Two rational numbers are each less than 1. Is their product less than 1?

Answer:

b and e are correct and f maybe

Step-by-step explanation:

The scaled values sum up to 1/10.

        k subscript 1 + k subscript 2 = 1

        E[10 k subscript 1 theta with hat on top subscript 1 + 10 k subscript 2 theta with hat on top subscript 2] = 10 k  subscript 1 E[theta with hat on top subscript 1] + 10 k subscript 2 E[theta with hat on top subscript 2]

        E[theta with hat on top subscript 1] = theta

        E[theta with hat on top subscript 2] = theta

        E[10 k subscript 1 theta with hat on top subscript 1 + 10 k subscript 2 theta with hat on top subscript 2] = 10 k subscript 1 theta + 10 k subscript 2 theta = theta (10 k subscript 1 + 10 k subscript 2) = theta

        k subscript 1 + k subscript 2 = 1

        10 k subscript 1 + 10 k subscript 2 = 10

       k subscript 1 + k subscript 2 = 1

       k subscript 1/10 + k subscript 2/10 = 1/10

Therefore, their sum is equal to 1, and their scaled values sum up to 1/10.

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Answer:

RQ=35.51 km

PR=34.62 km

Step-by-step explanation:

Bearing of Q from P = 72 degrees

Bearing of R from Q=320 degrees

320=270+50

Therefore, the second angle of Q is 50 degrees.

\(\angle P=72^\circ\\\angle Q=68^\circ\\\angle R=180^\circ-(72^\circ+68^\circ)=40^\circ\)

Using Law of Sines

\(\dfrac{r}{\sin R} =\dfrac{p}{\sin P} \\\dfrac{24}{\sin 40} =\dfrac{p}{\sin 72} \\p=\sin 72 \times \dfrac{24}{\sin 40}\\\\p=RQ=35.51$ km\)

Using Law of Sines

\(\dfrac{q}{\sin Q} =\dfrac{r}{\sin R} \\\dfrac{q}{\sin 68} =\dfrac{24}{\sin 40} \\q=\dfrac{24}{\sin 40}\times \sin 68\\\\q=PR=34.62$ km\)

To find the y-coordinate of point P on the unit circle, given that its x-coordinate is 5/13, we can utilize the Pythagorean identity for points on the unit circle.

The Pythagorean identity states that for any point (x, y) on the unit circle, the following equation holds true:

x^2 + y^2 = 1

Since we are given the x-coordinate as 5/13, we can substitute this value into the equation and solve for y:

(5/13)^2 + y^2 = 1

25/169 + y^2 = 1

To isolate y^2, we subtract 25/169 from both sides:

y^2 = 1 - 25/169

y^2 = 169/169 - 25/169

y^2 = 144/169

Taking the square root of both sides, we find:

y = ±sqrt(144/169)

Since we are dealing with points on the unit circle, the y-coordinate represents the sine value. Therefore, the y-coordinate of point P is:

y = ±12/13

So, the y-coordinate of point P can be either 12/13 or -12/13.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Yes, there is a continuous utility function that represents a rational preference relation when it is both continuous and monotone.

In a two-commodity framework, let's assume the two commodities are represented by X and Y. We can construct a diagram with the axes representing the quantities of X and Y. The indifference curves, which represent the bundles of X and Y that yield the same level of utility, can be plotted on this diagram.

Since the preference relation is continuous and monotone, we can draw the indifference curves as smooth, upward-sloping curves without any gaps or jumps. The upward slope reflects the monotonicity, indicating that more of either X or Y is preferred to less.

To represent this preference relation with a continuous utility function, we can assign utility levels to different bundles of X and Y. For example, we can assign a utility level of 1 to a specific bundle (X₁, Y₁), and higher utility levels to bundles that are preferred to (X₁, Y₁).

By assigning utility levels in a continuous manner across the diagram, we can construct a continuous utility function that represents the rational preference relation. This function will map each bundle of X and Y to a corresponding level of utility.

In conclusion, for a rational preference relation that is continuous and monotone in a two-commodity framework, there exists a continuous utility function that represents this preference relation. The utility function can be constructed by assigning utility levels to different bundles of commodities, and the resulting indifference curves on a diagram will be smooth, upward-sloping curves. This relationship between the utility function and the preference relation allows us to mathematically model and analyze the choices and preferences of individuals in economics.

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According to the given statement :

(1/4)c  + 3d= 45/2 when c = 6   & d = 7

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator as well as the denominator of a complex fraction.

Fractions can be used to represent decimals. Place your decimal number above its place value to convert it to a fraction. For instance, since the number six occupies the tenths place in the fraction 0.6, we must multiply it by 10 to get the comparable fraction, 6/10.

Evaluate  (1/4)c  + 3d

when c = 6   & d = 7

x  =  (1/4)c  + 3d

putting c = 6

& d = 7

=> x = (1/4) * 6  + 3*7

=> x = 3/2  + 21

=> x = (3 + 42)/2

=> x = 45/2

=> x = 22.5

=>  (1/4)c  + 3d= 22.5  when c = 6   & d = 7

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The data supports your claim that the mean time to finish undergraduate degrees is longer than the reported average at the 19 levels of significance. To determine if the data supports your claim, a hypothesis test can be conducted.

Using a significance level of 0.05 (19 levels), the null hypothesis (H0) assumes that the mean time is 4.5 years, while the alternative hypothesis (Ha) assumes that the meantime is greater than 4.5 years.

A one-sample t-test can be employed to compare the sample mean to the population mean. With a sample size of 49, a sample mean of 5.1, and a sample standard deviation of 1.2, the test statistic (t-value) is calculated as 3.497.

By comparing the calculated t-value to the critical t-value of 1.96 at a significance level of 0.05, it can be determined if the data supports your claim.

Since the calculated t-value (3.497) exceeds the critical t-value (1.96), the null hypothesis can be rejected. This indicates that the data supports your claim that the mean time to finish undergraduate degrees is longer than the reported average at the 19 levels of significance.

It should be noted that this conclusion is specific to the given sample and assumes that the sample is representative of the entire population. Further analysis and replication of the study may be necessary for a more comprehensive understanding.

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Answer: 19. 1 miles

Step-by-step explanation:

21.5 - 6.2 = 15.3

15.4 + 3.8 = 19.1

Answer:

Mr. Cooper rode 21.5 miles away from his house, then he rode back toward his house 6.2 miles.  Then he rode away from his house for another 3.8 miles.

21.5 miles - 6.2 miles =  15.3 miles

15.3 miles + 3.8 miles =  19.1 miles

Mr. Cooper is 19.1 miles away from his house.

Step-by-step explanation:

Based on the information provided, we can conduct a hypothesis test to determine if a majority of all students at Ohio University believe the academics are 'very strong'.

Let's set up the null and alternative hypotheses:

Null hypothesis (H₀): The proportion of all students who believe the academics are 'very strong' is equal to 50% or less.

Alternative hypothesis (H₁): The proportion of all students who believe the academics are 'very strong' is greater than 50%.

To test these hypotheses, we can use a one-sample proportion test. We will compare the sample proportion (55%) to the hypothesized proportion (50%) and assess if the difference is statistically significant.

Using appropriate statistical methods, such as calculating the test statistic and obtaining the p-value, we can evaluate the evidence against the null hypothesis. If the p-value is less than the chosen significance level (e.g., 0.05), we would reject the null hypothesis and conclude that a majority of all students at Ohio University believe the academics are 'very strong'. Otherwise, if the p-value is greater than the significance level, we would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim of a majority belief.

Please note that without the actual test results or the p-value, we cannot make a definitive conclusion in this particular case.

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Answer: #x^3

Step-by-step explanation:

        x^3

note: An algebraic expression doesn't have an equal sign (=)

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When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13  degrees

The distance between point a to point b = 5.3 feet

The length of the top side = 3 feet

Therefore, it will form a right triangle

Here we have to use trigonometric function

Here adjacent side and the hypotenuse of the triangle is given

The trigonometric function that suitable for the given conditions is

cos θ = Adjacent side / Hypotenuse

Substitute the values in the equation

cos θ = 3 / 5

θ = cos^-1(3 / 5)

θ = cos^-1(0.6)

θ = 53.13 degrees

Therefore, the value of θ is 53.13  degrees

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The number of integer values of n for which the value 4000 × (0.4)ⁿ is an integer is; 9

We are given the expression;

4000 × (0.4)ⁿ

This can also be expressed as;

4000 × (²/₅)ⁿ which can further be expressed in exponent form as;

(2⁵ × 5³) × (²/₅)ⁿ = 2⁽⁵ ⁺ ⁿ⁾ × 5⁽³ ⁻ ⁿ⁾

Since this expression is an integer, we need:

1) 5 + n ≥ 0 for which n ≥ -5

2) 3 - n ≥ 0 for which n ≤ 3

Taking the intersection gives;

-5 ≤ n ≤ 3

Thus;

Number of Integer Values = 3 - (-5) + 1 = 9

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For a bicycle with tires having a diameter of 26 inches, the radius and circumference of each tire can be calculated.

The radius of a circle is equal to half of its diameter. Therefore, to find the radius of each tire, we divide the diameter by 2.

Given that the diameter of the bicycle tires is 26 inches, the radius can be calculated as 26/2 = 13 inches.

The circumference of circle is the distance around its perimeter and can be calculated using the formula C = 2πr, where r is the radius.

Substituting the value of the radius (13 inches) into the formula, we get C = 2π(13) = 26π inches.

To round the answers to the nearest hundredth, we can use an approximation of π as 3.14.

Therefore, the radius of each tire is approximately 13 inches, and the circumference of each tire is approximately 26π inches or approximately 81.64 inches (rounded to the nearest hundredth).

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Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

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Given statement solution is :- To construct a grouped frequency distribution for the given test scores data, we will use the provided classes: 30-40, 40-50, and so on. Here's the grouped frequency distribution:

Classes Frequency

30-40 2

40-50 3

50-60 4

60-70 8

70-80 9

80-90 7

90-100 7

To construct a grouped frequency distribution for the given test scores data, we will use the provided classes: 30-40, 40-50, and so on. Here's the grouped frequency distribution:

Classes Frequency

30-40 2

40-50 3

50-60 4

60-70 8

70-80 9

80-90 7

90-100 7

To create this distribution, we count the number of scores that fall within each class range. For example, the class 30-40 has 2 scores falling within that range (35 and 39), and the class 40-50 has 3 scores (45, 48, and 48).

Note: It seems there is an inconsistency in the data provided. The class range 70-80 has 9 scores, but the frequencies given for the other classes do not match the actual number of scores falling within those ranges. Therefore, I have used the actual counts from the data to construct the grouped frequency distribution.

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Answer;

5. 22°

6. 74°

Step-by-step explanation:

5. Since rectangle JKLM has two equal diagonals that intersect each other, therefore JN = MN.

If JN = MN therefore:

m<NMJ = m<NJM

Thus:

3x + 38 = 7x - 2

Solve for x. Collect like terms

3x - 7x = -38 - 2

-4x = - 40

Divide both sides by -4

x = 10

✔️Find m<NMJ

m<NMJ = 7x - 2

Plug in the value of x

m<NMJ = 7(10) - 2 = 70 - 2

m<NMJ = 68°

✔️Find m<NML;

m<NML = 90 - 68° (Complimentary angles)

m<NML = 22°

6. Diagonal of a rhombus bisects teach vertex angle, this means that <U is divided into two equal parts. Therefore:

10x - 23 = 3x + 19

Solve for x. Collect like terms

10x - 3x = 23 + 19

7x = 42

Divide both sides by 7

x = 6

✔️Find m<RST:

m<SUT = m<RST (opposite angles of a rhombus are congruent)

Thus,

m<SUT = (10x - 23) + (3x + 19)

Plug in the value of x

m<SUT = (10(6) - 23) + (3(6) + 19)

= (60 - 23) + (18 + 19)

= 37 + 37

m<SUT = 74°

Also, m<RST = 74°

The total volume of gold used for both pendants is 15 + 5 = 20 cubic centimeters.

To find the amount of gold used to make the pendants, we first need to calculate the volume of each pendant.

The volume of the triangular prism is given by:

V = Bh

Where B is the base area (10 square centimeters) and h is the height (1.5 centimeters).

So, the volume of the triangular prism is:

V = 10 x 1.5 = 15 cubic centimeters

The volume of the triangular pyramid is given by:

V = (Bh) / 3

Where B is the base area (10 square centimeters) and h is the height (1.5 centimeters).

So, the volume of the triangular pyramid is:

V = (10 x 1.5) / 3 = 5 cubic centimeters

The total volume of gold used for both pendants is 15 + 5 = 20 cubic centimeters.

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Answer:

Distribution means to spread the product throughout the marketplace such that alarmed number of people can buy it.

Answer:

(18 + 36 + 27) = 9 x (2+4+3)

(88 + 66 + 22) = 22 x (4+3+1)

(36 + 96 + 12) = 12 x (3+8+1)

(126 + 28 + 14) = 14 x (9+2+1)

(54 + 81 + 27) = 27 x (2+3+1)

(16 + 28 + 48) = 4 x (4+7+12)

Step-by-step explanation:

The equations in the solution represent each expression as a multiple of a sum of whole numbers with no common factor.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

As per the given question, the required solution would be as:

(18 + 36 + 27) = 9 × (2+4+3)

This equation represents each expression as a multiple of a sum of whole numbers with no common factor.

Similarly further equations like as :

(88 + 66 + 22) = 22 × (4+3+1)

(36 + 96 + 12) = 12 × (3+8+1)

(126 + 28 + 14) = 14 × (9+2+1)

(54 + 81 + 27) = 27 × (2+3+1)

(16 + 28 + 48) = 4 × (4+7+12)

Thus, the above equations represent each expression as a multiple of a sum of whole numbers with no common factor.

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Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

To find the ordered pair solution for this system of equations, we need to find the value of x that satisfies both equations and then find the corresponding value of f(x) using either of the equations. the ordered pair solution is: (2, 1)

Setting the two functions equal to each other, we have:

\(x^2 + 4 = 4x\)

Rearranging, we get:

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

This quadratic equation can be factored as:

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

Therefore, the only solution is \(x = 2.\)

Substituting x = 2 into either of the original equations, we have:

\(f(2) = 2^2 + 4 = 8\)

Therefore,  the ordered pair solution is: \((2, 1)\)

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The cash flow to stockholders for 1998 is -$4 million.

To calculate the cash flow to stockholders for 1998, follow these steps:

Identify the dividends paid: Brandy's Candies paid $23 million in dividends during 1998.

Determine the net common stock repurchases: Brandy's Candies made net common stock repurchases of $27 million during 1998.

Subtract the net common stock repurchases from the dividends paid: $23 million - $27 million = -$4 million.

The resulting cash flow to stockholders for 1998 is -$4 million, indicating a net outflow of cash from stockholders.

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Answer:

$12

Step-by-step explanation:

They each get $6

6 + 6 = 12

Hope this helps!

The product of the expression is 2x⁶ + 23x³ + 63

First, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.

These algebraic expressions are also made up of mathematical operations, such as;

From the information given, we have that;

2x3 +9 and x3 +7?

Then,

(2x³ + 9)(x³ + 7)

expand the bracket

2x⁶ + 14x³ + 9x³ + 63

add like terms

2x⁶ + 23x³ + 63

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110 is the initial fee.

intial fee is the y-intercept.

The equation \(\(3x^2 + 12x + 4y^2 + 8y^4 = 0\)\) does not represent any of the given options: a hyperbola with a new origin (2, -1), an ellipse with a new origin (2,-1), a hyperbola with a new origin (2, 1), or an ellipse with a new origin (-2,1).

The given equation can be rewritten as\(\(3(x^2 + 4x) + 4(y^2 + 2y^4) = 0\).\) By completing the square, we can rewrite it as\(\(3(x^2 + 4x + 4) + 4(y^2 + 2y^4 + 1) = 12 + 4\).\)Simplifying further, we get\(\(3(x + 2)^2 + 4(y^2 + 2y^4 + 1) = 16\).\)

This equation represents an ellipse with its center at the point (-2, 0) in the x-direction and (0, 0) in the y-direction. The term \(x + 2^2\)\)indicates a horizontal shift of the ellipse to the left by 2 units. The term\(\(y^2 + 2y^4 + 1\)\)represents the vertical stretching and compression of the ellipse. Since the coefficient of \(\(y^2\)\)is positive, the ellipse is elongated vertically.

Therefore, the equation represents an ellipse with a new origin at (-2, 0).

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The amount of the the initial investment (principal) is $4,188( nearest dollar)

Compound interest is calculated on the principal amount and the accumulated interest of previous periods.

Compound interest is given as A = P(1+r/100)^t

where A is the amount over a period of time

P is the Principal amount before the interest and t is the time and r is the interest rate

Therefore 5485.85= P( 1+4.61/100)⁶

5485.85= P(1+0.0461)⁶

5485.85= P (1.0461)⁶

5485.85= 1.31P

divide both sides 1.31

P = 5485.85/1.31

P= $4188( nearest dollars)

therefore the principal amount is $4188

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Answer:

Circumference = 62.8

Step-by-step explanation:

The equation for discovering a circle's circumference is simple:

-------------------------------------------------------

C = 2πr

C is the circumference (how long is the circle around)

R is the radius (half of the width of the circle)

--------------------------------------------------------

So, instead of giving us the radius, they gave us the diameter. (the full width of the circle) So, we divide that by 2 to get the radius.

20/2=10

Now, time to fill in the equation.

C = 2π10

C = 20π

C = 62.8

*They told us to use 3.14 for pi.