Another way to write (3x-4)^2?

Answer:

w = pt

Step-by-step explanation:

\(p=\frac{w}{t}\\\\p*t=\frac{w}{t}*t\\\\pt=w\\\\\boxed{w=pt;t\neq 0}\)

Hope this helps.

The 500 sample size and 95% confidence level will both tend to increase the width of the confidence interval.

In this question, we have been given  the combinations of sample size and confidence level.

We need to select a combinations of sample size and confidence level that will give the widest interval.

We know that the confidence level is typically set in the range of 99% to 80%. The 95% confidence interval will be wider than the 90% interval and which will be wider than the 80% interval.

As we know increasing the confidence will increase the margin of error which results in a wider interval.

But increasing the sample size decreases the width of confidence intervals, as it decreases the standard error.

This means, for the widest interval we need to select a high confidence interval and small sample size.

Therefore, the sample size = 500 and the confidence interval = 95% will give the widest interval.

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Answer:

Option 3

(3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Step-by-step explanation:

Factorize polynomials:

Use exponent law:

                   \(\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}\)

9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²

25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²

Now use the identity:  a² - b² = (a +b) (a -b)

Here, a = 3xy³ & b = 5x²y⁴

9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²

                       = (3xy³)² - (5x²y⁴)²

                      = (3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Answer:

Hope the picture will help you

Answer:

The answer to your problem is, A. 536,866,822

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

If a fair coin is tossed 29 times, the total number of outcomes will be expressed as: \(2^{29} = 536,870,476\)

If at least 2 tails occur, the expected outcome will be 29 times

Pr(at least 2 tails occur) = \(2^{29} - 29 - 1\)

Pr(at least 2 tails occur) = \(536,870,912 - 30 = 536,866,822\)

Thus the answer to your problem is, A. 536,866,822

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Answer:

8

Step-by-step explanation:

Answer:

8 people are chewing gum

Step-by-step explanation:

32/8=4, meaning there are 4 sets of 8 students.

If 2 students are chewing gum for every 8, and there are 32 students, that would mean that multiplying 4 by 2 to get 8 total kids chewing gum.

You could also say that 6*4=24, and 32-24=8 if you want to double check.

Hope this helps :)

the regular price is "x", which of course is the 100%, but we also know that $459 is 32% off that, hmmmmm well 100% - 32% = 68%, so $459 is really 68% of "x", because $459 is whatever "x" is minus 32%.

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 459&68 \end{array}\implies \cfrac{x}{459}=\cfrac{100}{68}\implies \cfrac{x}{459}=\cfrac{25}{17} \\\\\\ 17x = 11475\implies x = \cfrac{11475}{17}\implies x = 675\)

Answer:

24xy+6

Step-by-step explanation:

Remove parentheses:

=4x times 6y+6

multiply the numbers:

which gives you: 24xy+6

Answer:

$1,679.62

Step-by-step explanation:

129.60*12=$1,555.20

You then do 1,555.2*.08, and get:124.416

You then add the 2 together to find the amount needed to be paid back.

There are no solutions to the system of inequalities Option (d)

Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.

A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is

y > 3x + 1

y < 3x - 3

The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.

The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.

Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.

To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.

When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.

There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.

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Complete Question :

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

Options:

a)Only values that satisfy y > 3x + 1 are solutions.

b)Only values that satisfy y < 3x – 3 are solutions.

c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

d)There are no solutions.

Answer:

D

Step-by-step explanation:

Answer:

7.625

Step-by-step explanation:

The percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78% and 9 cm respectively

Percentage of the boys in the class deals with a ratio of the boys to the number of students in the class

The given parameters that will help us to get the percentage are

Mean height of the class = 152 cm

Mean height of the boys = 158 cm

The standard deviation of the boys = 5 cm

Mean height of the girls = 148 cm

Standard deviation of the girls = 4 cm

(1) The percentage of boys in the class is

Total mean height = 158 +148 = 306

Percentage = 158/306 * 100 = 51.6%

Then the  percentages 51.6/100 * 152 = 78%

(2) The total standard deviation of all the students

Boys + girls = 5+4 = 9 cm

Therefore, the percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78 students and 9 cm respectively

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If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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Answer:

B. Yes, because A is acute and a < h

Step-by-step explanation:

Answer:

B) yes, because A is acute and a > b

Step-by-step explanation:

The other person was technically right, it is option B, but they put h instead of b

Answer:

A

Step-by-step explanation:

Answer:

$1 for 60

Step-by-step explanation:

60$ is a better deal.

Answer:

6x4= 24

x4)+(3x4)=12

bsnskzifkznsnaksifi

The complete sentence is 6 x 4 =( 3 x 4) + (3 x 4)

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

6 x 4 =( x 4) + (3 x 4)

Now, split 6 as two equal quantities

6 = 3+ 3

So, 6 x 4 =24

( 3x 4) + (3 x 4)

= 12+ 12

= 24

Hence, LHS = RHS.

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3) The equation of the linear model would be y = 7.5x+60.

4) If Adam studies for 6 hours then his score would be 88.

What is the Linear equation?

An algebraic equation with only a constant and a first-order (linear) term is said to be linear if it has the formula y = mx + b, where m is the slope and b is the y-intercept. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

y = mx + c

where m denotes the slope.

The y-intercept is represented by the constant c. (Where x is zero)

In our instance, y-intercept equals 60.

The line's equation will therefore be:

y = mx + 60

y = mx + 60

There are given the line's coordinates (4, 90). These considerations will thus satisfy the equation.

90 = 4*m + 60

4.m = 30 m = 7.5 m = 7.5 y = 7.5x + 60 y = 7.5 * 6 + 60 y = 45 + 60 y = 105 is

y = 7.5x + 60.

If Adam's study for 6 hours then his score would be

y = 7.5x + 60.

y = 7.5(6) + 60

y = 105

Hence,

3) The equation of the linear model would be y = 7.5x+60.

4) If Adam studies for 6 hours then his score would be 88.

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According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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Answer:

the slope is either -2/1 or -1/2

Step-by-step explanation:

hope this helped sorry i didnt know the y intercept but i think its 0

The length of the curve segment y = 4x^2 from x = 0 to x = 1 can be calculated by evaluating the definite double integral over the region of the x-y plane bounded by the curve y = 4x^2 and the x-axis,

The square root of the sum of the squares of the partial derivatives of x and y with respect to the arclength parameter.

To evaluate this integral, we first note that

y = 4x^2, so dy/dx = 8x.

Thus, the integral with respect to x is:

s = ∫_0^1 sqrt(1 + (8x)^2) dx

To evaluate this integral,

we can use the substitution

u = 8x,

which gives us

du = 8 dx.

Thus,

the integral becomes:

s = (1/8) ∫_0^8 sqrt(1 + u^2) du

This can be evaluated using trigonometric substitution.

Letting v = arctan(u),

we have

dv = du / sqrt(1 + u^2),

and the integral becomes:

s = (1/8) ∫_{arctan(0)}^{arctan(8)} sqrt(1 + tan^2(v)) dv

This can be evaluated using the substitution

v = tan(v),

which gives us

dv = sec^2(v) dv.

Thus, the integral becomes:

s = (1/8) ∫_0^{arctan(8)} sec(v) dv

This can be evaluated using the substitution

u = tan(v),

which gives us

du = sec^2(v) dv.

Thus, the integral becomes:

s = (1/8) ∫_0^8 1 / sqrt(1 + u^2) du

This can be evaluated using the substitution

u = sinh(v),

which gives us

du = cosh(v) dv.

Thus, the integral becomes:

s = (1/8) ∫_0^8 cosh(v) dv

This can be evaluated using the identity

cosh(v) = (exp(v) + exp(-v)) / 2,

giving us:

s = (1/8) [exp(v) / 2 - exp(-v) / 2]

evaluated from 0 to 8

Finally, evaluating this expression gives us:

s = (1/8) [exp(8) / 2 - exp(-8) / 2]

This is the length of the curve segment y = 4x^2 from x = 0 to x = 1.

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The equation for the Volume (V) of the cone given is,

We are to isolate 'h' in the equation above

SOLUTION

Multiply both sides by 3

Simplify

Divide both sides by πr²

Simplify

Hence, the answer is

The geometric sequence is:

\(\boxed{15,9,\frac{27}{5},\frac{81}{25}, \frac{243}{125} }\)

A geometric sequence, or geometric progression, is a sequence of numbers where each successive number is the product of the previous number and some constant  \(\text{r}\).

Now,

We need to find the 2nd, 3rd and 4th term of the geometric sequence. To find these terms, we need to know the common difference. The common difference can be determined using the formula,

Where \(\text{a}_1=15\) and \(\text{a}_5=\frac{243}{125}\)

For \(\text{n}=5\), we have,

\(\dfrac{243}{125}=15(\text{r})^4\)

Simplifying, we have,

\(\sf r= \dfrac{3}{5}\)

Thus, the common difference is \(\sf r= \frac{3}{5}\)

Now, we shall find the 2nd, 3rd and 4th terms by substituting \(\sf n=2,3,4\) in the formula \(\text{a}_{\text{n}}=\text{a}_1(\text{r})^{\text{n}-1}\)

For \(\sf n=2\)

\(\text{a}_2=15\huge \text(\dfrac{3}{5}\huge \text)^1\)

   \(=\bold{{9}}\)

Thus, the 2nd term of the sequence is 9

For \(\sf n=3\), we have,

\(\text{a}_3=15\huge \text(\dfrac{3}{5}\huge \text)^2\)

\(=15\huge \text(\dfrac{9}{25}\huge \text)\)

\(\bold{=\dfrac{27}{5}}\)

Thus, the 3rd term of the sequence is \(\bold{{\frac{27}{5}}}}\)

For \(\sf n=4\), we have,

\(\text{a}_4=15\huge \text(\dfrac{3}{5}\huge \text)^3\)

\(=15\huge \text(\dfrac{27}{25}\huge \text)\)

\(\bold{=\dfrac{81}{25}}\)

Thus, the 4th term of the sequence is \(\bold{\frac{81}{25}}\)

Therefore, the geometric sequence is:

\(\boxed{\bold{15,9,\frac{27}{5},\frac{81}{25}, \frac{243}{125}}}\)

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Answer:

1. b

2. b

Step-by-step explanation:

Sorry, I'm not so sure for c

Answer:

the correct answer is:-

1) b

2) b

3) c

Step-by-step explanation:

1 ) b

2 ) b

3) c