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4 years ago

If the length of the square is increased by 2 and the width is decreased by 2, by how many units is the area of

Mathematics

1 answer:

mrs_skeptik [129]4 years ago

3 0

Answer:

4 units

Step-by-step explanation:

Let x represent the length of the square

Area of the square = x^2

So, the dimension of the rectangle formed is:

length = x + 2

width = x - 2

Area of the rectangle = ( x + 2 ) * ( x - 2 )

solve the parenthesis

x^2 - 2x + 2x - 4

Area of the rectangle = x^2 - 4

subtract this area from that of the square

x^2 - ( x^2 - 4 )

=x^2 - x^2 + 4

= 4 units

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A boogie board that has a regular price of $6. If the sales tax on the boogie board is 7%, what is the total cost of the board?

zavuch27 [327]

Answer:

6.42$

Step-by-step explanation:

6.00 divided by 100 equals 0.6 multiplied by 7 equals 0.42 so the sales tax is 0.42 cents and the total is 6.42$

7 0

3 years ago

4) Dan Ariely and colleagues have conducted some extremely interesting studies on cheating (see, for example Mazar, Amir, &

lianna [129]

I've attached the complete question.

Answer:

Only participant 1 is not cheating while the rest are cheating.

Because only participant 1 has a z-score that falls within the 95% confidence interval.

Step-by-step explanation:

We are given;

Mean; μ = 3.3

Standard deviation; s = 1

Participant 1: X = 4

Participant 2: X = 6

Participant 3: X = 7

Participant 4: X = 0

Z - score for participant 1:

z = (x - μ)/s

z = (4 - 3.3)/1

z = 0.7

Z-score for participant 2;

z = (6 - 3.3)/1

z = 2.7

Z-score for participant 3;

z = (7 - 3.3)/1

z = 3.7

Z-score for participant 4;

z = (0 - 3.3)/1

z = -3.3

Now from tables, the z-score value for confidence interval of 95% is between -1.96 and 1.96

Now, from all the participants z-score only participant 1 has a z-score that falls within the 95% confidence interval.

Thus, only participant 1 is not cheating while the rest are cheating.

8 0

4 years ago

Ill give brainliest for the answer and no guessing

Vsevolod [243]

Answer:

12350%

Step-by-step explanation:

. 76 - 34 = 42

. 42 divided by 34 = 1.23529411765

. 1.23529411765 multiplied by 100 = 123.529411765

. 123.529411765 ≈ 123.5 * 100 = 12350%

7 0

3 years ago

Triangle JKL has vertices J(2,5), K(1,1), and L(5,2). Triangle QNP has vertices Q(-4,4), N(-3,0), and P(-7,1). Is (triangle)JKL

Tems11 [23]

Answer:

Yes they are

Step-by-step explanation:

In the triangle JKL, the sides can be calculated as following:

J(2;5); K(1;1)

=> JK = $\sqrt{(1-2)^{2} + (1-5)^{2} } = \sqrt{(-1)^{2}+(-4)^{2} } = \sqrt{1+16}=\sqrt{17}$

J(2;5); L(5;2)

=> JL = $\sqrt{(5-2)^{2} + (2-5)^{2} } = \sqrt{3^{2}+(-3)^{2} } = \sqrt{9+9}=\sqrt{18} = 3\sqrt{2}$

K(1;1); L(5;2)

=> KL = $\sqrt{(5-1)^{2} + (2-1)^{2} } = \sqrt{4^{2}+1^{2} } = \sqrt{1+16}=\sqrt{17}$

In the triangle QNP, the sides can be calculate as following:

Q(-4;4); N(-3;0)

=> QN = $\sqrt{[-3-(-4)]^{2} + (0-4)^{2} } = \sqrt{1^{2}+(-4)^{2} } = \sqrt{1+16}=\sqrt{17}$

Q (-4;4); P(-7;1)

=> QP = $\sqrt{[-7-(-4)]^{2} + (1-4)^{2} } = \sqrt{(-3)^{2}+(-3)^{2} } = \sqrt{9+9}=\sqrt{18} = 3\sqrt{2}$

N(-3;0); P(-7;1)

=> NP = $\sqrt{[-7-(-3)]^{2} + (1-0)^{2} } = \sqrt{(-4)^{2}+1^{2} } = \sqrt{16+1}=\sqrt{17}$

It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP

=> They are congruent triangles

7 0

3 years ago

Read 2 more answers

Find the sum of a finite geometric sequence from n=1 to n=8, using the expression -2(3)^n-1

MissTica

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}
\end{cases}
\\\\\\
\sum\limits_{n=1}^{8}~-2(3)^{n-1}~~
\begin{cases}
n=8\\
a_1=-2\\
r=3
\end{cases}\implies S_8=-2\left( \cfrac{1-3^8}{1-3} \right)
\\\\\\
S_8=\underline{-2}\left( \cfrac{1-6561}{\underline{-2}} \right)\implies s_8=1-6561\implies S_8=-6560$

8 0

3 years ago