what’s 2/3 times 1/8????

Answer:

Rosie is 10 years old

Step-by-step explanation:

A)

Rosie is x years old

Rosie's age (R) = x

R = x

Eva is 2 years older

Eva's age (E) = x + 2

E = x + 2

Jack is twice Rosie’s age

Jack's age (J) = 2x

J = 2x

B)

R + E + J = 42

x + (x + 2) + (2x) = 42

x + x + 2 + 2x = 42

4x + 2 = 42

4x = 42 - 2

4x = 40

\(x = \frac{40}{4} \\\\x = 10\)

Rosie is 10 years old

Given:

\(a_n\) is an arithmetic sequence.

To find:

The value of \(\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}\).

Solution:

We have,

\(\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}\)

It can be written as:

\(=\dfrac{d}{d}\left[\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{d}{a_1a_2}+\dfrac{d}{a_2a_3}+...+\dfrac{d}{a_{39}a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{a_2-a_1}{a_1a_2}+\dfrac{a_3-a_2}{a_2a_3}+...+\dfrac{a_{40}-a_{39}}{a_{39}a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{1}{a_1}-\dfrac{1}{a_2}+\dfrac{1}{a_2}-\dfrac{1}{a_3}+....+\dfrac{1}{a_{39}}-\dfrac{1}{a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{1}{a_1}-\dfrac{1}{a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{a_{40}-a_1}{a_1a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{a_1+(40-1)d-a_1}{a_1a_{40}}\right]\)       \([\because a_n=a_1+(n-1)d]\)

\(=\dfrac{1}{d}\left[\dfrac{39d}{a_1a_{40}}\right]\)

\(=\dfrac{39}{a_1a_{40}}\)

Therefore, the value of given expression is \(\dfrac{39}{a_1a_{40}}\).

Answer:

y = 2x + 7

Step-by-step explanation:

Step 1: Find slope

m = (9 - 3)/(1 + 2)

m = 2

y = 2x + b

Step 2: Find b

9 = 2(1) + b

9 = 2 + b

7 = b

Step 3: Rewrite equation

y = 2x + 7

Answer:

B) y - 9 = 2(x - 1)

Step-by-step explanation:

(-2, 3) ;(1,9)

\(Slope =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{9-3}{1-[-2]}\\\\=\frac{6}{1+2}\\\\=\frac{6}{3}\\\\=2\)

(1, 9 ) ;  m = 2

Equation: \(y - y_{1}=m(x - x_{1})\\\\\)

y - 9 = 2(x - 1)

y - 9 = 2x -2

      y = 2x - 2 + 9

      y = 2x + 7

Answer:

Hollerith tabulating machine

Step-by-step explanation:

The Hollerith tabulating machine was invented by Herman Hollerith in other to assist in the data processing of the United States 1890 election. This machine was used to read and summarize the information stored on punchcards. This machine paved the way for the development of enhanced models which were employed for accounting and some other aspects related to business management.

Answer:

C

Step-by-step explanation:

C

This is False in light of the stated statement. Due to the employment of a regression line to calculate the mean of y for x that are outside the x-range of the data.

How is regression calculated?

Y = mX + b, where X is the predictive (independent) factor, m is really the approximately slope, and b is the expected intercept, is the methodology for simple linear regression.

The relationship between scattered data points in any set is shown by a regression line. When there is a linear pattern, it displays the relationship between the dependent y variable and independent x variables.

The correlation between the independent variables (IVs) and the dependent variable is described by a linear regression equation (DV). The DV for the IV values you indicate can also be predicted for new values.

Hence we get the required answer.

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Step-by-step explanation:

SURFACE AREA of a cylinder is 2×pi×r×(h+r)

=> 2×3.14×7×(8+7)

=>43.96×(15)

=>659.4 mm^2

hope it helps

please give brainliest

Step-by-step explanation:

.

Answer:

\(\sf\: Area \: of \: the \: triangle \: = \boxed{\boxed{\bf\:50 \: cm^{2}}}\)

Step-by-step explanation:

Given,

The triangle is an isosceles triangle.

Since, we are given the hypotenuse, the triangle will be an isosceles right angled triangle.

We know that, area of a right angled triangle = ½ × b × h

By substituting the values in the above formula...

½ × b × h

= ½ × 10 × 10

= ½ × 100

= \(\boxed{\boxed{\bf\:50 \: cm^{2}}}\)

______________

Have a wonderful day!

Step-by-step explanation:

\(f(x) = - 5x - 4\)

\( \: \)

Inverse

\(y = - 5x - 4\)

\(x = - 5y - 4\)

\(x + 4 = - 5y\)

\(y = - \frac{(x + 4)}{5} \)

\( {f}^{ - 1} (x) = - \frac{(x + 4)}{5} \)

(-2, 5) Minimum

Step-by-step explanation:

y-5=(1/3)(x + 2)²

y-5=(1/3)(x²+4x+4))

y-5=1/3x²+4/3x+4/3

y=1/3x²+4/3x+4/3+5

y=1/3x²+4/3x+4/3+15/3

y=1/3x²+4/3x+19/3

graph is attached

x= -b/2a

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

x= (-4/3)/(2/3)

x= (-4/3)*(3/2)

3's cancel

x= (-4/1)*(1/2)

x = -4/2

x = -2

plug -2 back into

y=1/3x²+4/3x+19/3

y=1/3*4+4/3*-2+19/3

y=4/3-8/3+19/3

y=15/3

y=5

(-2,5)

if a is positive

graph looks like a smile

so minimum

if a is negative

graph looks like a frown

so maximum

quadraticswbi.weebly.com

Answer:

The answer is 97!

Step-by-step explanation:

The formula for Pythagorean Theorem is a^2+b^2=c^2. (65)^2 + (72)^2 is 9409, which has a square root of 97. Hope this helped! :)

Answer:

Below

Step-by-step explanation:

Realize that the angles are supplementary

x-17   +     7x+5  = 180

8x -12 = 180

8x = 192

x = 24

To ensure the preservation of the clinical specimen for viral isolation, it should be stored at a specific temperature. The recommended temperature for storing the specimen is generally between 2 to 8 degrees Celsius (36 to 46 degrees Fahrenheit).

Storing the clinical specimen in viral transport medium at a temperature range of 2 to 8 degrees Celsius (36 to 46 degrees Fahrenheit) is commonly advised for preserving the viability of the virus. This temperature range helps to slow down the viral activity and prevents the specimen from deteriorating while awaiting processing. It provides an environment that can maintain the integrity of the viral particles until laboratory procedures can be carried out the following week. It's important to follow the recommended storage temperature to ensure accurate results and successful viral isolation from the specimen.

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\(Given function:q(x) = (1 + sin x) / cos Now we'll apply calculus for each part(a), (b), (c), and (d):\)

a) The function is said to be increasing if the derivative of the function is greater than 0. q'(x) > 0.

\(q'(x) = [cos x (cos x) - (1 + sin x)(-sin x)] / (cos x)^2 = (cos^2 x + sin^2 x - cos x) / (cos x)^2 = 1/cos x - 1; here we have a denominator of cos x which means that we can't have cos x = 0.\)

That's why the function is increasing on (- π/2, 0) and (0, π/2).

b) The function is said to be concave up if its second derivative is greater than 0. q''(x) > 0.

\(q''(x) = [-sin x (cos x) - (-sin x) (-sin x)] / (cos x)^3 = -sin x/cos^2 x;\)again we have a denominator of cos x which means that we can't have cos x = 0.

That's why the function is concave up on (- π/2, π/2).

c) For stationary points we should find the roots of q'(x) and check the second derivative at that point(s).

\(q'(x) = 1/cos x - 1 = 0 gives cos x = 1/2 on (- π/3, π/3) only.\)

\(The second derivative at this point is q''(π/3) = - sin (π/3) / cos^2 (π/3) < 0.\)

It means that the function has a maximum point at π/3.

\(The coordinates of this point are: (π/3, 3√3 / 2).\)

d) The function will have a point of inflection at x = an if its second derivative changes sign from negative to positive or vice versa at x = a. q''(x) changes sign at x = π/2, thus the function has a point of inflection at x = π/2.

Sketch of the graph: We know that the function is increasing o\(n (- π/2, 0) and (0, π/2), it's concave up on (- π/2, π/2),\) it has a maximum point at (π/3, 3√3 / 2), and it has a point of inflection at x = π/2.

With this information, we can sketch the graph of the function:  The red dot is the maximum point at\((π/3, 3√3 / 2),\) and the green dot is the point of inflection at x = π/2.

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The points of inflection occur at x = 0, π/2, π, 3π/2, 2π, etc.

To determine the open intervals on which q(x) = 1 + sin(x)cos(x) satisfies the given properties, we need to analyze the first and second derivatives of q(x) and consider the critical points, intervals of increase/decrease, and concavity.

(a) To determine where q(x) is increasing or decreasing, we analyze the first derivative:

q'(x) = d/dx (1 + sin(x)cos(x))

= 0 + cos^2(x) - sin^2(x) [using the product rule and trigonometric identities]

= cos(2x)

The first derivative q'(x) = cos(2x) is positive when cos(2x) > 0, and negative when cos(2x) < 0.

Cosine is positive in the intervals [0, π/2) and (3π/2, 2π), and negative in the intervals (π/2, 3π/2). Therefore, q(x) is increasing on the intervals (0, π/4) and (3π/4, π) and decreasing on the interval (π/4, 3π/4).

(b) To determine where q(x) is concave up or down, we analyze the second derivative:

q''(x) = d/dx (cos(2x))

= -2sin(2x)

The second derivative q''(x) = -2sin(2x) is positive when sin(2x) < 0, and negative when sin(2x) > 0.

Sin(2x) is negative in the intervals (0, π) and (2π, 3π), and positive in the intervals (π, 2π) and (3π, 4π). Therefore, q(x) is concave up on the intervals (0, π/2) and (3π/2, 2π), and concave down on the intervals (π/2, 3π/2).

(c) To find the location of all critical points, we set the first derivative q'(x) = cos(2x) equal to zero and solve for x:

cos(2x) = 0

2x = π/2 + kπ, where k is an integer

x = π/4 + kπ/2

Therefore, the critical points occur at x = π/4, 3π/4, 5π/4, 7π/4, etc.

(d) To sketch the points of inflection, we set the second derivative q''(x) = -2sin(2x) equal to zero and solve for x:

sin(2x) = 0

2x = kπ, where k is an integer

x = kπ/2

Therefore, the points of inflection occur at x = 0, π/2, π, 3π/2, 2π, etc.

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A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.

We know that,

A dummy variable is a binary variable that takes a value of 0 or 1.

In regression analysis, a dummy variable is one that takes only the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.

The number of dummy variables we must create is equal to k - 1, where k is the number of different values that the categorical variable can take on.

It is an artificial variable created to represent an attribute with two or more distinct categories/levels.

These are being used in order to sort out data into mutually exclusive groups.

It is used typically in time series analysis, response modelling, bio-medical studies, economic forecasting and credit scoring.

Therefore, a variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.

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(a)image averaging is a very effective method of reducing noise in images. Image averaging reduces noise by adding multiple images of the same scene together and then dividing by the number of images added.The conditions that must be fulfilled for the image averaging method are as follows:-

(i) The background of the image must not move between each image capture.- The noise present in the image must be random.- The source of the noise must be consistent.

(ii)The mathematical expression that characterizes the noise in the resultant image when K images are averaged, as K becomes large is given by;sigma_n^2/K

Where;sigma_n^2 is the variance of the noise and K is the number of images that have been averaged.

Therefore, as K increases, the variance of the noise in the resultant image reduces, and thus, the noise reduces.When either method can be used for noise reduction, the temporal image averaging method would be the preferred method to select.

(iii)This is because it uses a sequence of images that are taken at different times, usually at high speeds, to produce a single image that is free of noise. This method is best when dealing with fast-moving objects, and it can be used in situations where the camera cannot be stabilized and is experiencing unwanted vibration or shaking.

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Answer:

\(y=\frac{2}{3}x+1\frac{1}{3}\)

Step-by-step explanation:

when a line is parallel the slope is the same for both

y=mx+b is slope intercept form where m is slope and b is intercept

we know the slope is 2/3 so to find b we just fill it in with coordinates

-2=2/3(-5)+b

-2=-10/3+b

+10/3 +10/3

4/3=b

y=2/3x+4/3

hopes this helps please mark brainliest

The solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

To simplify the equation 3(x-6) - 1/2(8x+10) = -25, we can start by applying the distributive property and then combining like terms.

First, let's distribute the 3 and the -1/2 to the terms inside the parentheses:

3(x-6) - 1/2(8x+10) = 3x - 18 - (4x + 5)

Now, let's simplify further by combining like terms:

3x - 18 - 4x - 5 = -x - 23

So, the simplified equation is -x - 23 = -25.

To solve for x, we can isolate the variable by adding 23 to both sides of the equation:

-x - 23 + 23 = -25 + 23

This simplifies to:

-x = -2

Finally, we can solve for x by multiplying both sides of the equation by -1:

(-1)(-x) = (-1)(-2)

This gives us:

x = 2

Therefore, the solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

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So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
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Answer:

B

Step-by-step explanation:

The slope is -1, which equals m= -1.

The answer is B.

Answer:

1.78260245797

Step-by-step explanation:

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The area of the surface generated when the curve y=8x is revolved about the x-axis is approximately 71294.3 square units.

To find the surface area generated when the curve y=8x is revolved about the x-axis, we can use the formula for the surface area of a solid of revolution:

A = 2π∫a^b y√(1+(dy/dx)^2) dx

where a and b are the limits of integration and dy/dx is the derivative of y with respect to x.

In this case, y=8x, so dy/dx=8. We want to revolve the curve about the x-axis, so the axis of rotation is y=0.

Plugging in these values, we get:

A = 2π∫33^65 8x√(1+8^2) dx

= 2π∫33^65 8x√65 dx

Simplifying the expression under the square root sign:

√65 = √(64+1) = √64(1+1/64) = 8√(1+1/64)

Plugging this into the integral and simplifying:

A = 2π∫33^65 8x × 8√(1+1/64) dx

= 2π × 64√(1+1/64) ∫33^65 x dx

= 2π × 64√(1+1/64) × [(65^2 - 33^2)/2]

= 2π × 64√(1+1/64) × 2016

≈ 71294.3 square units.

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#4= -8

#5= 781

#6= 1.34×10(3) (Exponent)

Answer:

3

Step-by-step explanation:

Find the value of x for which n(x) = 0.

-6x+18 = 0

6x = 18

x = 3

According the question given you jogged around the distance of 26\(\frac{2}{3}\) miles.

What is an improper fraction?

When the numerator value exceeds the denominator value, the fraction is incorrect. Incorrect fractions can also be expressed in the form of a whole number and a proper number, where the numerator is the remainder and the denominator is left unchanged.

Here, we have

Given: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week.

We have to find out how many miles did you jog.

The total jogging distance will be

= 4(6 2/3) miles

= 4 × 20/3 miles

= 80/3 miles

= 26\(\frac{2}{3}\) miles.

Hence, you jog 26\(\frac{2}{3}\) miles.

Question: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week, how many miles did you jog?

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The correct answer is not provided among the given choices.

The y-intercept of the function f(x) = 3x + 2 is (0, 2).

To find the y-intercept of the function f(x) = 3x + 2, we need to determine the value of y when x is equal to 0.

The y-intercept represents the point where the graph of the function intersects the y-axis.

Substituting x = 0 into the equation, we get:

f(0) = 3(0) + 2

f(0) = 0 + 2

f(0) = 2

So, when x = 0, the corresponding value of y is 2.

Therefore, the y-intercept of the function f(x) = 3x + 2 is (0, 2).

Among the given answer choices:

A. (9, 0) does not represent the y-intercept.

B. (0, 9) does not represent the y-intercept.

C. (0, -9) does not represent the y-intercept.

D. (9, -9) does not represent the y-intercept.

None of the given answer choices correctly represent the y-intercept of the function f(x) = 3x + 2, which is (0, 2).

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The point (9, 10) satisfies the inequality 16x - 7y 16 because the inequality is true.

To determine if the point (9, 10) satisfies the inequality 16x - 7y ≥ 16, we need to substitute the values of x and y into the inequality and check if it is true:

16(9) - 7(10) ≥ 16

144 - 70 ≥ 16

74 ≥ 16

Since the inequality is true, the point (9, 10) satisfies the inequality 16x - 7y ≥ 16.

Inequalities are mathematical expressions that compare the values of two quantities. They are represented using symbols such as > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to). Inequalities are often used in real-world situations to represent limits or constraints. For example, a company may have a production limit of 100 units per day, which can be represented as x ≤ 100, where x is the number of units produced per day. Solving inequalities involves finding the possible values of the variable that make the inequality true. This can be done using algebraic methods such as adding, subtracting, multiplying or dividing both sides of the inequality by the same number.

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Answer:

x = 84°

Step-by-step explanation:

180 - 143 = 37

37 + 59 = 96

180 - 96 = 84°

Answer:

x = 84 degrees

Step-by-step explanation:

To solve this, we need to keep the following 2 things in mind:

a. A straight line will have an angle of 180 degrees.

b. A triangle's inside angles will have a sum of 180 degrees.

Knowing the first fact, we know that the unnamed angle to the left in the triangle PLUS the 143 degree angle, will equal 180.

143 + v = 180

I'm calling that angle v here.

Subtracting 143 from both sides:

v = 180 - 143 = 37

That angle is 37 degrees.

Now, our 2nd fact says that all inside angles in a triangle will add to 180.

Angle 1 = 59 degrees (bottom right)

Angle 2 = 37 degrees (bottom left)

Angle 3 = x (top)

59 + 37 + x = 180

96 + x = 180

Subtracting 96 from both sides:

x = 84

Answer:

x = 84 degrees

Answer:

1 meter = 3.28 feet

Step-by-step explanation:

The unit of conversion from meters to feet is given as follows;

By convention

1 yard = 09144 meters

1 yard = 3 feet

Therefore, we have;

1 foot = 0.9144/3 = 0.3048 m

Alternatively we can get;

1 inch = 0.0254 meters

1 foot = 12 inches

Therefore, we have;

1 foot = 12 × 0.0254 = 0.3048 meter

Which gives;

1 foot = 0.3048 meter

Given that 0.3048 meter = 1 foot, to find the measure of 1 meter, we proceed by dividing both sides of the equation by 0.3048 to get

0.3048/0.3048 meter = 1/0.3048 foot = 3.28084 feet

1 meter = 3.28084 feet. ≈ 3.28 feet to the nearest hundredth