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2 years ago

Find (4.54×10^8)-(3.98×10^8)

Mathematics

1 answer:

horrorfan [7]2 years ago

5 0

Answer:

$5.6 *10^7$

Step-by-step explanation:

Given

$(4.54*10^8)-(3.98*10^8)$

Required

Solve

$(4.54*10^8)-(3.98*10^8)$

Apply distributive law of algebra

$(4.54 - 3.98) *10^8$

Evaluate the expression in bracket

$(0.56) *10^8$

Remove bracket

$0.56 *10^8$

When a number is in standard form: $a * 10^n$

The value of a must be: $1 \le a \le 10$

So, the expression becomes:

$5.6 *10^{-1}*10^8$

Apply law of indices

$5.6 *10^{-1+8}$

$5.6 *10^7$

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Mileage tests are conducted for a particular model of automobile. If a 98% confidence interval with a margin of error of 1 mile

Llana [10]

Answer: 37

Step-by-step explanation:

Given : Significance level : $\alpha:1-0.98=0.02$

Critical value : $z_{\alpha/2}=z_{0.01}=2.33$

margin of error : E= 1 mile per gallon

Population standard deviation: $\sigma=2.6$ miles per gallon.

We know that when the population standard deviation is known then the formula to find the sample size is given by :

$n=(\dfrac{z_{\alpha/2}\times \sigma}{E})^2$

$n=(\dfrac{(2.33)\times 2.6}{1})^2=36.699364\approx37$ [Round to the next whole number.]

Hence, the required number of automobiles should be used in the test = 37

7 0

3 years ago

What is the value of the remainder if 10x4 – 6x3 + 5x2 – x + 1 is divided by x – 3?

natita [175]

Answer:

Remainder is 691.

Step-by-step explanation:

Given function is $10x^4-6x^3+5x^2-x+1$ .

Now we need to find remainder if we divide given function $10x^4-6x^3+5x^2-x+1$ by (x-3)

(x-3) means plug x=3 into $10x^4-6x^3+5x^2-x+1$ to find remainder.

$10x^4-6x^3+5x^2-x+1$

$=10(3)^4-6(3)^3+5(3)^2-(3)+1$

$=10(81)-6(27)+5(9)-(3)+1$

$=810-162+45-3+1$

$=856-162-3$

$=856-165$

$=691$

Hence remainder is 691.

8 0

3 years ago

Read 2 more answers

A. In a school year the ratio of boys to girls is 3:4. If there are 372 boys, how many girls are there

natima [27]

Answer:

a. 496 girls

b. 110 boys

Step-by-step explanation:

a. 3:4 ------- divide 372 by 3 and you get 124 now multiply that by 4 and you get 496

b. 2:5 -------- divide 275 by 5 and you get 55 now multiply that by 2 and you get 110

7 0

3 years ago

Please help me. this is trig and all I need is an explanation on how to start

nikklg [1K]

Step-by-step explanation:

Hypotenuse : Opposite the right angle.

Opposite : Opposite the angle.

Adjacent : the last side left.

Your formulas.

Soh Cah Toa (Sin Cos Tan)

You'll be using Cos (Cah) because hypotenuse and adjacent are the only sides with something in it.

You rearranged formula :

Side length × Cos (Angle) = your answer to x

7 0

2 years ago

Galena is solving the following system. 3x+2y+3z =5 7x+y +7z=-1 4x-4y-z=-3

babymother [125]

Answer:

She did not multiply equation 3 in step 2 by the correct value.

Step-by-step explanation:

Given:

$3x+2y+3z=5\\7x+y+7z=-1\\4x-4y-z=-3$

In order to solve this, we need to eliminate any one variable and then form a simultaneous equation with the remaining two variables. Then, we nee to solve the simultaneous equation.

Here, Galena is trying to eliminate the variable $z$ first.

Step 1: She multiplies equation (3) by 3 and adds it to equation (1)

Let us multiply equation (3) by 3

$(4x-4y-z=-3)\times 3 = (3\times 4x)-(3\times 4y)-(3\times z)=3\times -3\\(4x-4y-z=-3)\times 3 =12x-12y-3z=-9$

Now, adding this to equation 1 will cancel out z terms.

$12x-12y-3z+3x+2y+3z=-9+5\\(12x+3x)+(-12y+2y)+(3z-3z)=-4\\15x-10y+0=-4$

Now, she need to make one more equation in $x\ and \ y$ .

Step 2: She multiplies equation (3) by -7 and adds it to equation (2)

Multiplying equation (3) by -7 will give,

$(4x-4y-z=-3)\times -7 = (-7\times 4x)-(-7\times 4y)-(-7\times z)=-7\times -3\\(4x-4y-z=-3)\times 3 =-28x+28y+7z=21$

Now, adding this to equation 2 will not cancel out z terms.

$-28x+28y+7z+7x+y+7z=21-1\\(-28x+7x)+(28y+y)+(7z+7z)=20\\-21x+29y+14z=20$

So, she makes mistake in step 2 as the $z$ terms are not being cancelled.

6 0

3 years ago

Read 2 more answers