\(\frac{b^{-2} }{b^{4} }\) in scientific notation

No, we cannot conclude that 90% of households have between .7 and 2.1 children based on the confidence interval alone.

Based on the confidence interval alone, we cannot come to the conclusion that 90% of households have a number of children between .7 and 2.1. A confidence interval only provides a range of values that likely contains the true population parameter (in this case, the average number of children per household) with a certain level of confidence (in this case, 90%). It does not provide information about the distribution of the variable within the population. Therefore, we cannot make any conclusions about what percentage of households have a certain number of children based on the confidence interval alone.

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Answer:

1.its B

2.G

Step-by-step explanation:

Answer:

-5, -4, -1

Step-by-step explanation:

To find the terms of the sequence, you have to use the given expression.

n ( n - 2 ) - 4

Here,

n ⇒ term number,

Accordingly, let us find the first 3 terms in this sequence.

For that, replace n with the term number

When n = 1,

T₁ = n ( n - 2 ) - 4

T₁ = 1 ( 1 - 2 ) - 4

T₁ = -5

When n = 2,

T₂ = n ( n - 2 ) - 4

T₂ = 2 ( 2 - 2 ) - 4

T₂ = - 4

When n = 3,

T₃ = n ( n - 2 ) - 4

T₃ = 3 ( 3 - 2 ) - 4

T₃ = - 1

Answer:

x = 10

Step-by-step explanation:

The figure is symmetrical, so 7x+5 = 9x - 15

7x + 5 = 9x - 15

5 = 2x - 15

20 = 2x

x = 10

Note that the figure is not drawn to scale, but computations don't lie :)

Answer:

6.7

Step-by-step explanation:

Answer:

73

Step-by-step explanation:

Set up as if you're finding the average:  total the 6 scores and add 'x', then divide by 7 and set this equal to 75

'x' = score she must meet or exceed to achieve an average of 75

452 + x = 75

     7

cross-multiply:  452 + x = 75(7)

452 + x = 525

x = 73

There are 30 different combinations of two members who can be selected to serve on the spring formal committee.

Permutation is the arrangement of elements in a specific order. In this scenario, the elements are the six members of the student council, and the order in which they are arranged is important.

To find the number of permutations, we use the formula nPk, where n is the number of elements and k is the number of elements we want to arrange.

In this case, n = 6 and k = 2,

so we have

=> 6P2 = 6!/(6-2)!

=> 6!/(4!) = 6 x 5/1 = 30.

So, there are 30 possible spring formal committees that can be formed from the six members of the student council.

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Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

Answer:

$4625.10

Step-by-step explanation:

Her account already had $904.31

You now need to add $375.

Then add $500 twice.

Because of how banks work, we need to find out how much they pay monthly. There are 12 months in a year. 5.5 divided by 12 is 0.45.

45% of 1279.31 is 575.68

Now we add the $575.68 to $1279.31

April is a new month and she deposited $500.

45% of 1854.99 is 834.74

Add $834.74 to $1854.99

Then she deposits 500 on May, another new month.

I think this step is obvious. Just follow what you did last time.

This leaves her with $4625.10

By observation or by inspection, 7.40 appears the most, thus mode.

The value that appears most frequently in a data set is called the mode. One mode, several modes, or none at all may be present in a set of data. The mean, or average of a set, and the median, or middle value in a set, are two more common measurements of central tendency.

Data can be disseminated in statistics in a number of different ways. The traditional normal (bell-curve) distribution is the one that is referenced the most. The midpoint of this distribution, as well as some others, coincides with the peak frequency of observed values and is where the mean (average) value is located.

The mean, median, and mode all have the same values for such a distribution. This indicates that this value—the one that appears the most frequently in the data—is the average value, the middle value, and the mode.

When analyzing categorical data, such as automobile models or soda taste varieties, where a mathematical average median value based on ordering cannot be computed, mode is most helpful as a gauge of central tendency.

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Answer:

8-10 feet

Step-by-step explanation:

If the length of the carpet is two more than the width, the width can be expressed as x and the length can be expressed as x+2. This means that the area(x^2+2x) must be greater than 48 but no less than 80.

Now we can solve for both the maximum and minimum cases:

x^2+2x=48, x^2+2x-48=0, now we can factor, (x+8)(x-6)=0, and now we can use the Zero Product Property to find x=-8;x=6. Since we cant have negative width, x at least has to be equal to 6.

x^2+2x=80,x^2+2x-80=0, now we can factor, (x+10)(x-8), and now using the Zero Product Property to find x=-10;x=8, and since it must be positive, at most x can equal 8.

Now since the length is two more than the width, x, you add two to both of these values and get a range of 8-10 feet.

Answer:

One solution, as there is only one intersection between these two lines.

x = 2, and y = 1 (point of interesection (2, 1) )

y = 2x-3

y = -x + 3

first step is to substitute the y of one equation into the other and solve for x.

- x + 3 = 2x - 3

___________

+x. +x

_____________

3 = 3x-3

_____________

+3 +3

____________

6 = 3x

_____________

÷3 ÷3

_______________

2 = x

______________

x = 2

_______________

We can verify this value is true by substituting it back into the equations and as a result also solving for the working y value.

x = 2 -> y = 2(x) - 3

2(2) - 3 = 4 - 3 = 1

y = 1

____________

x = 2 -> y = -(x) + 3

-(2) + 3 = -2 + 3 = 1

y = 1

You can't, the only factor in both is 1

1(a^4 + 4b^4)

Hope this helps!

Answer:

\( x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5} \)   or   \( x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5} \)

Step-by-step explanation:

\( 5x^2 - 2 = 4x \)

\( 5x^2 - 4x - 2 = 0 \)

\( x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

\( x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(5)(-2)}}{2(5)} \)

\( x = \dfrac{4 \pm \sqrt{16 + 40}}{10} \)

\( x = \dfrac{4 \pm 2\sqrt{14}}{10} \)

\( x = \dfrac{2 \pm \sqrt{14}}{5} \)

\( x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5} \)   or   \( x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5} \)

Answer:

Answer:

x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5}x=

5

2

+

5

14

or x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5}x=

5

2

−

5

14

Step-by-step explanation:

5x^2 - 2 = 4x5x

2

−2=4x

5x^2 - 4x - 2 = 05x

2

−4x−2=0

x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=

2a

−b±

b

2

−4ac

x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(5)(-2)}}{2(5)}x=

2(5)

−(−4)±

(−4)

2

−4(5)(−2)

x = \dfrac{4 \pm \sqrt{16 + 40}}{10}x=

10

4±

16+40

x = \dfrac{4 \pm 2\sqrt{14}}{10}x=

10

4±2

14

x = \dfrac{2 \pm \sqrt{14}}{5}x=

5

2±

14

x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5}x=

5

2

+

5

14

or x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5}x=

5

2

−

5

14

The option B is true which is m2=m1+3, s2=s1

From the given information,

The required correct answers are,

m2= m1 + 3

s2= s1

Hence,

Option b. is correct.

A standard deviation (or σ) is a proportion of how distributed the information is comparable to the mean. A low standard deviation implies information is grouped around the mean, and an elevated requirement deviation demonstrates information is more fanned out.

The standard deviation of a population or sample and the standard error of measurement (e.g., of the example mean) is very unique however related. The example implies the standard error is the standard deviation of the arrangement of implies that would be found by drawing an endless number of samples from the population and registering a mean for each sample. The mean standard error ends up equaling the population standard deviation partitioned by the square base of the example size and is assessed by utilizing the example standard deviation separated by the square foundation of the sample size.

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Answer:

8feet

Step-by-step explanation:

Given the equation that models the arch of a school expressed as;

\($y=-0.5\left(x+4\right)\left(x-4\right)$\)

If the x axis represents the ground;

At the ground level, x = 0

Substitute x = 0 into the equation to get y;

y = -0.5(0+4)(0-4)

y = -0.5(4)(-4)

y = -0.5 * -16

y = 8ft

Hence the y axis at the ground level is 8feet

Answer:

rational

Step-by-step explanation:

can be put into a fraction

\(\dfrac {17}{36}\)  is a rational number.

Rational numbers are those numbers that can be expressed in terms of fraction or ratio of two integers.

Here are some examples of rational numbers i.e. \(-8, \dfrac{2} {5}, 7.75.\)

Irrational numbers are those numbers that can not be written in terms of fraction. These numbers can not be expressed in any finite way.

Here are some examples of irrational numbers: \(\sqrt{2}\), \(\sqrt{2.5}\).

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The confidence associated with an interval estimate is called the confidence level.

When making an interval estimate, such as estimating a population parameter based on a sample, it is important to provide an indication of the level of confidence we have in the estimate. The confidence level represents the probability or level of certainty that the true population parameter falls within the calculated interval.

For example, if we calculate a 95% confidence interval for the mean height of a population, it means that we are 95% confident that the true population mean height lies within that interval. This implies that if we were to repeat the sampling and interval estimation process multiple times, approximately 95% of the intervals would contain the true population parameter.

The confidence level is typically expressed as a percentage, such as 90%, 95%, or 99%. A higher confidence level indicates a greater level of certainty in the interval estimate but also results in a wider interval.

In summary, the confidence level associated with an interval estimate represents the level of confidence or probability that the interval contains the true population parameter.

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Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

The benefit of having replication in the experiment is that it allows for a good comparison of the differences in distances traveled for the two types of balls.

What are the benefits of having replication in the experiment?

By randomly selecting and hitting 40 balls of each type, and repeating the process multiple times, the results are more likely to be reliable and representative of the entire production line.

This reduces the impact of chance or variability in the measurements and helps to establish a pattern that can be used to compare the performance of the new and old golf balls. Therefore, option B is the right answer.

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Answer:

y = -x + 9

Step-by-step explanation:

You are given (-5,14), (-2,11), (1,8), and (4,5).  Your first objective is to find the slope.

Slope is delta y divided by delta x - the amount of height the graph gains divided by the amount of horizontal length the graph gains.  Take any two points and plug it into this: \(\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\).

i.e. (-2,11) and (4,5): \(\frac{11-5}{-2-4}\) which is \(\frac{6}{-6}\), or -1.  Thus, the slope is -1.

We now have y = -1(x) + b, or just y = -x + b.

Next, find the y-intercept.  Set the value of x to 0, as the y-intercept is found along the y-axis, which is at the horizontal center of the graph, 0.  We now know that the y-intercept is (0,y).  To find the y-value, plug one of the coordinate pairs of choice into x and y.

i.e. (-5,14): 14 = (-1)(-5) + b

14 = 5 + b

14 - 5 = 5 + b - 5

9 = b

So, the y-intercept is (0,9).

Finally, the equation is:

y = -x + 9

x(t) = \(c_1e^1^4^t+c_2e^-^t\)  , y(t) = \(2c_1e^1^4^t-c_2e^-^t\)   is the general solution of the sytem of differention eqution dx/dt = 4x+ 5y , dy/dt = 10x + 9y .

given  dx/dt = 4x+ 5y  and dy/dt = 10x + 9y

X'(t) = \(\left[\begin{array}{ccc}4&5\\10&9\end{array}\right]\)  X

where X = \(\left[\begin{array}{ccc}x\\y\\\end{array}\right]\)

so A = \(\left[\begin{array}{ccc}4&5\\10&9\end{array}\right]\)

now we need to find eigen value of the matrix and the corresponding eigen vector.

| A- λI | = 0

so after equation the value to zero

λ = 14 and λ = -1

now for the  λ = 14 corresponding eigen vector = \(\left[\begin{array}{ccc}1\\2\\\end{array}\right]\)

for λ = -1 corresponding eigen vector =  \(\left[\begin{array}{ccc}1\\-1\\\end{array}\right]\)

So general equation is given by:

X(t) = \(c_1e^1^4^t\)  \(\left[\begin{array}{ccc}1\\2\\\end{array}\right]\)  +  \(c_2e^-^t\)   \(\left[\begin{array}{ccc}1\\-1\\\end{array}\right]\)

after solving this

x(t) = \(c_1e^1^4^t+c_2e^-^t\)

y(t) = \(2c_1e^1^4^t-c_2e^-^t\)

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Answer:

A) x=sq rt 80

Step-by-step explanation:

by the Pythagorean theorem

4^2+8^2=x^2

16+64=x^2

80=x^2

x=sq root 80

Answer:

Step-by-step explanation:

Pythagorean theorem,

Hypotenuse² = Altitude² + Base²

x² = 8² + 4²

   = 64 + 16

  = 80

x = √80

The volume of the oblique pyramid is approximately 58.33 cubic centimeters.

To find the volume of the oblique pyramid with a square base and an edge length of 5 cm, and a height of 7 cm, you can follow these steps:

1. Determine the area of the square base:
  A = side x side = 5 cm x 5 cm = 25 square centimeters.

2. Apply the formula for the volume of a pyramid:
  Volume = (1/3) x Base area x Height = (1/3) x 25 square centimeters x 7 centimeters.

3. Calculate the volume:
  Volume = (1/3) x 25 x 7 = 58.33 cubic centimeters (rounded to two decimal places).

So, the volume of the oblique pyramid is approximately 58.33 cubic centimeters.

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The volume of the oblique pyramid with a square base of edge length 5 cm and height 7 cm is 58.33 cubic centimeters.

The base of the pyramid is a square with an edge length of 5 cm, so its area is 5cm x 5cm = 25cm2. We multiply this by the height of the pyramid, which is 7 cm, and then divide by 3:

Volume = (25cm2 x 7cm) / 3 = 175cm3 / 3 = 58.333cm3

Therefore, the volume of the oblique pyramid is approximately 58.333 cubic centimeters.

To find the volume of the pyramid, we'll use the formula for volume of a pyramid which is 1/3 * base area * height. For an oblique pyramid with a square base and an edge length of 5 cm, the base area is side length squared, which is 5 * 5 = 25 sq cm. The pyramid's height is given as 7 cm. The volume then becomes 1/3 * (25 sq cm) * (7 cm), which equals 58.33 cubic centimeters.

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Answer:

ok so i just got done with the test it is c 51

Step-by-step explanation:

The 99% confidence limit will be option B which is (45, 55)

90% confidence limits for the population mean are (46,54)

mean = 46+54 / 2 = 50.

the margin of error E = 54-46/2 = 4

For 90% Confidence Z- Critical value is = 1.645

But the margin of error

E = ZS/√n

4=(1.645)S/√n

S/√n = 4 / 1.645

= 2.4316

For 95% confidence Z-critical value is 1.96

A 95% confidence interval is = mean ± E

(50 ± 1.96) S/√n = (50 ± 1.96)×2.4316

= 50+ 4.7660

= 45.2340, 54.7660

= (45, 55)

Hence the correct option is B which is (45, 55) as the 99% confidence limit.

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The expression that represents Lonnie's final number is 2(x + 3) - 6

From the given information, we are to write the expression that represents Lonnie's final number

From the given information,

"kristy asks lonnie to think of a number, add 3 to it"

Let the number be x

Then,

The statement becomes

x + 3

"multiply the sum by 2" we get

2×(x +3)

= 2(x + 3)

" subtract 6",

The expression becomes

2(x + 3) - 6

This is the expression that represents Lonnie's final number

Hence, the expression that represents Lonnie's final number is 2(x + 3) - 6

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Answer:

∠b=35

Step-by-step explanation:

Hello There!

Complementary angles add up to equal 90

so to find the measure of angle B we subtract the given angle from 90

90-55=35

so we can conclude that ∠b = 35

By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.

A gradient is a generalization of the tangent curve used for multivariate function, that is, a function with more than one variable. In this case we have a function with one variable, which means that the gradient is equal to the slope:

\(\nabla f = \frac{df}{dx}\)     (1)

Now we proceed to calculate the gradient of the curve:

\(\nabla f = 6\cdot x^{2}-7\)

\(\nabla f = 6\cdot (-2)^{2}-7\)

\(\nabla f = 17\)

By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.

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Answer: The y-intercept is 3. The slope is 1.

Step-by-step explanation: Since the y coordinate is intercepting the y axis, the y-intercept is 3. To find the slope, the formula is change of y over change of x. The coordinates on this plane is (0,3) and (-3,0). That means the equation is (3-0) divided by (0-(-3)). That equals 3 divided by 3 which is obviously 1. Mark Brainliest plz!