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3 years ago

14

Write standard form, word form, expanded form . Write 5 numbers that are at least 8 digits long under standard form. Write expan

ded form and the word form for each number under the appropriate heading

1 answer:

Leno4ka [110]3 years ago

4 0

The answer is 1233466585958

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Tutor O-Rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math por

Novosadov [1.4K]

Answer:

See below

Step-by-step explanation:

The score increase was 35 points. They claimed an increase of at least 50 points. For a significance level of 5%, the z-score for the situation needs to be at smaller than -1.645. For a significance level of 1%, the z-score needs to be smaller than -2.325

The z score for our situation: z = (385 - 350)/50 = 0.7

The average score of 385 of Tutor O-Rama scores is not significantly different from the average of the other students SAT scores. The evidence doesn't support their claim of being effective tutoring.

4 0

2 years ago

When you divide a fraction less than one by a whole number greater than one, is the Quotient less than, greater than, or equal t

Olin [163]

Answer:

bw eghw d32h n wqkjrd k2wsdtep explanation: less than ewrdi2qwed

5 0

2 years ago

What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2

Margaret [11]

<u>Answer-</u>

$\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}$

<u>Solution-</u>

Given expression is $(x+2)^4$

Applying Binomial Theorem

$\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$

Here,

a = x, b = 2 and n = 4

So,

$\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i$

Expanding the summation

$=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4$

$=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4$

$=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16$

$=x^4+8x^3+24x^2+32x+16$

4 0

3 years ago

Read 2 more answers

The perimeter of an equilateral triangle is 21.33 centimeters. What is s, the length of each side of the triangle.

crimeas [40]

Answer: Each side of the triangle equals 7.11 centimeters

Step-by-step explanation: The question states that what we have is an equilateral triangle. That’s a triangle with all three sides equal. Having that in mind, if one side measures 2cm for example, then the other two sides measure 2cm as well. Hence if one side of the equilateral triangle measures x (the dimensions are still unknown), then the other two sides each measure x as well. If the perimeter of the triangle is given as 21.33 cm, and each side of the equilateral triangle is x, then

x + x + x = 21.33

3x = 21.33

Divide both sides of the equation by 3

x = 7.11

Therefore, each side of the equilateral triangle equals 7.11 cm

8 0

2 years ago

Find the exact solutions of the equation in the interval [0, 2pi). (Enter your answers as a comma-separated list.)

Otrada [13]

there are different ways of solving this:

one way is the follwing:

cos^2(x) -sin^2(x) =cos (2x)

then, equation becomes:

cos (2x) -sin (x)=0

but sin(x) is also equivalent to : cos ((pi/2)-x),

so, the equation now is:

cos (2x) - cos ((pi/2)-x)=0 -------> cos (2x) = cos ((pi/2)-x) ---------> 2x=(pi/2) -x

but since it is an angle, the answer would be repeating so:

2x= 2k(pi) +((pi/2)-x)

3x= pi( 2k+1/2)

x= (pi/3) (2k+1/2)

for k=0, x= pi/6

for k=1, x= 5pi/6

for k=2, x= 3pi/2

<h2>so answers are : (pi/6,5pi/6,3pi/2)</h2>

7 0

2 years ago