Latasha explores some passages in a cave. The elevations of the passages are all above - 10 meters. Let y be the elevation of a passage in meters. Write an inequality that represents elevations above -10 meters.

The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

Given that,

Mean = 195

Standard deviation = 14

Thus, the probability between 183 and 218 is the ρ value of z when x = 195

Subtracting by the ρ value of z when x = 183

so, x = 218

z = 218-195/14 = 1.64

when x = 183

z = 183-195/14= -0.85

Thus, z value is 1.64 then the probability is 0.94950 and when z value is -0.85 then the probability is 0.21886

Now, 0.94950 - 0.21886 = 0.73064

Therefore, The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

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Answer:

5800

Step-by-step explanation:

that is to the nearest hundred

Answer:

5,800

Step-by-step explanation:

In 5,816. the number in the hundred place is the 8. The rule in rounding is 5 and above goes up, under 5 stay the same. The number after the 8 is the 1 and 1 is less than 5, so stays the same. So the 5,816 rounded to the hundred place is 5,800.

Answer:

x2+x-4=0

Step-by-step explanation:

You need to adjust the tube of the microscope to 6.83cm in order to view the sample in focus with a completely relaxed eye

Given, Focal length of the eyepiece,  = 2.50 cm

The focal length of the converging lens, f = 1.00 cm

The distance of the object, p = 1.30 cm

Lens equation, \(\frac{1}{f} = \frac{1}{p} + \frac{1}{q}\)

Substitute the values in the above equation

\(\frac{1}{1.00} = \frac{1}{1.30} + \frac{1}{q}\)

q = 4.33 cm

now, the image is formed at the focal point of the eyepiece,

therefore, the distance between the objective and the eyepiece, d =  + q = 2.50 cm + 4.33 cm

d = 6.83 cm

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Answer:

\(2^{2}\) × \(5^{3}\)

Step-by-step explanation:

500

= 2 x 250

= 2 x 10 x 25

= 2 x 2 x 5 x 5 x 5

= \(2^{2}\) × \(5^{3}\)

Answer:

#refer to the attachment!!

\(Factors \:of \:500\)

\(\\ \longmapsto\) 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, and 500.

\(Prime \:Factorization \:of\: 500\)

\(\\ \longmapsto\) 500=\(2^{2}\) × \(5^{3}\)

In a case whereby Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles Adam traveled a distance of about 335 miles.

The distance traveled in a unit of time is called speed. It refers to a thing's rate of movement. The scalar quantity known as speed is the velocity vector's magnitude. It has no clear direction.

Speed = Distance/ time

speed =72.4 miles

time=4.62 hours

Distance =speed * time

= 72.4 *4.62

Distance = 334.488 miles

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complete question;

Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles. Rounding decimals to the nearest whole number, Adam traveled a distance of about miles.

a) The minimum value of the function f(x) = xcos(x) in the range 0 ≤ x ≤ 5 is approximately -4.92, and it occurs at x ≈ 3.38.

b) The maximum value of the function f(x) = xcos(x) in the range 0 ≤ x ≤ 5 is approximately 4.92, and it occurs at x ≈ 1.57 and x ≈ 4.71.

To find the minimum and maximum values of the function f(x) = xcos(x) in the specified range, we need to evaluate the function at critical points and endpoints.

a) To find the minimum, we look for the critical points where the derivative of f(x) is equal to zero. Taking the derivative of f(x) with respect to x, we get f'(x) = cos(x) - xsin(x). Solving cos(x) - xsin(x) = 0 is not straightforward, but we can use numerical methods or a graphing calculator to find that the minimum value of f(x) in the range 0 ≤ x ≤ 5 is approximately -4.92, and it occurs at x ≈ 3.38.

b) To find the maximum, we also look for critical points and evaluate f(x) at the endpoints of the range. The critical points are the same as in part a, and we can find that f(0) ≈ 0, f(5) ≈ 4.92, and f(1.57) ≈ f(4.71) ≈ 4.92. Thus, the maximum value of f(x) in the range 0 ≤ x ≤ 5 is approximately 4.92, and it occurs at x ≈ 1.57 and x ≈ 4.71.

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Answer: you didnt add a question or possible answer choices so nobody can answer this question

Step-by-step explanation:

Divide the ones column dividend by the divisor.

Multiply the divisor by the quotient in the right place column.

Subtract the product from the ones column.

a) Linear Interpolation Spline for the data points are -

-2 <= x < -1: y = -x + 0

-1 <= x < 0: y = x + 2

0 <= x < 1: y = x + 2

1 <= x <= 2: y = -x + 4

b) Quadratic Interpolation Spline for the data points are -

-2 <= x <= -1: y = -x² - 2x + 2

-1 <= x <= 0: y = 2x² + 2

0 <= x <= 1: y = x² + 2x + 2

1 <= x <= 2: y = x² + 2x + 2

a) Linear Interpolation Spline:

To find the linear interpolation spline, we need to determine the line segments that connect adjacent data points.

Given data points:

X = [-2, -1, 0, 1, 2]

Y = [2, 1, 2, 3, 2]

Step 1: Determine the slopes between adjacent points

m1 = (Y[1] - Y[0]) / (X[1] - X[0]) = (1 - 2) / (-1 - (-2)) = -1 / 1 = -1

m2 = (Y[2] - Y[1]) / (X[2] - X[1]) = (2 - 1) / (0 - (-1)) = 1 / 1 = 1

m3 = (Y[3] - Y[2]) / (X[3] - X[2]) = (3 - 2) / (1 - 0) = 1 / 1 = 1

m4 = (Y[4] - Y[3]) / (X[4] - X[3]) = (2 - 3) / (2 - 1) = -1 / 1 = -1

Step 2: Determine the y-intercepts of the line segments

b1 = Y[0] - m1 × X[0] = 2 - (-1) × (-2) = 2 - 2 = 0

b2 = Y[1] - m2 × X[1] = 1 - 1 × (-1) = 1 + 1 = 2

b3 = Y[2] - m3 × X[2] = 2 - 1 × 0 = 2

b4 = Y[3] - m4 × X[3] = 3 - (-1) × 1 = 3 + 1 = 4

Step 3: Define the linear interpolation spline for each segment

For the first segment (-2 <= x < -1):

y = m1 × x + b1 = -1 × x + 0

For the second segment (-1 <= x < 0):

y = m2 × x + b2 = x + 2

For the third segment (0 <= x < 1):

y = m3 × x + b3 = x + 2

For the fourth segment (1 <= x <= 2):

y = m4 × x + b4 = -x + 4

b) To find the quadratic interpolation spline, we will use quadratic polynomial equations to interpolate between the given data points.

Given data points:

X = [-2, -1, 0, 1, 2]

Y = [2, 1, 2, 3, 2]

Step 1: Determine the coefficients of the quadratic polynomials

We will find three quadratic polynomials, each interpolating between three consecutive data points.

For the first quadratic polynomial (interpolating points -2, -1, and 0):

Using the formula y = ax² + bx + c, we substitute the given data points to form a system of equations:

4a - 2b + c = 2

a - b + c = 1

c = 2

Solving the system of equations, we find a = -1, b = -2, and c = 2.

Thus, the first quadratic polynomial is y = -x² - 2x + 2.

For the second quadratic polynomial (interpolating points -1, 0, and 1):

Using the same process, we find a = 0, b = 2, and c = 2.

Thus, the second quadratic polynomial is y = 2x² + 2.

For the third quadratic polynomial (interpolating points 0, 1, and 2):

Using the same process, we find a = 1, b = 2, and c = 2.

Thus, the third quadratic polynomial is y = x² + 2x + 2.

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Answer:

Step-by-step explanation:

-x - 1 = x + 3

-2x - 1 = 3

-2x = 4

x = -2

y = -2 + 3

y = 1

(-2, 1)

Answer:

As i understand this:

We have cards with the values:

0, 1, 2 and 6.

We want to create a two digit number such that:

Not all the cards are used.

6 is one digit of our number.

When we round to the nearest ten, we get 20.

Now, first remember how rounding works.

If we have a number like ab, where a and b are single digits (a is in the tens place and b is in the units place), then:

if b is 5 or more, we round up

if b is less than 5, we round down.

Now in this case we want to have a digit equal 6, if we use this in the units place, then when rounding, we will round up.

Then the other digit can be 1, such that we use the cards:

1 and 6.

then our number is 16:

When rounding, 6 > 5, then we round up to 20.

So this number meets all the conditions.

Answer:

\((fof^{-1})(x)=x\)

Step-by-step explanation:

Composition of two functions f(x) and g(x) is represented by,

(fog)(x) = f[g(x)]

If a function is,

f(x) = (-6x - 8)² [where x ≤ \(-\frac{8}{6}\)]

Another function is the inverse of f(x),

\(f^{-1}(x)=-\frac{\sqrt{x}+8}{6}\)

Now composite function of these functions will be,

\((fof^{-1})(x)=f[f^{-1}(x)]\)

                  = \([-6(\frac{\sqrt{x}+8}{6})-8]^{2}\)

                  = \([-\sqrt{x}+8-8]^2\)

                  = \((-\sqrt{x})^2\)

                  = x

Therefore, \((fof^{-1})(x)=x\)

Answer:

judging from the list of numbers i would pick a

Answer:

y = 392x + 6350

Step-by-step explanation:

Here, we calculate the average rate of change in the number of muffins sold between the two years

Mathematically that will be the difference in number of muffins divided by the number of years

We have this as;

(8310-6350)/(2015-2010)

= 392

an average of 392 muffins were sold in a year

The general form of the equation of a straight line is;

y = mx + c

we have m as 392

so;

y = 392x + c

To get c, we make a substitution

2015 is 5 years after 2010, so x will be 5 and y will still be 8310

so;

8310 = 392(5) + c

c = 8310 - 2960

c = 6350

So the equation is;

y = 392x + 6350

All closed intervals of length 1 in which a function has a unique zero, we need to find all pairs of zeros that are exactly 1 unit apart and consider the intervals between them as described above.

To find all closed intervals of length 1 in which a function has a unique zero, we need to look for intervals where the function changes sign exactly once. This is because if a function has a unique zero, it must change sign from positive to negative or negative to positive at that point.

Let's call the function f(x). To find these intervals, we can use the Intermediate Value Theorem. This theorem states that if a function is continuous on a closed interval [a, b] and takes on values f(a) and f(b) at the endpoints, then it must also take on every value between f(a) and f(b) somewhere on the interval.

So, to apply this theorem, we need to find values of x such that f(x) = 0. Then, we can look at the intervals between these values and see if f(x) changes sign exactly once on any of them.

Let's say we find two zeros of the function at x = a and x = b, where a < b. Then, we can consider the intervals [a, a+1] and [b-1, b] (assuming these intervals have length 1). If f(x) is positive on the interval [a, a+1] and negative on the interval [b-1, b], or vice versa, then f(x) must change sign exactly once on each of these intervals and therefore has a unique zero in each interval.

In general, to find all closed intervals of length 1 in which a function has a unique zero, we need to find all pairs of zeros that are exactly 1 unit apart and consider the intervals between them as described above.

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Answer:

1/16

Step-by-step explanation:

Probability helps us to know the chances of an event occurring. The probability that all four pennies will be tails is (1/16).

Probability helps us to know the chances of an event occurring.

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

The probability of a penny getting a tail is 0.5 or (1/2), therefore, the probability of four penny getting a tail can be written as,

\(\rm Probability = \dfrac14 \times \dfrac14 \times \dfrac14 \times \dfrac14 = \dfrac1{16}\)

Hence, the probability that all four pennies will be tails is (1/16).

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Answer:

8πcm or 25.12cm

Answer:

Asking four boys and four girls from each first period class which type of cake they prefer.

Step-by-step explanation:

cant really explain it just knew it off the top of my head.

Answer:

The answer is \(y + 6 = 3(x + 7)\)

-

Step-by-step explanation:

☆The point-slope form looks like:

\(y - y_1 = m(x - x_1)\)

☆All you simply need to do is plug in according to the formula!

☆\(y + 6 = 3(x + 7)\)

(a) In a poker hand consisting of 5 cards, the probability of holding 3 face cards is to be calculated. Since a deck of cards contains 52 cards, there are only 12 face cards, which means that the total number of ways of getting 3 face cards from 12 is;   12C3.

The remaining two cards may be any of the 40 non-face cards, so there are 40C2 ways of choosing those two cards. Hence the total number of ways of obtaining three face cards and two non-face cards is; 12C3 × 40C2. Hence the probability of getting three face cards and two non-face cards is; 12C3 × 40C2 / 52C5 = 0.0043. Hence the answer is 0.0043. Therefore the probability of holding three face cards in a poker hand consisting of 5 cards is 0.0043. (Rounded to four decimal places as needed).

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Answer: 6^12 (or 2176782336)

When you multiply exponents with the same base, you add the exponents together. (e.g., x^m · x^n = x^m+n)

6^4 · 6^8 = 6^4+8 = 6^12

The area of the sector is A = π cm² and amplitude is a = 0.75 cm

Given data ,

The area of a sector is given by the formula:

A = (1/2) x r² x θ

where r is the radius of the sector and θ is the central angle in radians.

On simplifying , we get

A = π cm²

r = 1.5 cm

Substituting these values into the formula, we get:

π = (1/2) x (1.5)² x θ

π = (3/4) x θ

Solving for θ, we get:

θ = (4/3) x π

The amplitude of the sector is half of the radius, so:

amplitude = (1/2) x 1.5 cm = 0.75 cm

Hence , the amplitude of the sector is 0.75 cm

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Answer:

52

Step-by-step explanation:

We can write this out as an equation. Let's say that the teacher's age is x. Triple the teachers age plus the students age is 163, which can be written out as:

\(3x + 7 = 163\)

We want to isolate the variable, so subtract 7 from both sides. This gives us:

\(3x = 156\)

Finally, we divide both sides by  3, giving:

\(x=52\)

So the teacher is 52 years old.

Hope this helps!

Answer: The teacher is 52.

Equation: 7+3t=163

Step-by-step explanation:

y³+ 4y²-13y+25 or 25-13y+4y²+y³. are the standard form of the polynomial ...

standard form means arranging the term in ascending and descending order in order of the degree of terms ..

.

plz mark my answer as brainlist plzzzz vote me also so that .... hope this helps you ...

The test statistic is given as follows:

z = -1.29.

The p-value is given as follows:

0.0985.

The equation for the test statistic is given as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

The parameters for this problem are given as follows:

\(\overline{p} = \frac{380}{1000} = 0.38, p = 0.4, n = 1000\)

Hence the test statistic is calculated as follows:

\(z = \frac{0.38 - 0.4}{\sqrt{\frac{0.4(0.6)}{1000}}}\)

z = -1.29.

Looking at the z-tabe with z = -1.29, the p-value is given as follows:

0.0985.

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Sales for the dress department last year were $82,000. The manager for the department plans an increase of 12.5% this year. So, the projected sales volume for this year is $92,250.

To calculate this year's projected sales volume we will add 12.5% of the sales of the last year to the sales of last year. This can be calculated by using the formula:

S = P + (P × r / 100)

Where S is new sales, P is old sales, and r is a rate of increase.

In this problem, the value of P is $82,000 and the rate of increase is 12.5%. Now, let's plug these values into the formula and solve for S:

S = P + (P × r / 100)

S = $82,000 + ($82,000 × 12.5 / 100)

S = $82,000 + $10,250S = $92,250

Hence, the projected sales volume for this year is $92,250.

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The area covered by Red flowers are is x/3 square yards.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

The area of a plane figure is the area that its perimeter encloses.

The quantity of unit squares that cover a closed figure's surface is its area.

We have, 1/3 of triangle ABD will have red flowers.

let x be the total area of Triangle.

Here, 1/3(x) is occupied by Red flowers.

Thus, the area covered by Red flowers are:

= x/3 square yards.

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Question

the triangular area between points A, B, and D will be decorated with red, white and blue flowers. 1/3 of triangle ABD will have red flowers. How much area, in square yards, will have red flowers?