a dressmaker needs to cut 12-inch pieces of ribbon from rolls of ribbon that are 3 feet in length. how many 12-inch pieces can the dressmaker cut from 10 of these rolls of ribbon?

The population of rabbits in the year 2013 is 1186.

To predict the population of rabbits in the year 2013, we can use exponential growth. The formula for exponential growth is:

P = P₀ * e^(rt)

where:

P = final population

P₀ = initial population (950)

r = the growth rate (we need to find this)

t = time elapsed (13 years)

We can use the data from 2003 to find the growth rate:

1000 = 950 * e^(r * 3)

1000 = 950 * e^(3r)

1000/950 = e^(3r)

ln (1000/950) = 3r

r = (ln(1000 / 950)) / 3

r = 0.0171

Now that we have the growth rate, we can use it to find the population in 2013:

P = 950 * e^(0.0171 * 13)

P = 1186

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Answer:

Number of pounds of cashews = x = 14.96 pounds

Number of pounds of Brazil nuts = y = 19.04 pounds

Step-by-step explanation:

Let us represent:

Number of pounds of cashews = x

Number of pounds of Brazil nuts = y

The nut shack sells cashews for $6.00 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to make a 34 pound mixture that sells for $5.44 per pound

Our system of equations is given as:

x + y = 34...... Equation 1

x = 34 - y

6x + 5y = 34 × 5.44

6x + 5y = 184.96.......Equation 2

Ww substitute : 34 - y for x in Equation 2

6(34 - y) + 5y = 184.96

204 - 6y + 5y = 184.96

Collect like terms

- 6y + 5y = 184.96 - 204

-y = -19.04

y = 19.04 pounds

Solving for x

x = 34 - y

x = 34 - 19.04

x = 14.96 pounds

Number of pounds of cashews = x = 14.96 pounds

Number of pounds of Brazil nuts = y = 19.04 pounds

Answer:

  it depends

Step-by-step explanation:

I like to choose the units to be compatible with the use of the number.

In Engineering, we often choose units so the number itself is between 1 and 1000. Here, that means 3.4×10^-7 mm would be better expressed as 3.4 angstroms or 340 pm (picometers). (The purpose of SI prefixes is to facilitate this way of representing metric measures.)

If you're comparing the length to something measured in km, then the representation as 3.4×10^-13 km might be the most useful

If you're comparing the distance to something measured in mm, then 3.4×10^-7 mm would be more appropriate than 3.4×10^-13 km.

The law or definition used between steps 3 and 4 is the De Morgan's Law.

De Morgan's Law states that the complement of the union of two sets is equal to the intersection of their complements, and the complement of the intersection of two sets is equal to the union of their complements. In this case, the complement of the intersection of sets b and c is equal to the union of their complements, which is represented by the expression (x∉a) ∧ (b ∪ c).

Therefore, the De Morgan's Law is used to transform the expression (x∈a) v (b ∩ c) into ¬((x∉a) ∧ (b ∪ c)) between steps 3 and 4.

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The probability is based on actual observations or data, which makes it an experimental probability. It is important to note that experimental probabilities may not always match theoretical probabilities due to factors such as bias or chance.

The given scenario is an example of experimental probability. Experimental probability refers to the probability of an event based on actual observations or data collected through experimentation or observation. In this case, the experiment involved rolling a die containing the numbers 1-6, and observing the number that appears on the top face of the die. Out of the 15 times the die was rolled, it landed on an even number 8 times. The experimental probability of rolling an even number can be calculated by dividing the number of times an even number was rolled by the total number of rolls, which is 8/15 in this case.

Theoretical probability, on the other hand, refers to the probability of an event based on mathematical calculations and assumptions. For instance, the theoretical probability of rolling an even number on a fair six-sided die can be calculated as 3/6 or 1/2, since there are three even numbers (2, 4, and 6) and six possible outcomes. However, in this case, the probability is based on actual observations or data, which makes it an experimental probability. It is important to note that experimental probabilities may not always match theoretical probabilities due to factors such as bias or chance.

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Answer:

it started off with 7 members

(read the whole explanation)

Step-by-step explanation:

Question: the chess club accepts 5 new members each week and it had 37 members after 6 weeks ? how many members per week and how many members did it start off with.

If the chess club accepts 5 each week and they had 6 members after 6 weeks you should multiply 5x6=30. We don't know when the chess club started.. it could be 6 or 7 weeks ago and I'm pretty sure we all know that 7x5=35. but it only says 6 weeks ago so the answer is 7,

hope this helps!!!!

Answer:

c = 11.46 yd

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ c² = (8.1)² + (8.1)²

→ c² = 65.61 + 65.61

→ c² = 131.22

→ c = √131.22

→ [ c = 11.46 yd ]

Hence, value of c is 11.46 yd.

The solutions to the system of equations f(x) = x² + x - 6 and g(x) = -2x² - 2x + 12 are (-3, 0) and (2, 0). So, correct option is 1.

To graph the functions f(x) and g(x) using a calculator, we can enter the equations into the calculator's graphing function and choose an appropriate window to display the graph. Once the graphs are displayed, we can look for the points of intersection to find the solution to the system of equations.

Using a graphing calculator, we can see that the graphs of f(x) and g(x) intersect at two points: (-3, 0) and (2, 0). These points represent the x-coordinates of the solutions to the system of equations.

To verify that these points are indeed the solutions, we can substitute each of them into both equations and check that they satisfy both equations simultaneously.

For point (-3, 0):

f(-3) = (-3)² + (-3) - 6 = 0

g(-3) = -2(-3)² - 2(-3) + 12 = 0

Therefore, (-3, 0) is a solution to the system of equations.

For point (2, 0):

f(2) = 2² + 2 - 6 = 0

g(2) = -2(2)² - 2(2) + 12 = 0

Therefore, (2, 0) is also a solution to the system of equations.

The point (0, -6) and (0, 12) are not the points of intersection and (-6, 12) is not a solution to the system of equations.

Therefore, the answer is option 1.

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A) The null and alternative hypotheses are:

B We can perform a two-sample t-test with equal variances to test the hypothesis. Using a statistical software or calculator, the test statistic is:

t = 1.4636, degrees of freedom = 14, and p-value = 0.0832

C) Since the p-value (0.0832) is greater than the significance level (0.01), we fail to reject the null hypothesis.

The null hypothesis is that there is no difference between the mean number of bacteria per cubic foot in carpeted rooms and uncarpeted rooms. The alternative hypothesis is that the mean number of bacteria per cubic foot is higher in carpeted rooms than in uncarpeted rooms.

The two-sample t-test with equal variances is appropriate because we are comparing the means of two independent samples of continuous data that are approximately normally distributed. The test statistic is t = 1.4636, which measures how many standard errors the sample means are from each other.

Therefore, there is not significant evidence at the alpha equals 0.01 level of significance to conclude that carpeted rooms have more bacteria than uncarpeted rooms. The appropriate conclusion is: do not reject H0.

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In the first equation, the missing expression should be "1/a." The derivative of a constant multiplied by the natural logarithm of a variable is equal to the constant divided by the variable.

For the second equation, the missing expression should be "e." The derivative of the exponential function e raised to the power of a variable is simply equal to the exponential function itself.

In the third equation, the missing expression should be "1/(x * ln(a))." The derivative of the logarithm function with base "a" of a variable is equal to 1 divided by the variable multiplied by the natural logarithm of the base "a."

In the fourth equation, the missing expression should be "-1/x^2." The derivative of the reciprocal function 1 divided by a variable is equal to -1 divided by the square of the variable.

Lastly, in the fifth equation, the missing expression should be "-2x / (V(1-x^2))^2." The derivative of the reciprocal function 1 divided by the square root of a quantity (1 minus the square of a variable) is equal to -2 times the variable divided by the square of the square root of the quantity.

To summarize, the missing expressions in the given equations are 1/a, e, 1/(x * ln(a)), -1/x^2, and -2x / (V(1-x^2))^2, respectively. These expressions represent the derivatives of the respective functions with respect to their variables.

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If the similar sides and angles of two triangles are proportionate, then the triangles are similar.

We must assess if two triangles have the same shape but perhaps different sizes in order to determine their similarity. The triangles are similar if their corresponding sides are proportionate. The triangles are not comparable if they are not proportionate. We only need to determine whether two triangles' respective sides are proportionate if we are given two triangles and are aware that their corresponding angles are congruent.

In conclusion, in order to establish whether two triangles are comparable, we must look at both the proportionality of the respective sides and the congruency of the corresponding angles. The triangles are similar if both requirements are satisfied, and we can create a similarity assertion by using the matching triangle vertices.

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Answer:

Set up each problem by writing down what you need to find with a question mark. Then set it equal to the information that you are given. The problem is solved by multiplying the given data and its units by the appropriate unit factors so that only the desired units are present at the end.

Side Angle Side Theorem can be describe as: Triangles are congruent if two sides and an included angle of a triangle are equal to two sides and an included angle of another triangle.

Side Angle side Theorem:

The word "congruent" for figures means the same thing in all respects, mainly shape and size. The relationship between two congruent entities is described by congruence. Congruence is a term used to describe the relationship between two congruence diagrams. Now let's discuss the SAS congruence of triangles. We don't necessarily have to ask every side and every angle to make sure that two triangles are similar. Congruence of triangles means:

SAS Criterion:

According to this criterion, two triangles are congruent if two sides of a triangle are equal to two sides of another triangle and the angles formed by those sides of the two triangles are equal. The SAS criterion expresses the "side angle side" triangle congruence theorem.

The SAS Congruence Rule:

The Congruent Side Angle Theorem states that if two sides and the angle formed by those two sides are equal to the included angles of the two sides and another triangle is called a contract.

Let's do an activity that demonstrates the detection of SAS.

Given: AB=PQ, BC=QR, ∠B=∠Q.

To prove: ΔABC ≅ ΔPQR

Place triangle ΔABC over triangle ΔPQR such that B is above Q and side AB is along side PQ.

AB=PQ so point A falls on point P.

∠B=∠Q, so edge BC falls along edge QR.

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The probability that both are red is 0.0791.

Given,

Total marbles: 37 + 15 = 52

According to the number of red cards out of all the cards, there is a 15/52 possibility that a red card will be pulled during our initial pull.

Depending on how many red/total marbles are still in there, there is a 14/51 probability that the second marble pulled will also be red.

Our two fractions are multiplied together from here,

15/52 * 14/51

We can start by simplifying a little bit; the numbers 14 and 52 share a 2;

15/26 * 7/51

Our result is 35/442

Depending on whether you choose to maintain it in fractional, ratio, or percentage form, the result of dividing is around 0.0791, which rounds to 7.91%.

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Answer:

C

Step-by-step explanation:

The y-intercept is approximately 191.1. The correct option is (B).

To compute the y-intercept, we need to use the equation of the regression line, which is:

y = a + bx

where a is the y-intercept, b is the slope, x is the independent variable (in this case, x-bar), and y is the dependent variable (in this case, y-bar).

The formula for the slope of the regression line is:

b = r * (sy/sx)

where r is the correlation coefficient, sx is the standard deviation of x, and sy is the standard deviation of y.

Substituting the given values, we get:

b = 0.341 * (37/12) = 1.05025

Now, we can use the formula for the y-intercept:

a = y-bar - b * x-bar

Substituting the given values, we get:

a = 251 - 1.05025 * 57 = 191.10925

Therefore, the y-intercept is approximately 191.1.

The answer is B) 191.1.

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Answer:

5:80, there are only 2 numbers

Step-by-step explanation:

The ratio of blue triangles to all triangles is 1 : 17.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

A Pattern has 5 blue triangles to every 80 yellow triangles.

Here, Number of blue triangles = 5

Number of all triangles = 5 + 80

                                    = 85

Thus, The ratio of blue triangles to all triangles is,

⇒ Number of blue triangles : Number of all triangles

⇒ 5 : 85

⇒ 1 : 17

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Answer: B

Step-by-step explanation:

The correct answer to the above question is Option C. divergent i.e., The series [infinity] ∑ sin(n) + 3^n is divergent.

To determine the convergence of the series, we need to check both the convergence of sin(n) and 3^n series.

Since both series diverge, their sum will also diverge, and the given series is therefore divergent.

In summary, the given series [infinity] ∑ sin(n) + 3^n is divergent as both the sin(n) and 3^n series diverge.

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Answer:

22

Step-by-step explanation:

Justin will put $22 into each account. First add $50 and $16 to find how much money Justin earned. Justin earned a total of $66 mowing yards and washing cars. Then divide the total by 3 to find out how much money will go into each account.

The summary of the results is as follows:How many possible outcomes are there in the outcomes space.- 36 How many elements are in the event of getting different numbers without repetitions. - 30 How many elements are in the event of getting different numbers without repetitions but the second number must be a 4? - 6

There are six possible outcomes in the outcomes space. Let us solve each part of the question.How many possible outcomes are there in the outcomes space?The possible outcomes in the outcomes space for the given problem is calculated by multiplying the number of outcomes of the first roll by the number of outcomes of the second roll.Number of possible outcomes of each roll

= 6 (as there are six faces on a dice)Total possible outcomes in the outcomes space

= 6 × 6

= 36So, there are 36 possible outcomes in the outcomes space.How many elements are in the event of getting different numbers without repetitions?In this case, the two rolls are independent. This means the first roll doesn't affect the second roll. Thus, all possible outcomes with different numbers are 6 × 5

= 30. So, there are 30 elements in the event of getting different numbers without repetitions.How many elements are in the event of getting different numbers without repetitions but the second number must be a 4?In this case, we can have any one of the six numbers in the first roll. Then, only one number 4 is left for the second roll. Thus, there are 6 possible outcomes where the second number is a 4. Hence, there are 6 elements in the event of getting different numbers without repetitions but the second number must be a 4.The summary of the results is as follows:How many possible outcomes are there in the outcomes space.- 36 How many elements are in the event of getting different numbers without repetitions. - 30 How many elements are in the event of getting different numbers without repetitions but the second number must be a 4? - 6

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A possible value for the missing term of the geometric sequence 1250,__,50,.. is 250.

In Mathematics and Geometry, the nth term of a geometric sequence can be calculated by using this mathematical equation (formula):

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁ = ar²/ar

x/1250 = 50/x

x² = 1250 × 50

x² = 62500

x = √62500

x = 250

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Complete Question;

What is a possible value for the missing term of the geometric sequence 1250,__,50,..?

Answer:

d) Infinitely many

Step-by-step explanation:

−5a + 5a + 8 = 8

8 = 8

Since this is an identity solution, that means it's infinitely many.

Answer:

a none

Step-by-step explanation:

please mark this answer as brainliest

Answer:

X=5/16                    

Explaination:

Answer:

Step-by-step explanation:

If AB and DE are equidistant from the center, that means that they are the same length. We set the equations equal to one another and solve for x:

3x - 7 = 5(x - 5) and

3x - 7 = 5x - 25 and

18 = 2x so

x = 9. Now we sub that into the expression for AB (or DE since they're the same length):

3(9) - 7 = 20

Both AB and DE measure 20 units.

The probability of two planes having no cracks is 0.063 and The probability of no plane having critical cracks is 0.405.

(a) The probability of one plane having a critical crack is 10% or 0.10. The probability of two planes having detectable cracks is (0.21)^2 = 0.0441. The probability of two planes having no cracks is (0.69)^2 = 0.4761. So, the desired probability is 0.10 * 0.0441 * 0.4761 = 0.063.

(b) To find the probability that at least one plane has critical cracks, we can use the complementary probability approach, i.e., finding the probability that no plane has critical cracks and then subtracting it from 1. The probability of no plane having critical cracks is (0.90)^5 = 0.595. So, the desired probability is 1 - 0.595 = 0.405.

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Based on the evaluation of the conditions, the output "x < 0 and z > 0" will be printed. Therefore, the correct answer is B. x < 0 and z > 0.

The correct indentation of the statement would be as follows:

if (x > 0)

if (y > 0)

System.out.println("x > 0 and y > 0");

else if (z > 0)

System.out.println("x < 0 and z > 0");

Given that x = 1, y = -1, and z = 1, let's evaluate the conditions:

The first if statement checks if x > 0, which is true since x = 1.

Since the condition in the first if statement is true, we move to the inner if statement, which checks if y > 0. However, y = -1, so this condition is false.

The inner if statement is followed by an else if statement that checks if z > 0. Since z = 1, this condition is true.

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Answer:

Your right

Step-by-step explanation:

For the linear equations provided by the coordinates in the table;

The first equation of this system is y = -2x.

The second equation of this system is y = x - 3.

The solution to the system is (1, -2).

We have four points (-5,10), (-1,2), (0,0), and (11,-22) for first equation, and four points (-8,-11), (-2,-5), (1,-2), and (7,4) the second equation.

The slope (m) is given by the formula (y2 - y1) / (x2 - x1).

For the first line, we can use the points (-5,10) and (-1,2)

m1 = (2 - 10) / (-1 - (-5)) = -8/4 = -2.

the first equation is y = -2x

the second line, we can use the points (-8,-11) and (-2,-5)

m2 = (-5 - -11) / (-2 - -8) = 6/6 = 1.

the second line has a slope of 1,

the equation should have the form y = x + c.

To find c, we can use one of the points, for instance (-2,-5):

-5 = -2 + c => c = -5 + 2 = -3.

So, the second equation is y = x - 3.

the solution to the system, we need to find where the two lines intersect.

y = -2x

y = x - 3

Setting both equation equally

-2x = x - 3

=> 3x = 3

=> x = 1.

Substituting x = 1 into the first equation

y = -2(1) = -2.

the solution to the system of linear equation would be (1, -2).

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Answer:

after working for at least 10 1/4 years

Step-by-step explanation:

After working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

A quadratic equation, \(ax^{2} +bx+c=0\) is solved by

\(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

Given function \(f(x)=x^4-10x^2+10000\)

Function that has monthly salary $20,000 will be \(x^4-10x^2+10000=20000\)

\(x^4-10x^2+10000-20000=0\)

\(x^4-10x^2-10000=0\)

Now using the formula \(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

\(x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}\)

\(x^2=\frac{10 \pm \sqrt{40100} }{2}\)

\(x^2=\frac{10 \pm 200.2}{2}\)

\(x^2=5 \pm 100.1\)

\(x^2=105.1\)

\(x=\sqrt{105.1}\)

\(x=10.25\)

Hence, after working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

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The given rational and irrational numbers can be ordered from least to greatest as follows; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.

It follows from the task content that the numbers given are rational and irrational numbers.

To order the numbers, they should be converted to decimal numbers as follows;

-2 3/5 = -2.6

√20 = 4.47

3.9 = 3.9

10/3 = 3.33

3 7/8 = 3.875

Hence, the order from least to greatest is; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.

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