Do couples get engaged or not? If they are engaged, how long did they date before becoming engaged? A poll of 1000 couples conducted by Bruskin and Goldring Research for Korbel Champagne Cellars gave Time Never Engaged Number of Couples 200 the following information: Time Number of Couples Never Engaged 200 Less than 1 year 240 1 to 2 years 210 More than 2 years 350 What is the sample space in this problem?

Yes, the table contains the solution of the system of equations, and the solution is (7, 6).

Here we have a table that defines a system of equations of the form:

ya = f(x)

yb = f(x)

And a solution of that system is a point of the form:

yb = f(x) = ya

So we wan to find a pair such that for the same value of x, the values of ya and yb are the same ones.

We can see that when x = 6 that happens, then yes, the table has the solution to the system of equations, and the solutions is (6, 7)

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False. The population of Los Angeles in 2011 was approximately 9.77 times the population of Oakland, not 10 times. However, it is worth noting that population numbers can fluctuate over time and these figures may have changed since 2011.

Additionally, comparing the population of cities in different states or countries can be difficult as they may have different population growth rates, economic factors, and cultural influences.
In 2011, the population of Los Angeles, California was approximately 3.81 x 10^6, and the population of Oakland, California was approximately 390,000. To determine whether the statement is true or false, we need to compare these two populations.
3.81 x 10^6 (Los Angeles population) divided by 390,000 (Oakland population) is approximately 9.77. This shows that the population of Los Angeles was about 9.77 times the population of Oakland in 2011.
Since the statement claims that the population of Los Angeles was approximately 10 times the population of Oakland, it can be considered true, given that 9.77 is close to 10. So, the answer is true.

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Answer:

Option (4)

Step-by-step explanation:

Coplanar points-

If two or more points are in the same plane, points are called to be coplanar points. Three points in space are always coplanar.

Collinear points-

If two or more points are on a straight line, points are collinear.

Two points are always collinear.

From the diagram attached,

Points R,T,Q and S are neither coplanar nor collinear.

Therefore, Option (4) will be the answer.

Answer:

neither collinear nor coplanar

Step-by-step explanation:

Solution,

Principal=£ 500

Time=2 years

Interest=£40

Rate=?

Now,

R=I*100/P*T

= 40*100/500*2

=4000/1000

=4%

Hope it helps

Good luck on your assignment

Answer:

\(4\%\)

Step-by-step explanation:

\(p = 500 \\ r = x \\ t = 2\)

\(simple \ \: \: \: = \frac{prt}{100} \\ interest \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 40= \frac{500 \times x \times 2}{100} \\ \: \: \: \: \: \: \: 40 \: \: \: \: \: \: \: \: \: = \frac{1000x}{100} \\ \frac{40 \times 100}{1000} = x \\ x = 4\)

Answer:The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Add 10 10 to both sides of the equation. Using the slope-intercept form, the y-intercept is 10 .

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

4x-12+3x=5+7x-17

7x-12=5+7x-17

so no

Explanation:

On the left side we have 4x+3x turn into 7x. The -12 stays as it is because it has nothing to pair with. The left side simplifies to 7x-12

The right side simplifies to 7x-12 as well because the like terms 5 and -17 combine to 5+(-17) = 5-17 = -12.

The original equation 4x-12+3x = 5+7x-17 has both sides simplify to 7x-12=7x-12. Both sides are identical which makes the original equation always true. No matter what number you replace x with, both sides will be the same result.

For instance, let's try x = 0

4x - 12 + 3x = 5 + 7x - 17

4(0) - 12 + 3(0) = 5 + 7(0) - 17

0 - 12 + 0 = 5 + 0 - 17

-12 = -12

The measure of the reflected angle is equal to the measure of the original angle

An image or figure reflected are mirror images of each other. While the coordinate points of the vertices of a figure are affected by reflection, the angles remain the same.

Hence if an angle is reflected across the y−axis, the measure of the reflected angle is equal to the measure of the original angle

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Only statements (a) and (e) must be true.

Let's start by tracking the number of candies each person has after each round:

* Round 1: Lizzy has $x$ candies, Megan has $x$ candies, Oscar has $x$ candies, and Patrick has $0$ candies.

* Round 2: Lizzy has $0$ candies, Megan has $2x$ candies, Oscar has $x$ candies, and Patrick has $0$ candies.

* Round 3: Lizzy has $0$ candies, Megan has $0$ candies, Oscar has $3x$ candies, and Patrick has $x$ candies.

As you can see, the number of candies Patrick has is always a multiple of 2. This is because in each round, the total number of candies is multiplied by 2. Therefore, statement (a) must be true.

Now, let's consider statement (e). If $x$ is even, then the number of candies Patrick has in the end will be divisible by 4. However, if $x$ is odd, then the number of candies Patrick has in the end will be 1 more than a multiple of 4, and therefore not divisible by 4. Therefore, statement (e) must be true.

The remaining statements (b), (c), and (d) are not necessarily true. For example, if $x$ is a multiple of 3, then statement (c) will be true, but if $x$ is not a multiple of 3, then statement (c) will not be true. Similarly, statements (b) and (d) are also not necessarily true.

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All the trigonometric values for sin θ, cos θ and tan θ are valued below. Each trigonometric value is mentioned.

sin θ has boundaries from 0 to 1.

Since the sine function is a periodic function, we can represent sin 1° as, sin 1 degree = sin(1° + n × 360°), n ∈ Z. ⇒ sin 1° = sin 361° = sin 721°, and so on.

sin \(-\pi /2\)  = -1

sin  \(-\pi /3\) = -0.87

sin \(-\pi /6\) = -0.5

sin 0 = 0

sin \(\pi /6\) = 0.5

sin \(\pi /3\) = 0.87

sin \(\pi /2\) = 1

sin \(2\pi /3\) = √3/2

sin \(5\pi /6\) = 1/2

sin \(\pi\) = 1

sin \(7\pi /6\) = -0.5

sin \(4\pi /3\) = -0.87

sin \(3\pi /2\) = -1

sin \(5\pi /3\)  = -0.87

sin \(11\pi /6\) = -0.5

sin 2\(\pi\) = 0

Similarly cos θ has boundaries.

The complementary angle equals the given angle subtracted from a right angle, 90°. For instance, if the angle is 30°, then its complement is 60°. Generally, for any angle θ, cos θ = sin (90° – θ).

cos \(-\pi /2\)  = 0

cos   \(-\pi /3\)  = 0.5

cos \(-\pi /6\)  = 0.87

cos 0 = 1

cos \(\pi /6\) = 0.7

cos \(\pi /3\) = 0.5

cos  \(\pi /2\) = 0

cos  \(2\pi /3\)  = -0.5

cos \(5\pi /6\)  = -0.87

cos \(\pi\)  = -1

cos  \(7\pi /6\) = -0.87

cos  \(4\pi /3\) = -0.5

cos  \(3\pi /2\)  = 0

cos \(5\pi /3\)  = 0.5

cos \(11\pi /6\)  = 0.87

cos2\(\pi\)  = 1

But tan θ has no boundaries.

The tangent function 'or' Tan Theta is one of the three most common trigonometric functions, along with sine and cosine. The tangent function in a right-angle triangle is defined as the ratio of the opposite side to the adjacent side.

tan  \(-\pi /2\) = undefined

tan   \(-\pi /3\)= -0.8

tan \(-\pi /6\)= -1.73

tan 0 = 0

tan \(\pi /6\)= \(\frac{1}{\sqrt{3} }\)

tan \(\pi /3\) = \(\sqrt{3}\)

tan  \(\pi /2\) = undefined

tan   \(2\pi /3\) =-3

tan \(5\pi /6\)  = -0.5774

tan \(\pi\)  = undefined

tan  \(7\pi /6\) = -1.73

tan  \(4\pi /3\) = 1.73

tan  \(3\pi /2\) = undefined

tan \(5\pi /3\) = -1.73

tan  \(11\pi /6\) = -0.58

tan2\(\pi\)  = 0

Hence, all the values mentioned in the table, were written above.

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Answer: C

Step-by-step explanation:

It the only one that includes both.

Answer:

the answer is 401/99

brainliest plzz

Answer:

The commission rate is 14%.

Step-by-step explanation:

1% of 2100 is $21. $294 ÷ $21 = 14. Therefore, the commission rate is 14%.

Hope this helps!

The probability values are calculated and listed below

They are both black

Here, we have

Black = 3

Yellow = 5

Sice the balls are not replaced, we have

P(Both black) = 3/8 * 2/7

P(Both black) = 3/28

They are both yellow

Sice the balls are not replaced, we have

P(Both Yellow) = 5/8 * 4/7

P(Both Yellow) = 5/14

The first is yellow and the second is black

Sice the balls are not replaced, we have

P(Yellow and black) = 5/8 * 2/7

P(Both Yellow) = 5/28

One is yellow the other is black

Sice the balls are not replaced, we have

P(One Yellow and One black) = 5/8 * 2/7 * 2

P(One Yellow and One black) = 5/14

They are of the same colour​

Here, we have

P(Same) = 3/28 + 5/14

P(Same) = 13/28

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The production manager's claim that no more than 4,000 insulating washers are defective per day is likely to be true, based on the sample of 200 washers.

Proportion refers to the relationship between two quantities or numbers, indicating how they are related to each other in size or amount.

To determine whether the production manager's claim is likely to be true, we can use hypothesis testing. We can formulate the following hypotheses:

Null hypothesis (H0): The true proportion of defective insulating washers is equal to or less than 0.02 (4,000/225,000).

Alternative hypothesis (Ha): The true proportion of defective insulating washers is greater than 0.02.

We can use a significance level of 0.05, which means we are willing to accept a 5% chance of rejecting the null hypothesis when it is actually true.

To test these hypotheses, we need to calculate the test statistic and p-value. We can use the normal approximation to the binomial distribution, since the sample size (200) is large enough and the proportion of defective washers is relatively small (0.02).

The test statistic is calculated as:

z = (0.02 - 0.02) / √(0.02×(1-0.02)/200) = 0

The p-value is the probability of getting a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. Since we are testing the alternative hypothesis that the true proportion of defectives is greater than 0.02, we need to calculate the right-tailed p-value. We can use a standard normal distribution to calculate the p-value:

p-value = P(Z > z) = P(Z > 0) = 0.5

We are unable to reject the null hypothesis since the p-value is higher than the significance level of 0.05. This means we do not have sufficient evidence to conclude that the true proportion of defective insulating washers is greater than 0.02.

Therefore, the production manager's claim that no more than 4,000 insulating washers are defective per day is likely to be true, based on the sample of 200 washers.

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Answer:

11

Step-by-step explanation:

You would add 5 + 4.2 + 5 - 2.2 - 1 in a calculator and it would come out to be 11.

Answer:

k > 13 OR K < 4

Step-by-step explanation:

-1 plus 14 is 13

19 minus 15 is 4

Since the limit is less than 1, by the ratio test, the series converges absolutely.

To determine the convergence or divergence of the series, the ratio test is applied. The ratio test involves taking the limit of the absolute value of the ratio of the (k+1)-th term and the k-th term as k approaches infinity. If this limit is less than 1, then the series converges. If the limit is greater than 1 or does not exist, then the series diverges.

In this case, the ratio test is applied to the series ∑(k=1 to infinity) ke^(-5k). After applying the ratio test and simplifying, the limit is found to be 0, which is less than 1. Therefore, the series converges. This means that the sum of the series exists and is a finite value.

Applying the ratio test:

lim k→∞ (k+1)e−5(k+1) / ke−5k

= lim k→∞ (k+1) / e5 * k

As k approaches infinity, the denominator (e5k) grows much faster than the numerator (k+1), so the limit is 0.

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Answer: 34.6 cm

Step-by-step explanation:

delta math

The radius of the hemisphere with a volume 86784cm³ as described is; 27.5cm

It follows from quantity measurements of solid shapes that the Volume of a sphere is given by the formula;

On this note, upon substitution;

86784 = (4/3) (3.14r³)

Hence, r³ = (86784 ×3)/(4 ×3.14)

r³ = 20728.7

r = ³√2.728.7

r = 27.5cm

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Let's break down the expression for Tony's combined total earnings step by step.

First, we consider Tony's earnings as a tutor. He earns $11 per hour as a tutor, so the amount he earns from tutoring is given by the product of his hourly rate ($11) and the number of hours he worked as a tutor (t). This can be represented as $11t.

Next, we consider Tony's earnings as a waiter. He earns $13 per hour as a waiter, so the amount he earns from waiting tables is given by the product of his hourly rate ($13) and the number of hours he worked as a waiter. Since Tony worked a total of 106 hours this month and spent t hours as a tutor, he must have worked (106 - t) hours as a waiter. This can be represented as $13(106 - t).

To calculate Tony's combined total earnings for the month, we add the amount he earned as a tutor ($11t) to the amount he earned as a waiter ($13(106 - t)). This yields the expression:

Earnings = $11t + $13(106 - t)

This expression represents the total dollar amount Tony earned this month, considering the number of hours he worked as a tutor (t) and waiter (106 - t).

a. Design B is 90° anti- clockwise rotation to Design A.

b.  Design E transformation to Design G as reflection.

c. Design E and Design G are the two designs shows a translation.

d. Design E is the reflection of the Design A.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

a. Design A Transformation to Design B.

Design A is 90° anti- clockwise rotated about the origin to get the Design B.

b.  Design E transformation to Design G.

Design G is the translation of Design E about the parallel axis such that the mirror image is design G is formed.

c. two designs shows a translation:

Design E and Design G are the two designs shows a translation.

d. From Design A, the design which is a reflection and a 90° clockwise rotation about the origin.

Design F is the 90° clockwise rotation about the origin of  Design A

Design E is the reflection of the Design A.

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An angle is fefined as the point where two lines meet. The measure of the segment FB is 21 units.

This theorem equates their relative lengths  of the triangle to the relative lengths of the other two sides of the triangle.

From the given figure, the line CF bisects the angle DFB, this shows that the line segment DF is equal to FB.

Given the following

DF = 4x + 9

FB = 6x + 3

Equate

DF = FB

4x + 9 = 6x + 3

4x - 6x = 3 - 9

-2x = -6

x = 3

Determine the length of FB

FB = 6x + 3

FB = 6(3) + 3

FB = 21 units

Hence the length of FB from the given figure is 21units.

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The answer is B) y= 7/4x

This is because when you graph it you would go up 7 and over 4- you just had to find the rise over run. I also just made sure it was correct on edmentum!

Caroline is planting her first 7 flowers in 4 minutes and then past 12 minutes, she plants 21 different flowers. That suggests that she is planting the flowers following the given equation  y=(7/4)x.

The dependent variable is defined as the variable whose evaluation of the independent variable determines the quality of the dependent variable. That is, it is consistently claimed that the word variable's estimate depends on the mathematical condition's free variable.

Let Caroline plant y flowers in x minutes.

By using the unitary method we can observe that

4 minutes  → 7 flowers

⇒ 1 minute → 7/4 flowers

⇒ x minutes → (7/4)x flowers

Hence, Caroline is planting y=(7/4)x flowers in x minutes. And y=(7/4)x this equation represents the variation perfectly.

NOTE: We took the number of flowers planted as y because it is a dependent variable. The number of flowers depends on the time elapsed.

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Answer:

Angle C > Angle A > Angle B

Step-by-step explanation:

Given the side lengths, we want to know how big the angles are

Mathematically, the bigger the angle, the bigger the side length that faces it

AB is the biggest side length and the angle that faces it is the angle C

BC faces the angle A

AC faces the angle B

so we have it that;

Angle C > Angle A > Angle B

The image of point A(3, 4) under the dilation with a scale factor of 7 is D7(A) = (21, 28).

To find the image of point A(3, 4) under the dilation with a scale factor of 7, we multiply the coordinates of point A by the scale factor.

The formula for dilation with center (0, 0) is given by (x', y') = (k * x, k * y), where (x, y) represents the original point and (x', y') represents the image point after dilation, and k is the scale factor.

Applying the formula, we have:

\(x' = 7 * 3 = 21\)

\(y' = 7 * 4 = 28\)

Therefore, the image of point A(3, 4) under the dilation with a scale factor of 7 is D7(A) = (21, 28).

The coordinates of the image point are (21, 28). This means that the image point is obtained by stretching the original point A(3, 4) by a factor of 7 from the origin (0, 0).

Note that in a dilation, the distances from the center of dilation to the original point and its image are proportional to the scale factor. In this case, the distance from (0, 0) to A(3, 4) is multiplied by 7 to obtain the distance from (0, 0) to D7(A) (21, 28).

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(4x+10y=-140\implies 10y=-4x-140\implies y=\cfrac{-4x-140}{10} \\\\\\ y=\cfrac{-4x}{10}-\cfrac{140}{10}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{5}}x-14\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-2}\implies {\Large \begin{array}{llll} \cfrac{5}{2} \end{array}}}}\)

The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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The brand that will have the lower lifetime cost is that the Brand U will be $976.92 cheaper than Brand V. The correct option is B.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Cost of operating Brand U,

Cost of Brand U = $2,250

Number of days in 24 years = (6×366) + (18×365) = 8766

Operational cost = 8766 × $0.16 = $1,402.56

Total cost for 24 years = $3,652.56

Cost of operating Brand V,

Cost of Brand U = 3 × $725 = $2,175

Number of days in 24 years = (6×366) + (18×365) = 8766

Operational cost = 8766 × $0.28 = $2,454.48

Total cost for 24 years = $4,629.48

Further, the difference between the cost of operation and buying will be,

Difference

= Total cost for 24 years for Brand V - Total cost for 24 years for Brand U

= $4,629.48 - $3,652.56

= $976.92

Hence, the brand that will have the lower lifetime cost is that the Brand U will be $976.92 cheaper than Brand V.

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We are given the following numbers

We are asked to arrange these numbers from least to greatest.

As you can see, the numbers are in different forms (decimal, fraction)

So, first we need to convert them into a single form then we can compare them

Let us convert all the numbers into decimals

So the order from least to greatest is

6.67, 7.111, 7.116, 7.15

Now write the numbers in their original form

Answer:

81.64

Step-by-step explanation:

2(3.14)=6.28

6.28*13=81.64

Plug r into the equation provided...

c = 2(3.14)(13)

c = 81.64cm