Convert The Following Repeating Consecutive Decimals To Fractions. For Example, 0.499999... 1/2 (a) 0.7777... (2024)

The statement many quantitative models of decision making are based on comparing a single measure of effectiveness, generally some form of utility to the decision maker is true. So, the correct optio is option a. true.

Decision theory is a branch of probability. It is concerned with analytic philosophy. It deals with the decision making processes based on probabilities depending on the various factors and the numerical consequences of the outcome.

Therefore, the statement about the decision theory based on comparing a single measure of effectiveness is true.

Know more about decision making here:

https://brainly.com/question/796795

#SPJ11

The total number of white shirts needed to be added by the store would be 13.

Word problem

Assuming that x is the number of white shirts that need to be added. After adding these shirts, the total number of shirts in the store will be:

2 + x white shirts and 10 black shirtstotal shirts = 12 + x shirts.

If the probability of selecting a white shirt from all the shirts is 3/5, then we can set up the following equation and solve for x accordingly:

(2 + x) / (12 + x) = 3/55(2 + x) = 3(12 + x)10 + 5x = 36 + 3x2x = 26x = 13

Therefore, the store needs to add 13 white shirts.

More on word problems can be found here: https://brainly.com/question/2610134

#SPJ1

The arrow notation that describes the translation is (x, y) ⇒ (x + 3, y + 6)

Using the arrow notation to describe the translation.

From the question, we have the following parameters that can be used in our computation:

W(-2,-6) to W'(4,9)

The translation is the difference between the pairs

So, we have

(x, y) = (9 - 6, 4 + 2)

Evaluate

(x, y) = (3, 6)

Hence, the translation is (x, y) ⇒ (x + 3, y + 6)

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

The boundaries between the various plot sections of electric field will be two vertical lines.

In this work, the distance from a point charge must be calculated under three different circ*mstances: (1) when the distance is less than the radius of the point charge; (2) when the distance is greater than the radius of the outer sphere; and (3) when the distance is between the radii of two concentric charged spheres.

Numerous calculations that connect the charge distribution and distance to the electric field are used to determine the electric field at each site. The absolute value of the electric field is then displayed as a function of distance using the numerous formulas that were employed, and the different places where the electric field varies are identified.

The boundaries between the various plot sections will be two vertical lines.

Learn more about electric field:

https://brainly.com/question/30544719

#SPJ4

The value of the angle x in the given polygon image is: x = 54°

How to find the angle in the polygon?

The formula to find the interior angles of a polygon is:

θ = 180(n - 2)/n

Thus, for a pentagon with 5 sides, we have:

θ = 180(5 - 2)/5

θ = 540/5

θ = 108°

Interior angle of a square is 90 degrees and since angle at a point is 360 degrees then we have:

x + 108 + 108 + 90 = 360

x = 360 - 306

x = 54°

Read more about Angle in Polygon at: https://brainly.com/question/1592456

#SPJ1

a) Area = √[s(s-a)(s-b)(s-c)] b) the area of the land 225.83 m^2 c) the total cost for the fencing the land three times at the rate of Rs. 25 per meter of the wire. is Rs. 43,500

How to determine the formula of finding the area of a triangle having all sides are not equall

a) The formula to find the area of a triangle when all sides are not equal is Heron's formula:

Area = √[s(s-a)(s-b)(s-c)]

where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of its sides.

To find the semi-perimeter, we add up the three sides and divide by 2:

semi-perimeter = (8+9+10)/2 = 27/2

Now we can substitute into the formula:

b) Area = √[27/2(27/2-8)(27/2-9)(27/2-10)]

= √[27/2(11/2)(9/2)(7/2)]

= √(27^2/4 * 11 * 9 * 7) / 4

= √51030.1875

≈ 225.83 m^2

b) To fence the land three times, we need to find the perimeter of the triangle and multiply by 3:

Perimeter = 8x + 9x + 10x = 27x

We know that the perimeter is 540 m, so we can solve for x:

27x = 540

x = 20

Now we can find the actual lengths of the sides:

8x = 8(20) = 160

9x = 9(20) = 180

10x = 10(20) = 200

The total length of wire needed to fence the land three times is the perimeter multiplied by 3:

Total length of wire = 3(160 + 180 + 200) = 1740 m

The cost of the wire is Rs. 25 per meter, so the total cost is:

Total cost = 1740 * 25 = Rs. 43,500

Learn more about perimeter at https://brainly.com/question/19819849

#SPJ1

The line-of-sight distance from the television camera to the case of the stadium is [tex]\text{x = 3826.71 m}[/tex]

Given data

From Δ ABC

AB = The altitude of the blimp is = 400 m

AC = The line-of-sight distance from the television camera to the case of the stadium = x

Now

[tex]\text{sin} \ 6=\dfrac{\text{AB}}{\text{AC}}[/tex]

[tex]x=\dfrac{\text{AB}}{\text{sin} \ 6}[/tex]

[tex]x=\dfrac{400}{\text{sin} \ 6}[/tex]

[tex]\bold{x = 3826.71 \ m}[/tex]

Therefore the line-of-sight distance from the television camera to the case of the stadium.

So you're telling me, you're seriously in high school and do not know this.

Ah, whatever.

Tree height = 55 meters

Tree height in feet = ?

1 m = 3.3 feet

Tree height in feet = 55 x 3.3 = 181.5 feet.

The required answer is the height of the tree is provided in meters (55 meters) in the given problem and convert it to 181.5 feet. By multiplying the given height by the conversion factor of 3.3 feet/meter, we obtain the height of the tree in feet

Feet to meter conversion:

To convert a value from feet to meters, we use the conversion factor of 1 meter equals 3.3 feet. This means that for every 1 meter, there are 3.3 feet. To convert a measurement from feet to meters, we multiply the given value in feet by the conversion factor.

To convert the height of a tree from meters to feet, we can use the conversion factor: 1 meter is equal to 3.3 feet. Let's solve the problem step by step:

Step 1: Multiply the given height in meters (55) by the conversion factor (3.3).

55 meters x 3.3 feet/meter

Step 2: Perform the multiplication operation:

55 x 3.3 = 181.5 feet

Step 3: Write the result as the height in feet:

The height of the tree is 181.5 feet.

Hence, the height of the tree is provided in meters (55 meters) in the given problem , and to convert it to 181.5 feet. By multiplying the given height by the conversion factor of 3.3 feet/meter, we obtain the height of the tree in feet.

Learn more about unit conversions and the relationship between feet and meters at:

https://brainly.com/question/16814684

#SPJ6

If the p-value is greater than 0.05, then there is evidence to conclude that there is a significant difference.

The p-value is a measure of the strength of evidence against the null hypothesis, which is the hypothesis that there is no difference between groups. A small p-value indicates that there is strong evidence against the null hypothesis, and that the observed difference is likely not due to chance.

If the p-value is less than 0.05, which is a commonly used significance level in many fields, it means that there is sufficient evidence to reject the null hypothesis and conclude that there is a statistically significant difference between groups.

Now, to answer your question, it would be helpful to know the exact p-value from the SPSS analysis. If the p-value is less than 0.05, then there is evidence to suggest that there is a significant difference in weight after the intervention program across racial groups.

To know more about p-value here

https://brainly.com/question/14790912

#SPJ4

Mollie can expect to lose $1.50 per game played.

To solve this problem

What is Mollie's expected profit per game, assuming players play only once?

First, let's calculate the expected revenue per game:

Probability of winning: 0.1

Revenue from winners: $5

Probability of losing: 0.9

Revenue from losers: $0

Expected revenue per game = (0.1 x $5) + (0.9 x $0) = $0.50

Now, let's calculate the expected cost per game:

Cost per game: $2

Expected cost per game = $2

Therefore, Mollie's expected profit per game is:

Expected profit per game = Expected revenue per game - Expected cost per game

Expected profit per game = $0.50 - $2

Expected profit per game = -$1.50

This means that, on average, Mollie can expect to lose $1.50 per game played.

Learn more about profit here : brainly.com/question/29785281

#SPJ1

The superposition principle states that the sum of two or more particular solutions is also a particular solution, so once the coefficients are found for each particular solution, the general solution can be obtained by adding them together.

The method of undetermined coefficients is used when the non-hom*ogeneous term of the differential equation is of a certain form, such as a polynomial, exponential, or trigonometric function. The form of the particular solution is then chosen based on the form of the non-hom*ogeneous term.

To know more about undetermined coefficients, refer here:
https://brainly.com/question/30898531#
#SPJ11

Let's call the number of points Brandon's team scored "n".

According to the problem, Brandon scored "2 points more than one third of his team's total points".

One third of the team's total points is (1/3)n.

So, Brandon scored (1/3)n + 2 points.

Therefore, the expression for the number of points Brandon scored is (1/3)n + 2.

a) The given proposition "Every hom*ogeneous linear system has a solution" is true.

A skew-symmetric matrix A satisfies the property that A×T = -A. By repeatedly multiplying a skew-symmetric matrix A by itself, the resulting matrix A×p will also be skew-symmetric for any positive integer p. This can be proven by induction.

You can learn more about hom*ogeneous linear systems at: brainly.com/question/31420945

#SPJ11

W fails to satisfy the closure property of a subspace, and is not a subspace of R2.

(a) Yes, 0 = [0 0] is in W because 0*0 = 0 and 0 is non-negative.

(b) Yes, if u is in W and c is any scalar, then cu is also in W. This is because if xy ≥ 0 and c ≥ 0, then (cu)x = c(ux) ≥ 0 since ux ≥ 0. Similarly, if xy ≥ 0 and c ≤ 0, then (cu)x = c(ux) ≤ 0 since ux ≥ 0. Therefore, cu is also in W.

(c) One possible choice for u and v such that u + v is not in W is u = [1 0] and v = [0 -1]. Then u and v are both in the first quadrant, but their sum u + v = [1 -1] is in the second quadrant and thus not in W

(d) No, W is not a subspace of R2 because it is not closed under vector addition. Specifically, if u and v are in W, then their sum u + v may not be in W, as shown in part (c). Therefore, W fails to satisfy the closure property of a subspace, and is not a subspace of R2.

To learn more about subspace visit:

https://brainly.com/question/30318872

#SPJ11

Therefore, there are approximately 402,653,184,000 bacteria after 24 hours.

Can we evaluate it at the given values using the given function f(x)=7x-1

c) Using the given function f(x) = 7x - 1, we can evaluate it at the given values as follows:

f(1/2) = 7(1/2) - 1 = 2.5 - 1 = 1.5

f(2.5) = 7(2.5) - 1 = 17.5 - 1 = 16.5

f(-1) = 7(-1) - 1 = -7 - 1 = -8

f(1/4) = 7(1/4) - 1 = 1.75 - 1 = 0.75

Therefore, f(1/2) = 1.5, f(2.5) = 16.5, f(-1) = -8, and f(1/4) = 0.75.

d) Using the given function g(x) = (1/3)^(x+1), we can evaluate it at the given values as follows:

g(1/2) = (1/3)^(1/2+1) = (1/3)^(3/2) ≈ 0.192

g(√3) = (1/3)^(√3+1) ≈ 0.011

g(-3.5) = (1/3)^(-3.5+1) = (1/3)^(-2.5) ≈ 3.755

g(-1.4) = (1/3)^(-1.4+1) = (1/3)^(-0.4) ≈ 1.427

Therefore, g(1/2) ≈ 0.192, g(√3) ≈ 0.011, g(-3.5) ≈ 3.755, and g(-1.4) ≈ 1.427.

e) The function that models the number of bacteria after t hours is given by:

N(t) = 1500 * 2^(t/1)

where 1500 is the initial number of bacteria and 2^(t/1) represents the number of times the bacteria double in t hours.

To find the number of bacteria after 24 hours, we can substitute t = 24 into the above function and evaluate:

N(24) = 1500 * 2^(24/1) = 1500 * 2^24 ≈ 402653184000

Therefore, there are approximately 402,653,184,000 bacteria after 24 hours.

Learn more about evaluation

brainly.com/question/12837686

#SPJ11

The equation of the circle is [tex](x - 3)^2 + (y - 10)^2 = 4[/tex]

What is circle?

A circle is a two-dimensional geometric shape that is defined as the set of all points that are equidistant from a fixed point, called the center. The distance from the center to any point on the circle is called the radius.

Circles have many interesting properties and are commonly studied in geometry. Some of the key properties of circles include:

All points on the circumference of a circle are equidistant from the center.

The diameter of a circle is a line that passes through the center and touches two points on the circumference. The diameter is twice the length of the radius.

The circumference of a circle is the distance around the outside edge. It is equal to the diameter multiplied by pi (π), which is a mathematical constant that is approximately equal to 3.14.

The area of a circle is the amount of space contained within the circumference. It is equal to pi multiplied by the square of the radius.

Now The standard form of the equation of a circle is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) is the center of the circle and r is the radius.

In this case, the center is (3,10) and the radius is 2. So we can plug these values into the standard form equation and simplify:

[tex](x - 3)^2 + (y - 10)^2 = 2^2[/tex]

[tex](x - 3)^2 + (y - 10)^2 = 4[/tex]

Therefore, the equation of the circle with center (3,10) and radius 2 is [tex](x - 3)^2 + (y - 10)^2 = 4[/tex] in standard form.

To know more about Circle visit:

https://brainly.com/question/29142813

#SPJ1

The area of Kai's garden is 150 sq m. The number of bags of grass seed needed is 5 and the cost of grass seed is £49.95

Area of Kai's triangle garden = [tex]\frac{1}{2} *b*h[/tex]

where b is the base of the triangle

and h is the height of the triangle

b = 20 m

h = 15 m

Area of triangle garden = [tex]\frac{1}{2}*20*15[/tex]

= 150 sq m

One bag of grass seeds cover = 35 sq m

150 sq m requires = 150 / 35 bags of grass seed

= 4.28 bag is required

Since Kai needs to buy a whole bag, 5 bags of grass seed is bought

Cost of 1 bag of grass seed = £8.99

Cost of 5 bags of grass seed = 8.99 * 5 = £49.95

Learn more about Areas:

https://brainly.com/question/23353279

Answer:

=√2/4

Step-by-step explanation:

[tex]sin(3\pi /4) = \frac{\sqrt{2}}{2} \\\\and \\\\cos(5\pi /3) = \frac{1}{2} \\\\[/tex]

Therefore, sin(3π/4) × cos(5π/3) = √2/2 × 1/2 = √2/4

Total amount of drink in the jug is 1 1/10 litre.

How much drink in the jug altogther?

To find the total amount of drink in the jug, we need to add the amount of water and the amount of lemon juice:

Amount of water = 3/5 litre

Amount of lemon juice = 1/2 litre

We need to find a common denominator to add these fractions. The smallest common multiple of 5 and 2 is 10. So we can rewrite the fractions with denominators of 10:

Amount of water = (3/5) x (2/2) = 6/10 litre

Amount of lemon juice = (1/2) x (5/5) = 5/10 litre

Now we can add the fractions:

Total amount of drink = 6/10 + 5/10 = 11/10 litre

Since the numerator is greater than the denominator, we have an improper fraction. We can convert it to a mixed number by dividing the numerator by the denominator:

11 ÷ 10 = 1 with a remainder of 1

So the total amount of drink in the jug is 1 1/10 litre.

to know more about fractions

brainly.com/question/10354322

#SPJ1

Answer: 4/5

Step-by-step explanation:

Sin ∅ = [tex]\frac{opposite}{hypotenuse}[/tex]

- opposite means, the length of the side opposite of the angle

-trig can only be sued in a right triangle, so the hypotenuse is always the side opposite of the right angle, or the longest side

Your question

sin A= [tex]\frac{32}{40}[/tex] you can reduce this ratio by 8, meaning you can divide the top and bottom by 8 to get a reduced fraction

sin A = [tex]\frac{4}{5}[/tex]

Answer: 24

Step-by-step explanation:

First, you need to find the slope length a single side of the square.

d=√((x2 – x1)² + (y2 – y1)²)

d=√((6 – 1)² + (1 – 2)²)

d=√(5² -1²)

=√(25 -1)

=√(24)

=√(24)

=4.8989794855663561963945681494118

Secondly, you need to use the area formula. side * side

4.8989794855663561963945681494118*4.8989794855663561963945681494118= 24

So, your answer is 24.

Hope this helps! :)

We can estimate that there were approximately 388 M&Ms in the bag. 5. The M&M bags may not be distributed as planned for a number of reasons.

What is percentage?

When a number is expressed as a fraction of 100, the denominator is always fixed at 100. It is frequently used to convey ratios, proportions, or rates in a way that is easier to grasp and compare.

On a test, for instance, if a student correctly answers 20 of the 25 questions, we can calculate their percentage by dividing 20 by 25, then multiplying the result by 100:

20/25 x 100 = 80%

Given that, you count 97 blue pieces, and they are 25%.

Thus,

0.25x = 97

x = 388

Hence, we can estimate that there were approximately 388 M&Ms in the bag.

5. The M&M bags may not be distributed as planned for a number of reasons. There is a chance that the sample of M&Ms we saw is not entirely representative of the population of M&Ms in the bag due to random sampling error. Another explanation is that there may be some natural fluctuation in the ratios of various colours in each batch of M&Ms because the manufacturing procedure at the factory is not always exact.

Learn more about percentage here:

https://brainly.com/question/28670903

#SPJ1

That the constant of integration C cancels out when we evaluate the definite integral, so we do not need to include it in the final answer.

We can evaluate the definite integral using the power rule of integration, which states that

∫ [tex]x^n dx = (x^(n+1))/(n+1) + C[/tex]

where C is the constant of integration.

So, for the given definite integral, we have:

∫ [tex](1/(5^(50)x^3)) dx[/tex]

[tex]= (-1/2) * (1/(5^(50))) * (1/x^2) + C[/tex]

Evaluating this from x = 1 to x = 1/5, we get:

[tex]= (-1/2) * (1/(5^(50))) * (1/(1/5)^2) - (-1/2) * (1/(5^(50))) * (1/1^2)[/tex]

[tex]= (-1/2) * (5^2) * (5^(50)) + (1/2) * (5^(50))[/tex]

[tex]= - (1/2) * (5^(52)) + (1/2) * (5^(50))[/tex]

[tex]= (1/2) * (5^(50)) * (1 - 5^2)[/tex]

[tex]= (1/2) * (5^(50)) * (-24)[/tex]

[tex]= -12 * (5^(50))[/tex]

So, the value of the definite integral is [tex]-12 * (5^(50))[/tex]. Note that the constant of integration C cancels out when we evaluate the definite integral, so we do not need to include it in the final answer.

To learn more about need visit:

https://brainly.com/question/26302665

#SPJ11

AnswER

410 A

Step-by-step explanation:

In this experiment, the experimental units are the cookies made from each of the six different recipes. The bakery testing the flours should create three treatment groups, one group for each type of flour, and use random assignment to assign each recipe to one of the three treatment groups.

To do this, the bakery could randomly assign a number (1, 2, or 3) to each recipe, and then assign the recipe to the corresponding treatment group (e.g., recipe 1 to treatment group 1, recipe 2 to treatment group 2, etc.). Alternatively, the bakery could use a randomization table or a computer program to randomly assign the recipes to the treatment groups.

After the cookies have been baked using the different types of flour, the bakery can measure the shelf life of the cookies and compare the results between the treatment groups. By using random assignment, the bakery can be more confident that any differences in shelf life are due to the type of flour used and not to other factors that could affect the results.

To know more about cookies:

https://brainly.com/question/15434033

#SPJ1

that is not important when estimating population properties using sample data, as even minor issues can significantly impact the accuracy of estimates.

One important issue affecting our ability to estimate the properties of a population when using only sample data is the representativeness of the sample. If the sample is not a good representation of the population, then the estimates based on the sample data may not accurately reflect the true properties of the population. Other factors that can affect estimates' accuracy include the sample size and the sampling method used. However, it is difficult to identify issues that are not important when estimating population properties using sample data, as even minor issues can significantly impact the accuracy of estimates.
Visit here to learn more about sample data:

brainly.com/question/13236722

#SPJ11

The length of the curve y = 4(x − 1)³/² from x=1 to x=4 is approximately 18.42 units.

We then plug this into the formula for arc length and simplify the integral. After integrating from x=1 to x=4, we get the length of the curve to be approximately 18.42 units.

To know more about derivative click on below link:

https://brainly.com/question/25324584#

#SPJ11

Much of the power of logarithms is their usefulness in solving exponential equations. Some examples of this include sound (decibel measures), earthquakes , the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity).

What is exponential equations?

An exponential equation is an equation in which a variable occurs in the exponent. For example, y = 5x is an exponential equation since the exponent is the variable x (also said as "5 to the power of x"), while y = x5 is not an exponential equation since the exponent is 5 and not a variable.

What is logarithmic functions?

The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log).

Learn more about exponential and logroithmic functions here :-

https://brainly.com/question/5956809

#SPJ4

the new value of the house is $225,500. we can solve this by substituting the given information into the equation from part (a)

what is equation ?

An equation is a mathematical statement that uses an equal sign to show that two expressions have the same value. Equations are used to represent a wide range of relationships between variables

In the given question,

(a) To write the new value in terms of the old value, we can use the fact that the value decreased by 18%, which means that the new value is equal to 100% - 18% = 82% of the old value. So, we can write:

New value = 0.82 x Old value

(b) To determine the new value, we can substitute the given information into the equation from part (a):

New value = 0.82 x 275,000

New value = 225,500

Therefore, the new value of the house is $225,500.

To know more about equation , visit:

https://brainly.com/question/29657983

#SPJ1

Answer: The test statistic ? is 3.17.

Step-by-step explanation:

To conduct a hypothesis testing to see if the population mean speed on the off-ramp is 45 mph at a 95% confidence level, we need to set up the null and alternative hypotheses:

Null hypothesis: The population mean speed on the off-ramp is 45 mph (μ = 45)

Alternative hypothesis: The population mean speed on the off-ramp is not 45 mph (μ ≠ 45)

We can use a two-tailed t-test since we do not have any prior knowledge about the direction of the difference.

Next, we need to calculate the test statistic:

t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size))

t = (46.5 - 45) / (4.1 / sqrt(60))

t = 3.17

The degrees of freedom (df) for this test is (n - 1) = 59. We can find the critical value using a t-table or a t-distribution calculator for a 95% confidence level with df = 59:

t_critical = ±2.002

Since our calculated t-value (3.17) is outside the range of the critical values (-2.002, 2.002), we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population mean speed on the off-ramp is not 45 mph at a 95% confidence level.

Answer: The test statistic ? is 3.17.