we get π9.5² and the answer is 90.25π.

Answer:

x < -15

Step-by-step explanation:

Divide both sides by -2.

Next you will reverse the sign because you are dividing by a negative number.

Answer:

-2

Step-by-step explanation:

    [tex]\frac{(-2)^3+3 (4)}{-8+6}[/tex]

 [tex]= \frac{-8 + 12}{-2}[/tex]

 [tex]= \frac{4}{-2}[/tex]    

 [tex]= -2[/tex]

Answer:

2.3

Step-by-step explanation:

First we must get rid of the exponent, which is that little 3 at the top.

To do this, we will do:

(-2) × (-2) × (-2) = -8

Now we have -8 + 3.4, which equals -4.6

Next we will combine the numbers in the denominator, to get -2.

Now, all together, we have -4.6/-2.

Last but not least, we will divide -4.6 by -2, to get 2.3

And that's your answer, hope this helps you :)

Sorry if it doesn't, though.

Answer:

Step-by-step explanation:

Given equation:

Solve for x, divide both sides by 3yz:

Correct choice is C

Answer:

Quotient: 18; Remainder: 26

Step-by-step explanation:

Please open the PDF file for work.

Hoped this helped.

[tex]GeniusUser[/tex]

Answer:

x = 6

Step-by-step explanation:

3x-5x+8x+x = 42

7x = 42

x = 6

Answer:t=10.05s

Step-by-step explanation:

Answer:

Step-by-step explanation:

A = 8(14) - 5(14 - 5 - 2) = 77 m²

Answer:

77m (squared)

Step-by-step explanation:

Hey there!

n * 25 = 5 * 60

25n = 5 * 60

25n = 300

DIVIDE 25 to BOTH SIDES

25n/25 = 300/25

CANCEL out: 25/25 because it gives you 1

KEEP: 300/25 because it helps solve for the n-value

NEW EQUATION: n = 300/25

SIMPLIFY IT!

n = 12

Therefore, your answer is: n = 12

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

n= 2.9

1:2.9

Step-by-step explanation:

Divide by 15 on both sides

15 divided by 15 is 1

43 divided by 15 is 2.8666666666=>

It states "Give any decimals in your answer to 1 d.p.

Mean we round it to one decimal place

so it is 2.9

Thus the answer for n is 2.9

Hope this helps!

Answer:

what's your question?  

Answer:

0

Step-by-step explanation:

sin²θ + cos²θ = 1

secθcosθ = (1/cosθ)cosθ = 1

1 - 1 = 0

Answer:

Solution: x = 1/6

Decimal form: 0.166667

Hope this helps :)

Answer:

x = 1/6

Step-by-step explanation:

10x + 7 - x : Combine like terms (In this case the x values)

9x+7 = 3x + 8 : Subtract 3x from both sides

6x + 7 = 8 : Now subtract 7 from both sides

6x = 1 : Divde both sides by 6

x = 1/6

Substitute x = √7 sin(t) and dx = √7 cos(t) dt. Then

∫ √(7 - x²) dx = ∫ √(7 - (√7 sin(t))²) • √7 cos(t) dt

… = √7 ∫ √(7 - 7 sin²(t)) cos(t) dt

… = 7 ∫ √(1 - sin²(t)) cos(t) dt

… = 7 ∫ √(cos²(t)) cos(t) dt

We require that -π/2 ≤ t ≤ π/2 in order for the substitution we made to be reversible. Over this domain, cos(t) ≥ 0, so

√(cos²(t)) = |cos(t)| = cos(t)

and the integral reduces to

… = 7 ∫ cos²(t) dt

Recall the half-angle identity for cosine:

cos²(t) = (1 + cos(2t))/2

Then the integral is

… = 7/2 ∫ (1 + cos(2t)) dt

… = 7/2 (t + 1/2 sin(2t)) + C

… = 7t/2 + 7/4 sin(2t) + C

Get the antiderivative back in terms of x. Recall the double angle identity for sine:

sin(2t) = 2 sin(t) cos(t)

We have t = arcsin(x/√7), which gives

sin(t) = sin(arcsin(x/√7)) = x/√7

cos(t) = cos(arcsin(x/√7)) = √(7 - x²)/√7

Then

∫ √(7 - x²) dx = 7/2 arcsin(x/√7) + 7/4 • 2 sin(arcsin(x/√7)) cos(arcsin(x/√7)) + C

… = 7/2 arcsin(x/√7) + x/2 √(7 - x²) + C