Solve the system of linear equations. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.)
2x1 + x2 − 2x3 = 4
4x1 + 2x3 = 10
−4x1 + 5x2 − 17x3 = −15

Answer:

d) Clothing prices decline because manufacturers shift to production in countries with lower wages.

Step-by-step explanation:

Demand is the quantity of goods or services consumers are able and willing and able to buy at a given price and at a particular time.

Movement along the demand curve also known as change in quantity demanded is an increase or decrease in the quantity demanded of goods or services due to change in the price of the good or service itself.

It is important to note that the only factor causing movement along the demand curve is change in the price of the product.

To maximize profit, the art club should find the combination of small and large greeting cards that satisfies the given constraints and generates the highest total profit. The optimal solution will provide the number of boxes of small and large cards that should be bought to maximize profit while staying within the given constraints.

To maximize profit, the art club should find the combination of small and large greeting cards that satisfies the given constraints and generates the highest total profit. Let's assume the art club buys x boxes of small cards and y boxes of large cards. The constraints are:

The objective is to maximize profit, given by:

52.20x + 85y

We need to solve this linear programming problem to find the values of x and y that maximize profit. The optimal solution will provide the number of boxes of small and large cards that should be bought to maximize profit while staying within the given constraints.

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Answer:

  a. a║b

  b. c║d

  c. AB║CD

  d. none

Step-by-step explanation:

a. If distinct lines in a plane are perpendicular to the same line, then they are parallel.

__

b. If same-side interior angles are supplementary where a transversal crosses two lines in the same plane, then those two lines are parallel.

__

c. If alternate interior angles are congruent where a transversal crosses two lines in the same plane, then those two lines are parallel. (Here, the measure of the upper angle at A is 180°-78°-67° = 35°, congruent with the lower angle at C. Those two angles are alternate interior angles with respect to lines AB and CD and transversal AC.)

__

d. The marked angles are unrelated to each other, so define nothing about the relationship between lines a and b, or between lines c and d. However, they do mean that if a║b, then c║d.

Parallelism between lines can be determined by applying geometrical principles or postulates via if-then statements, such as the Corresponding Angles Postulate, Alternate Interior Angles Theorem, or the Converse of the Same-Side Interior Angles Theorem, establishing congruity or supplementarity in the context of lines intersected by a transversal.

To determine which lines are parallel, you must look for certain geometrical properties or postulates. If-then statements or direct applications of properties such as the corresponding angles postulate, alternate interior angles theorem, or the converse of the same-side interior angles theorem can be used to identify parallel lines.

If two lines are cut by a transversal and the corresponding angles are equal, then the lines must be parallel (Corresponding Angles Postulate). If the alternate interior angles are congruent when two lines are cut by a transversal, then the two lines are parallel (Alternate Interior Angles Theorem). If two lines are cut by a transversal and the same-side interior angles are supplementary, then the lines are parallel (Converse of the Same-Side Interior Angles Theorem). Each of these statements is an application of 'if-then' logic.

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Answer:

f(t)/g(t) represents the average cost of producing a unit of commodity between the time frame 0-t.

Step-by-step explanation:

f(t) is cost in dollar while g(t) is in unit.  f(t)/g(t) will be cost per unit.

In other words  f(t)/g(t) is the total cost spent in time t divided by the amount of commodity produced in units produced in time t.

Answer:

Comb's share will be =  $12,180

Stratton's share will be = $31,320

Step-by-step explanation:

Given:

Comb's investment in the partnership = $140,000

Stratton's investment in the partnership = $360,000

The net income is shared in proportions of their investment.

Net income last year  = $43,500

To find the share of each partner of the net income.

Solution:

Ratio of the investments of Comb to Stratton = [tex]\frac{140,000}{360,000}[/tex][tex]= \frac{14}{36}=\frac{7}{18}[/tex] (Simplest ratio)

Thus, the investments must be shared in the ratio of 7 : 18

Let Comb's share in dollars be = [tex]7x[/tex]

Then, Stratton's share in dollars = [tex]18x[/tex]

Total net income can be given as = [tex]7x+18x=25x[/tex]

Net income = $43,500

So, we have:

[tex]25x=43,500[/tex]

Dividing both sides by 25.

[tex]\frac{25x}{25}=\frac{43,500}{25}[/tex]

∴ [tex]x=1740[/tex]

So, Comb's share will be = [tex]7\times 1740 = \$12,180[/tex]

Stratton's share will be = [tex]18\times 1740 = \$31,320[/tex]

Step-by-step explanation:

Circumference of a circle = πD, where D is the diameter.

Diameter of circle 1 = 1.125

Circumference of circle 1 = π x 1.125

Diameter of circle 1 = 2.25

Circumference of circle 1 = π x 2.25

[tex]\texttt{Ratio of circumferences = }\frac{\pi \times 1.125}{\pi \times 2.25}\\\\\texttt{Ratio of circumferences = }\frac{1}{2}[/tex]

Circumference of circle 1 : Circumference of circle 2 = 1 : 2

Answer:

1:1

Step-by-step explanation:

Answer:

Option C) -cosu is correct

Therefore the simplified expression is [tex]cos(u+\pi)=-cosu[/tex]

Step-by-step explanation:

Given expression is [tex]cos(u+\pi)[/tex]

To find the value of the given expression :

By using the formula [tex]cos(A+B)=cosAcosB-sinAsinB[/tex]

Substitute A=u and [tex]B=\pi[/tex] in the above formula we get

[tex]cos(u+\pi)=cosucos\pi-sinusin\pi[/tex]

[tex]=cosu(-1)-sinu(0)[/tex]  ( here [tex]cos\pi=-1[/tex] and [tex]sin\pi=0[/tex] )

[tex]=-cosu-0[/tex]

[tex]=-cosu[/tex]

[tex]cos(u+\pi)=-cosu[/tex]

Therefore option C) -cosu is correct

Therefore the simplified expression is [tex]cos(u+\pi)=-cosu[/tex]

Answer:

Option B) False            

Step-by-step explanation:

We define the following terms:

Range:

It is the difference between the minimum and maximum value of data.

It is effected by presence of outliers.

Interquartile range:

It is the difference between the third quartile and the first quartile of data.

Variance:

[tex]\text{Variance} = \displaystyle\frac{\sum (x_i -\bar{x})^2}{n}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.

It is a measure of spread of the data. It is effected by presence of outliers as they increase the variation in the data.

Thus, the given statement is false.

Answer:

[tex]\displaystyle y=- \frac{1}{2}x-3[/tex]

(first option)

Step-by-step explanation:

Linear Functions

They can be defined by knowing two points on them or a point and the slope of the line. The portion "a" of the piecewise function must have these conditions, only by looking at the graph

* It must be decreasing, the slope must be negative

* It must be defined for x<-2, because for x>-2, the function is defined by another piece.

* It must pass through the point (-2,-2)

Options 2 and 4 are immediately discarded, since x>2

Testing it (-2,-2) belongs to

[tex]\displaystyle y=- \frac{1}{2}x-3[/tex]

[tex]\displaystyle y=- \frac{1}{2}(-2)-3=1-3=-2[/tex]

The point (-2,-2) belongs to this function, so it's the correct choice. Let's verify the last function

[tex]\displaystyle y=- \frac{1}{2}x-6[/tex]

[tex]\displaystyle y=- \frac{1}{2}(-2)-6=-5[/tex]

This is not the point we are testing, so the portion of the graph labeled "a" is

[tex]\boxed{\displaystyle y=- \frac{1}{2}x-3}[/tex]

(First option)

Answer:

Option 1) 10 sides

Step-by-step explanation:

We are given a regular polygon. The sum of interior angles measure upto 1440 degrees.

Since it is a regular polygon, it satisfies the following properties:

Let the regular polygon have n sides.

Then, the sum of interior angle is given by:

[tex](n-2)\times 180^\circ[/tex]

Putting the values, we get,

[tex](n-2)\times 180 = 1440\\\\n-2 = \dfrac{1440}{180}\\\\n-2 = 8\\n = 8 + 2\\n =10[/tex]

Thus, there are 10 sides. The regular polygon is a regular decagon.

Answer:
Decagon

Step-by-step explanation:

Found other sources saying the same thing

Answer:

[tex] P( F \cap K) =0.7+0.85 -1=0.55[/tex]

Step-by-step explanation:

For this case we can define some notation first:

F ="One person is fool "

K="One person is knave"

And we have the following probabilities given:

[tex] P(F) = 0.7 , P(K) =0.85[/tex]

And from the given condition that everyone is fool or knave we can deduce that:

[tex] P(K UF) =1[/tex]

Solution to the problem

For this case we want to find this probability:

[tex] P( F \cap K)[/tex]

And we can use the total probability rule given by:

[tex] P(K \cup F) = P(F) +P(K) -P(K \cap F)[/tex]

And replacing the values that we have we got:

[tex] 1 = 0.7+0.85 -P(K \cap F)[/tex]

And if we solve for [tex] P( F \cap K)[/tex] we got:

[tex] P( F \cap K) =0.7+0.85 -1=0.55[/tex]

Answer: 10√17

Step-by-step explanation:

The movement of the boat takes the shape of a trapezium as shown in the attached photo.

The distance of the boat from its starting point is represented by x kilometers.

To determine the distance, x, we would apply Pythagoras theorem on the right angle triangle ABC formed. It is expressed as

Hypotenuse² = opposite side² + adjacent side². It becomes

x² = 40² + 10² = 1600 + 100

x² = 1700

x = √1700 = √100 × √17

x = 10√17

Answer:

The System of equation to determine the number of chickens purchased is [tex]\left \{ {{x+y =12} \atop {3.75x+2.5y =35}} \right.[/tex].

Alyssa purchased 4 Americana chickens and 8  Delaware chickens.

Alyssa will expect to make $23.33 at the end of first week with her 12 chickens.

Step-by-step explanation:

Given:

Let the number of Americana chickens be 'x'.

Let the number of Delaware chickens be 'y'.

Number of chickens purchased = 12

Now we know that;

Number of chickens purchased is equal to sum of the number of Americana chickens and the number of Delaware chickens.

framing in equation form we get;

[tex]x+y =12 \ \ \ \ equation\ 1[/tex]

Also Given:

Cost of Americana chickens = $3.75

Cost of Delaware chickens = $2.50

Total amount spent = $35

Now we know that;

Total amount spent is equal to sum of the number of Americana chickens multiplied by Cost of Americana chickens and the number of Delaware chickens multiplied Cost of Delaware chickens.

framing in equation form we get;

[tex]3.75x+2.5y =35 \ \ \ \ equation\ 2[/tex]

Hence The System of equation to determine the number of chickens purchased is [tex]\left \{ {{x+y =12} \atop {3.75x+2.5y =35}} \right.[/tex].

Now to find the number of each type of chickens she purchased we will solve the above equation.

First we will multiply equation 1 with 2.5 we get;

[tex]2.5(x+y)=12\times2.5\\\\2.5x.+2.5y = 30 \ \ \ \ equation \ 3[/tex]

Now we will subtract equation 3 from equation 2 we get;

[tex]3.75x+2.5y-(2.5x+2.5y)=35-30\\\\3.75x+2.5y-2.5x-2.5y=5\\\\1.25x=5[/tex]

Now Dividing both side by 1.25 we get;

[tex]\frac{1.25x}{1.25}=\frac{5}{1.25}\\\\x= 4[/tex]

Now we will substitute the value of 'x' in equation 1 we get;

[tex]x+y=12\\\\4+y=12\\\\y=12-4 = 8[/tex]

Hence Alyssa purchased 4 Americana chickens and 8  Delaware chickens.

Now Given:

Number of eggs laid by American chicken per day = 2 eggs

Number of eggs laid by Delaware chicken per day = 1 egg

Cost of 12 eggs = $2.5

Total number of days = 7

Now first we will find the Total number of eggs laid by both the chickens.

Total number of eggs laid per day = [tex]4\times2 + 8\times 1= 8 +8 =16\ eggs[/tex]

Total number of eggs laid in week = [tex]16\times7= 112[/tex] eggs

12 eggs = $2.5

112 eggs = Cost of 112 eggs.

By cross multiplication we get;

Cost of 112 eggs = [tex]\frac{2.5 \times 112}{12} = \$23.33[/tex]

Hence Alyssa will expect to make $23.33 at the end of first week with her 12 chickens.

The system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased are as follows;

A + D = 12

3.75A + 2.50D = 35

Alyssa purchased 4 Americans chicken and 8 Delaware chickens.

She is expected to take in $22.5 at the end of the first week with her 12 chickens.

number of Americana chickens  = A

number of Delaware chickens = D

Therefore,

A + D = 12

3.75A + 2.50D = 35

A  = 12 - D

3.75(12 - D) + 2.50D = 35

45 - 3.75D + 2.50D = 35

-1.25D  = -10

D = -10 / -1.25

D = 8

A = 12 - 8 = 4

A = 4

Therefore, Alyssa bought 4 Americans chickens and 8 Delaware chickens.

Each American chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day.

She only sells the egg in full dozen for $2.50.

The amount of money she expects to take in at the end of the first week with her 12 chickens is calculated as follows.

1 week = 7 days

Number of American chicken eggs(first week) = 7 × 4 × 2 = 56 eggs

Number of Delaware chicken eggs(first week) = 1 × 7  × 8 = 56 eggs

Total eggs =  56 + 56 = 112 eggs.

She can only sell full dozen of eggs. Therefore,

112 / 12 = 9.333

1 dozen = $2.50

9 dozen =

cross multiply

Amount made from the eggs = 9 × 2.50  = $22.5

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Answer:

a) [tex] p(A) = \frac{2}{5}[/tex]

b) [tex] p(B) =\frac{3}{5}[/tex]

c) [tex] p(A') = 1-p(A) = 1-\frac{2}{5} = \frac{3}{5}[/tex]

d) The probability for intersection on this case is 0 because the sets A and B not have any element in common, so then we have this

[tex] P(AUB) = P(A) +P(B) -0 = \frac{2}{5} +\frac{3}{5} =1[/tex]

e) The intersection for this case is the empty set between the sets A and B so for this reason the probability is 0

P(A∩B)=0

Step-by-step explanation:

For this case we have the following sample space:

[tex] S= [a,b,c,d,e][/tex]

And we have defined the following events:

[tex] A= [a,b][/tex]

[tex] B= [c,d,e][/tex]

For this case we can find the probabilities for each event using the following definition of probability:

[tex] p =\frac{Possible cases}{total cases}[/tex]

The total cases for this case are 5 , the possible cass for A are and for B are 3.

Usign this we have this:

[tex] p(A) = \frac{2}{5}, p(B) = \frac{3}{5}[/tex]

Then we can find the following probabilites:

a) P(A)

[tex] p(A) = \frac{2}{5}[/tex]

b) P(B)

[tex] p(B) =\frac{3}{5}[/tex]

c) P(A')

Using the complement rule we have this:

[tex] p(A') = 1-p(A) = 1-\frac{2}{5} = \frac{3}{5}[/tex]

d) P(A∪B)

For this case we can use the total probability rule and we got:

[tex] P(AUB) = P(A) +P(B) -P(A and B)[/tex]

The probability for intersection on this case is 0 because the sets A and B not have any element in common, so then we have this

[tex] P(AUB) = P(A) +P(B) -0 = \frac{2}{5} +\frac{3}{5} =1[/tex]

e) P(A∩B)

The intersection for this case is the empty set between the sets A and B so for this reason the probability is 0

P(A∩B)=0

The probability of each event in a random experiment is calculated by the ratio of the favorable outcomes to the total outcomes. The answer for each of the given events are: P(A)=2/5, P(B)=3/5, P(A')=3/5, P(A∪B)=1, P(A∩B)=0.

In the given random experiment, there are five equally likely outcomes: {a, b, c, d, e}. The event A consists of outcomes {a, b} and the event B consists of outcomes {c, d, e}. The probability of an event can be calculated by the ratio of the number of favorable outcomes to the total number of outcomes.

a) The probability of event A, P(A), is determined by the ratio of the number of outcomes in A to the total outcomes. Since A has 2 outcomes (a and b) and there are 5 total outcomes, the P(A) = 2/5.

b) The probability of event B, P(B), is determined in a similar manner. Since B has 3 outcomes (c, d and e) and there are 5 total outcomes, the P(B) = 3/5.

c) The probability of not A, P(A'), represents all outcomes not in A. Hence, since all outcomes in B and E are not in A, P(A') = P(B) = 3/5.

d) The probability of A or B, P(A∪B), means the probability of either event A or B occurring (or both). Since A and B include all of the outcomes in the sample space, P(A∪B) = 1.

e) The probability of A and B, P(A∩B), is the probability of both event A and event B occurring simultaneously. However, A and B have no common outcomes, so P(A∩B) = 0.

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Answer:

a. contrapositive because it's the converse and inverse. True.

b. converse because it's the reverse of conditional statement. True.

c. That is false so it's not converse, inverse, or contrapositive.

The given statement is: If two angles form a linear pair, then they are supplementary. The inverse is true, the converse is false, and the contrapositive is true.

The given statement is: If two angles form a linear pair, then they are supplementary. Let's analyze the options:

a. If two angles are not supplementary, then they do not form a linear pair. This is the inverse of the given statement. It is true because if two angles do not add up to 180 degrees, they cannot form a linear pair.

b. If two angles are supplementary, then they form a linear pair. This is the converse of the given statement. It is false because two supplementary angles may or may not form a linear pair.

c. If two angles do not form a linear pair, then they are supplementary. This is the contrapositive of the given statement. It is true because if angles do not form a linear pair, that means they do not add up to 180 degrees, and hence, they must be supplementary.

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Answer:

Option b) Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.            

Step-by-step explanation:

We are given the following in the question:

The distribution of systolic blood pressure of other women is a bell shaped distribution that is a normal distribution.

z-score = 1.50

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

Let x be the Gina's systolic blood pressure.

Thus, we can write:

[tex]1.50 = \displaystyle\frac{x-\mu}{\sigma}\\\\x = 1.5\sigma + \mu \\\text{where }\sigma \text{ is the standard deviation and }\\\mu \text{ is the mean for the given distribution of blood pressure.}[/tex]

Thus, we can write Gina's blood pressure  is 1.50 standard deviations above the average systolic blood pressure of women her age.

Option b) Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.

Gina's z-score of 1.50 indicates that her systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.

The best interpretation of Gina's standardized score (z-score) of 1.50 is option B: Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age. Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.

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Answer:

if a triangle had two right angles it would not be complete as to make it a triangle all corners have to meet while a 2 right angled triangle does not meet that.

i believe this is the answer

Answer:

Option A. 0.4 of an orange

Step-by-step explanation:

Formula to calculate the opportunity cost is

Opportunity cost = [tex]\frac{\text{Sacrificed}}{\text{Gained}}[/tex]

In this question for the high yield, sacrificed thing is 100 tubs of grapes and gain is to produce 250 tubs oranges.

Opportunity cost = [tex]\frac{100}{250}=0.4[/tex] of an orange

Therefore, Option A. 0.4 of an orange, will be the answer.

Answer:

The rain barrel an hold [tex]3\frac{1}{5}\ gallons[/tex] of water more.

Step-by-step explanation:

Given:

Amount of water barrel can hold = 12 gallons

Amount of water in the barrel before storm = [tex]2\frac{1}{5}\ gallons[/tex]

[tex]2\frac{1}{5}\ gallons[/tex] can be Rewritten as [tex]\frac{11}{5}\ gallons[/tex]

Amount of water in the barrel before storm =  [tex]\frac{11}{5}\ gallons[/tex]

Amount of water storm added = [tex]6\frac{3}{5}\ gallons.[/tex]

[tex]6\frac{3}{5}\ gallons.[/tex] can be Rewritten as [tex]\frac{33}{5}\ gallons.[/tex]

Amount of water storm added = [tex]\frac{33}{5}\ gallons.[/tex]

we need to find the amount of water barrel can hold more.

Solution:

Now we can say that;

the amount of water barrel can hold more can be calculated by Subtracting the sum of Amount of water in the barrel before storm and Amount of water storm added from Amount of water barrel can hold.

framing in equation form we get;

the amount of water barrel can hold more = [tex]12-(\frac{11}{5}+\frac{33}{5})= 12-\frac{11+33}{5}= 12- \frac{44}{5}[/tex]

Now we can see that 1 number is whole number and other is fraction.

So we will make the whole number into fraction by multiplying the numerator and denominator with the number in the denominator of the fraction.

so we can say that;

the amount of water barrel can hold more = [tex]\frac{12\times5}{5}-\frac{44}{5} = \frac{60}{5}-\frac{44}{5}[/tex]

Now we can see that denominator is common so we can subtract the numerator.

the amount of water barrel can hold more = [tex]\frac{60-44}{5}=\frac{16}{5}\ gallons \ OR \ \ 3\frac{1}{5}\ gallons[/tex]

Hence The rain barrel an hold [tex]3\frac{1}{5}\ gallons[/tex] of water more.

Final answer:

To find out how many more gallons of water the barrel can hold, subtract the total current water in the barrel from its maximum capacity.

Explanation:

In the question, it is asked how much more water a rain barrel can hold after it has been partially filled. To find this, we need to subtract the amount of water already in the barrel from its total capacity. Initially, the barrel contains 2 1/5 gallons, and the storm adds another 6 3/5 gallons.

We first convert these to improper fractions to make the addition easier.

The rain barrel can hold 12 gallons of water.

Before the storm, there were 2 1/5 gallons in the barrel.

The storm added 6 3/5 gallons of water to the barrel.

To find out how many more gallons of water can the barrel hold, we need to calculate: 12 - (2 1/5 + 6 3/5).

12 - (2 1/5 + 6 3/5) = 12 - (2.2 + 6.6) = 12 - 8.8 = 3.2 gallons.

Answer:

1 is the positive number for which the sum of it and its reciprocal is the smallest.

Step-by-step explanation:

Let x be the positive number.

Then, the sum of number and its reciprocal is given by:

[tex]V(x) = x + \dfrac{1}{x}[/tex]

First, we differentiate V(x) with respect to x, to get,

[tex]\frac{d(V(x))}{dx} = \frac{d(x+\frac{1}{x})}{dx} = 1-\dfrac{1}{x^2}[/tex]

Equating the first derivative to zero, we get,

[tex]\frac{d(V(x))}{dx} = 0\\\\1-\dfrac{1}{x^2}= 0[/tex]

Solving, we get,

[tex]x^2 = 1\\x= \pm 1[/tex]

Since x is a positive number x = 1.

Again differentiation V(x), with respect to x, we get,

[tex]\frac{d^2(V(x))}{dx^2} = \dfrac{2}{x^3}[/tex]

At x = 1

[tex]\frac{d^2(V(x))}{dx^2} > 0[/tex]

Thus, by double derivative test minima occurs for V(x) at x = 1.

Thus, smallest possible sum of a number and its reciprocal is

[tex]V(1) = 1 + \dfrac{1}{1} = 2[/tex]

Thus, 1 is the positive number for which the sum of it and its reciprocal is the smallest.

Answer: Probability that the first card dealt is black,the second red and the third black is O.127

Step-by-step explanation: Total number of cards=52

Total number of black cards =26

Total number of red cards=26

Probability of pulling black=26/52

Probability of pulling red=26/51

Probability of pulling a mother black=25/50

Probability of pulling 3 cards =26/52×26/51×25/50

16900/132600

=0.127

The probability that the first card dealt is black, the second is red, and the third is black is 13/102.

To find the probability that the first card dealt is black, the second is red, and the third is black, we need to consider the total number of possible outcomes and the number of favorable outcomes. Since we are drawing without replacement, we need to calculate the probabilities for each card.

To find the overall probability, we multiply the probabilities of each event together.

(1/2) * (26/51) * (1/2) = 13/102

Therefore, the probability that the first card dealt is black, the second is red, and the third is black is 13/102.

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Step-by-step explanation:

To solve this question I would use the sin rule.

The sin rule states that

[tex] \frac{a}{ \sin(a) } = \frac{b}{ \sin(b) } [/tex]

Therefore if you substitute in your numbers you get:

[tex] \frac{a}{ \sin(90) } = \frac{15}{ \sin(60) } [/tex]

If you rearrange that you get:

[tex]a = \frac{15}{ \sin(60) } \times \sin(90) [/tex]

Therefore a = 17.3 Inches (to 3 sf)

This can also be done with basic trigonometry where you would get

[tex] \sin(60) = \frac{15}{h} [/tex]

Rearranging to

[tex]h = \frac{15}{ \sin(60) } [/tex]

meaning the answer is 13.7 inches

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Work Shown:

h = unknown hypotenuse

sin(angle) = opposite/hypotenuse

sin(60) = 15/h

h*sin(60) = 15

h*sqrt(3)/2 = 15

h*sqrt(3) = 2*15

h*sqrt(3) = 30

h = 30/sqrt(3)

h = (30*sqrt(3))/(sqrt(3)*sqrt(3)

h = 30*sqrt(3)/3

h = (30/3)*sqrt(3)

h = 10*sqrt(3)

Answer:

Given Function is an even function

Step-by-step explanation:

Explanation:-

Even function :-

A function f is even if the graph of f is symmetric with respective to the y - axis.

Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f.

Odd function : -

A function f is odd if the graph of f is symmetric with respective to the origin

Algebraically, f is odd if and only if f(-x) = - f(x) for all x in the domain of f.

given function is [tex]f(x) = 3 x^2-1[/tex]

[tex]f(-x) = 3 (-x)^2-1=3 x^2 -1 = f(x)[/tex]

therefore f(-x) = f(x)

given function is an even function.

Answer:

Step-by-step explanation:

The total number of ducks in the pond is 75. 25 ducks are marked as a winner.

Probability is expressed as number of possible outcomes/total number of outcomes.

if you take 2 ducks out but don't replace them, the probability that the first duck that you took out is a winner is

25/75 = 1/3

The total number of ducks left would be 74 and the number of winners would be 24.

the probability that the second duck that you took out is a winner is

24/74 = 12/37

Therefore, the probability that both are winners is

1/3 × 12/37 = 4/37

Answer:

Option 1) x ≥ 0.5

Step-by-step explanation:

The given inequality is :     2(4x - 3) ≥ -3(3x) + 5x

And the options are:

1) x ≥ 0.5

2) x ≥ 2

3) (–∞, 0.5]

4) (–∞, 2]

==============================

So, the solution is as following:

2(4x - 3) ≥ -3(3x) + 5x

8x - 6≥ -9x + 5x

8x + 9x - 5x ≥ 6

12 x ≥ 6                

x ≥ 6/12

x ≥ 0.5

The answer is option 1) x ≥ 0.5

Answer:Probability of getting exactly 500 heads=0.025

Step-by-step explanation:Probability of getting exactly 500 heads= 1000C500(0.5)^1000=0.025

Answer: 0.383 and 0.6671

Step-by-step explanation:

Take 22%, that is 0.22 to be probability of success.

That means "1-0.22 = 0.78" is the probability of failure.

When dealing with selection in probability mathematics, the combination equation is used.

Probability of selecting number 'r' as a successful outcome from a given number 'n' is given as

nCr * p^r * q^n-r

Where p is the probability of success= 0.22

q is the probability of failure= 0.78

n is the total number of sample =10

r is the varying outcome of number of success.

For the first question, number of success is asked to be everything more than 2, that is probability of choosing 3,4,5,6,7,8,9,10 people with a successful outcome (adults who will pay more for environmentally friendly product.)

Instead of going through the long process of checking probability of success for choosing 3,4,5,6,7,8,9,10 adults who will pay more, we can simply find the probability of choosing 0,1,2 adults who will pay more and subtract the answer from 1.

By doing this, we first check for probability of choosing 0 adult that will pay More and this is gotten by putting r=0 in our probability Formula. The Formula becomes

=10C0 * 0.22^0 * 0.78^10

=1 *1 * 0.0834= 0.0834

Hence, Probability of Choosing 0 adult that will Pay more is 0.0834

To Check for probability of choosing 1 adult that will pay more becomes

=10C1 * 0.22^1 * 0.78^9

=10 * 0.22 * 0.1069 = 0.2352

Hence, Probability of choosing 1adult that will pay more = 0.2352

To Check for the probability of choosing 2adults that will pay more becomes

=10C2 * 0.22^2 * 0.78^8

=45 * 0.0484 * 0.1370 = 0.2984

Therefore the total sum of choosing 0,1,2 adults that are willing to pay more becomes

= 0.0834+ 0.2352+ 0.2984 = 0.617

So to determine the probability of choosing more than 2 adults, that is, 3,4,5,6,7,8,9,10 adults that are willing to pay more, we subtract 0.617 from 1.

This gives 1-0.617 = 0.383

Hence, probability of choosing more than 2 people that are willing to pay more than 2 = 0.383.

To determine the probability of choosing between two and five people inclusive, we follow the same probability formular but r becomes 2,3,4,5 differently.

For probability of choosing 2 adults, we already calculated it to be 0.2984 earlier.

For probability of choosing 3 adults, it becomes

10C3 * 0.22^3 * 0.78^7

=120* 0.0106 * 0.1757 = 0.2235

For the probability of choosign 4 adults, it becomes

10C4 * 0.22^4 * 0.78^6

= 210 * 0.0023 * 0.2252 = 0.1088

For the probability of choosing 5 adults, it becomes

10C5 * 0.22^5 * 0.78^5

= 252 * 0.0005 * 0.2887 = 0.0364

Hence, the probability of choosing between 2 and 5 adults becomes

0.2984 + 0.2235 + 0.1088 + 0.0364 = 0.6671

To find the probability of the number of adults who would pay more for environmentally friendly products, use the binomial probability formula.

To find the probability of the number of adults who would pay more for environmentally friendly products, we need to use the binomial probability formula.

The formula is: P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where:

Let's calculate the probabilities for the given scenario:

P(X > 2) = 1 - P(X <= 2)

P(X between 2 and 5 inclusive) = P(X=2) + P(X=3) + P(X=4) + P(X=5)

Question is not proper; Proper question is given below;

D'Angelo needs 100 lb of garden soil to landscape a building. In the company’s storage area, he finds 2 cases holding 24 3/4 lb of garden soil each, and a third case holding 19 3/8 lb. How much gardening soil does D'Angelo still need in order to do the job?

Answer:

D'Angelo required [tex]31 \frac{1}{8}\ lb[/tex] more garden soil to do the job.

Step-by-step explanation:

Given:

Total Amount of garden soil needed to do job = 100 lb

Amount of garden soil in 1st case = [tex]24\frac{3}{4}\ lb[/tex]

[tex]24\frac{3}{4}\ lb[/tex] can be rewritten as [tex]\frac{99}{4}\ lb[/tex]

Amount of garden soil in 1st case =  [tex]\frac{99}{4}\ lb[/tex]

Amount of garden soil in 2nd case = [tex]24\frac{3}{4}\ lb[/tex]

[tex]24\frac{3}{4}\ lb[/tex] can be rewritten as [tex]\frac{99}{4}\ lb[/tex]

Amount of garden soil in 2nd case =  [tex]\frac{99}{4}\ lb[/tex]

Amount of garden soil in 3rd case = [tex]19\frac{3}{8}\ lb[/tex]

[tex]19\frac{3}{8}\ lb[/tex] can be rewritten as [tex]\frac{155}{8}\ lb[/tex]

Amount of garden soil in 3rd case =  [tex]\frac{155}{8}\ lb[/tex]

We need to find Amount of garden soil required more.

Solution:

Now we can say that;

Amount of garden soil required more can be calculated by subtracting sum of Amount of garden soil in 1st case and Amount of garden soil in 2nd case  and Amount of garden soil in 3rd case from Total Amount of garden soil needed to do job.

framing in equation form we get;

Amount of garden soil required more = [tex]100-\frac{99}{4}-\frac{99}{4}-\frac{155}{8}[/tex]

To solve the fraction we will make the denominator common using LCM.

Amount of garden soil required more = [tex]\frac{100\times8}{8}-\frac{99\times2}{4\times2}-\frac{99\times2}{4\times2}-\frac{155\times1}{8\times1}= \frac{800}{8}-\frac{198}{8}-\frac{198}{8}-\frac{155}{8}[/tex]

Now denominators are common so we will solve the numerator.

Amount of garden soil required more = [tex]\frac{800-198-198-155}{8}=\frac{249}{8}\ lb \ \ OR \ \ 31 \frac{1}{8}\ lb[/tex]

Hence D'Angelo required [tex]31 \frac{1}{8}\ lb[/tex] more garden soil to do the job.

Answer:

After evaluating we get [tex]b^2-4ac = 52[/tex].

Step-by-step explanation:

Given:

[tex]b^2-4ac[/tex]

We need to evaluate the expression with a =3, b =8 and c= 1

Solution:

To evaluate the expression we will first substitute the values of a,b and c in the expression we get;

[tex]b^2-4ac = 8^2-4\times3\times1[/tex]

Now by using PEDMAS which states first operation needs to perform here is the exponent function.

so we get;

[tex]b^2-4ac = 64-4\times3\times1[/tex]

Now next operation to be performed is multiplication.

[tex]b^2-4ac = 64-12[/tex]

And finally we will perform subtraction operation.

[tex]b^2-4ac = 52[/tex]

Hence After evaluating we get [tex]b^2-4ac = 52[/tex].