find the values of t6 and d for the arithmetic sequence with t6= 4 and t10= -4
​

The probability that a plant will produce berries can be calculated as the proportion of female plants in the population, which is 7/11.

The probability that berries will be produced if the homeowner buys 4 plants at random can be calculated as the number of successful outcomes (i.e., buying 4 female plants) divided by the total number of possible outcomes (i.e., the number of ways to choose 4 plants from 11).

Since the plants are selected without replacement, this is equivalent to finding the number of combinations of 4 female plants out of 7. The formula for combinations is given by C(n,k) = n! / (k! (n-k)!).

So, the number of combinations of 4 female plants out of 7 is C(7,4) = 35. The total number of combinations of 4 plants out of 11 is C(11,4) = 330.

Therefore, the probability that berries will be produced is 35/330 = 7/66.

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Answer:

10.6, or 10 entire items

Step-by-step explanation:

Answer:

\(\frac{32}{3}\) items

Step-by-step explanation:

Please see the attached image.

I hope this helps!

It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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Answer:

98

Step-by-step explanation:

Mathematically, when we add all the angles of a triangle, we get 180

Thus;

x + 1 + 2x-2+ 3x-5 = 180

6x-6 = 180

6x = 186

x = 186/6

x = 31

so the measure of the biggest angle is 3x -5

= 3(31) + 5 = 93 + 5 = 98

The factors influencing sample size include the desired level of confidence, the higher desired level of confidence, the variability of the population, the size of the effect being measured, and the level of precision desired.

The desired level of confidence determines the sample size needed to achieve the desired level of confidence. The higher the desired level of confidence, the larger the sample size needs to be. The variability of the population is also a factor that influences sample size.

If the population is highly variable, a larger sample size is needed to achieve the desired level of confidence. the size of the effect being measured also affects sample size.if the effect is small, a larger sample size is needed to measure it accurately. Finally, the level of precision desired also affects the sample size.

The higher the level of precision desired, the larger the sample size needs to be. When drawing a sample to make sure the measure of interest is neither overestimated nor underestimated, all of the mentioned factors need to be taken into consideration. The sample size should be large enough to accurately measure the effect, given the desired level of confidence and the level of precision desired.

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Answer:

C:$13. 16 nickles left

Step-by-step explanation:

i know i took this test to on time4learning

Answer:

no point of intersection

Step-by-step explanation:

y=x-8

y=x^2-2x-3

The answer is square root of 3

The given equation contains square root forms hence we must simplify it before proceeding further

we know that 12= 2^2 *3

Thus applying it in the equation, the equation becomes

5\(\sqrt{3}\)-2\(\sqrt{12}\)

Thus writing 12 as 2^2X3

5\(\sqrt{3}\)-2\(\sqrt{2^2*3}\)

Now taking out square root of 2^2 which is 2,

the equation becomes

5\(\sqrt{3}\)-4\(\sqrt{3}\)

=\(\sqrt{3}\)

Thus the answer is square root of 3

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Answer:

Step-by-step explanation:

A/b = 7 / 2

Then

A / b = 3½

A = 3½ × b

Then, a is 3.5 times greater than b.

The age of the basalt (unit m) is approximately 1.14 x 10⁹ years years, if 0.5 half-lives of 40K/40Ar have elapsed and the half-life of 40K/40Ar is 1.3 billion years.

The age of the basalt can be calculated using the formula

age = (t₁/2 x loge(1 + (D/P)))/1.21 x 10⁻¹¹

where t₁/2 is the half-life of the radioactive isotope (in seconds), D is the ratio of the daughter isotope (in this case 40Ar) to the parent isotope (in this case 40K), and P is the initial ratio of the daughter isotope to the parent isotope.

In this case, we are given that

t₁/2 = 1.3 billion years = 4.1 x 10¹⁶ seconds (since 1 billion = 10⁹ and there are 31,536,000 seconds in a year)

0.5 half-lives of 40K/40Ar have elapsed, which means that D/P = 0.5 (i.e., half of the initial amount of 40K has decayed to 40Ar)

Plugging in these values, we get:

age = (4.1 x 10¹⁶ seconds x loge(1 + 0.5))/1.21 x 10⁻¹¹

= (4.1 x 10¹⁶ seconds x loge(1.5))/1.21 x 10⁻¹¹

= 1.14 x 10⁹ years

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Answer:

20 dollers and 50 cents

(x-h)²+(y-k)²=r²

(3-h)²+(3-0)²=5²

h²-6h+9+9=25

h²-6h-7=0 —> (h-7)(h+1)=0

h=7 , h=-1

h=7 —> (x-h)²+y²=r² —> (x-7)²+y²=25 —>

x²-14x+49+y²=25 —> x²+y²-14x+24=0

h=–1 —> (x-h)²+y²=r² —> (x+1)²+y²=25 —>

x²+2x+1+y²=25 —> x²+y²+2x–24=0

I hope it helped you ^_^

Answer:

G. 14:5 is the correct answer.

Step-by-step explanation:

a:b = 4:5

a:c = 2:7

so,

here in first ratio a = 4

in second ratio a = 2

making them equal:

Taking LCM of 2 and 4 = 4

so

a:c = 2/7 = (2×2)/(7×2) = 4/14

so,

a = 4

c = 14

b = 5

so ratio c : b = 14:5

Answer:

D

Step-by-step explanation:

Answer:

12.8 ft or exactly sqrt 164

Step-by-step explanation:

Pythagoreans is a^2+b^2=c^2

10^2+8^2=164

sqrt 164 = 12.8 ft

An isosceles right angled triangle has two equal sides, and those two equal sides make 90 degrees (right angle) internally. The correct option is A.

An isosceles right angled triangle has two equal sides, and those two equal sides make 90 degrees (right angle) internally.

Since the two of the angles of the triangle are equal, therefore, the length on the opposite sides of this angle will be equal to each other. Hence, we can write that the length of the side s will be equal to 4.

Hence, the correct option is A.

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The solutions to the rational equation x / (x + 4) = 20 / (x² + 3 · x - 4) + 2 / (x - 1) are 7 and - 4, respectively.

In this problem we find a rational equation that must be solved for x by means of algebraic properties. The complete procedure is shown below:

Step 1 - We have the following expression:

x / (x + 4) = 20 / (x² + 3 · x - 4) + 2 / (x - 1)

Step 2 - Factor x² + 3 · x - 4:

x / (x + 4) = 20 / [(x + 4) · (x - 1)] + 2 / (x - 1)                

Step 3 - By existence of multiplicative inverse, modulative, associative and commutative properties:

[x · (x - 1)] / [(x + 4) · (x - 1)] = 20 / [(x + 4) · (x - 1)] + [2 · (x + 4)] / [(x + 4) · (x - 1)]

Step 4 - By compatibility with multiplication, existence of multiplicative inverse, modulative, associative and commutative properties:

x · (x - 1) = 20 + 2 · (x + 4)                                            

Step 5 - By distributive property:

x² - x = 20 + 2 · x + 8                                                  

Step 6 - By compatibility with addition, distributive, modulative and associative properties:

x² - 3 · x - 28 = 0  

Step 7 - Factor x² - 3 · x - 28:

(x - 7) · (x + 4) = 0                                                        

Step 8 - By understanding the factors found in the previous, we get the folowing result:

x = 7 or x = - 4                                                               Result

The solution to the equation are 7 and - 4.

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Answer:

-4. my answers need to be 20 characters+ soooo

Answer:

The area of the shade is 12 feet

Step-by-step explanation:

To find the area you would do 6 * 4 which equals 24 but with every triangle you have to cut the area in half so the actual answer would be 12 feet

The given statement, "the margin-of-error refers to the number of percentage points by which survey results may vary" is true because the margin of error is an important factor to consider when interpreting the results of a poll.

In a poll, the margin of error refers to the amount of random sampling error that is expected to be present in the results of the survey. It is a measure of the statistical uncertainty associated with using a sample of a population to make inferences about the opinions or characteristics of the entire population.

The margin of error is typically reported as a plus or minus percentage, such as "plus or minus 3 percentage points," and it represents the range of values within which the true population parameter is likely to fall with a certain level of confidence. For example, if a poll has a margin of error of plus or minus 3 percentage points with a 95% level of confidence, this means that if the poll were conducted 100 times, the results would be expected to fall within plus or minus 3 percentage points of the true population parameter in 95 of those surveys.

Therefore, the margin of error is an important factor to consider when interpreting the results of a poll and helps to provide a measure of the precision and reliability of the survey findings.

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Answer: 86

Step-by-step explanation:

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

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The two true statements regarding the circle equation are:

"The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9"

"The center of the circle lies on the x-axis."

Remember that the equation for a circle of center (a, b) and radius R is:

(x - a)^2 + (y - b)^2 = R^2

Here we have the equation:

x^2 + y^2 - 2x - 8  =0

First we need to complete squares on x, remember the perfect square trinomial:

(a - b)^2 = a^2 - 2ab + b^2

So we can rewrite:

x^2 + y^2 - 2x - 8  =0

(x^2 - 2x) + y^2 = 8

Now we can add and subtract 1:

(x^2 - 2x) + y^2 + 1 - 1 = 8

(x^2 - 2x + 1) + y^2 - 1 = 8

(x - 1)^2 + y^2 = 8 + 1

(x - 1)^2 + y^2 = 3^2

So, the center is (1, 0) and the radius is 3.

Then the true statements are:

"The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9" it is also 3.

"The center of the circle lies on the x-axis." because the center is at (1, 0).

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The number of pounds of candy that sells for $0.79 per lb that  must be mixed with candy that sells for $1.35 per lb to obtain 8 tons of a mixture that should sell for $335 per ton is 580 pounds

Take x as the number of pounds of candy that sells for $0.79 per lb, and y as the number of pounds of candy that sells for $1.35 per lb.

x + y = 8 (i.e total amount of candy to be mixed)

0.79x + 1.35y = 335 (desired selling price per ton)

solve for x

y = 8 - x

0.79x + 1.35(8 - x) = 335

0.79x + 10.8 - 1.35x = 335

-0.56x = 324.2

x = 579.64

Thus x ≈ 580 to the nearest pound

Hence, about 580 pounds of candy that sells for $0.79 per lb must be mixed with candy that sells for $1.35 per lb to obtain 8 tons of a mixture that should sell for $335 per ton.

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Answer:

12

Step-by-step explanation:

area of a trapezoid :

\(A = \frac{a+b}{2} h\)

where a and b = length of bases and h = height

here, we are given the area, the length of one base and the height

we want to find the other base length

we can do this by plugging in what we are given and then solving for the unknown variable

first lets define our known variables

Area (A) = 42 , height (h) = 4 and length of one of the bases (a) = 9

we then plug this into the formula and solve for b, the other base length

recall formula : \(A = \frac{a+b}{2} h\)

A = 42 , h = 4 , a = 9

\(42 = \frac{9+b}{2} 4\)

now solve for b

divide both sides by 4

\(10.5=\frac{9+b}{2}\)

multiply both sides by 2

21 = 9 + b

subtract 9 from both sides

12 = b

the other base length is 12

Francisco teaches group lessons to all of the violin and viola students at the Scott School of Music. All of his classes have the same number of students.

What is the greatest number of students he can have in each class We can determine the greatest number of students that Francisco can teach in each class by finding the greatest common factor (GCF) of the total number of violin and viola students at the school.

Suppose there are a total of m violin students and n viola students. Then the total number of students at the school is m + n. Let's find the GCF of m and n in order to determine the greatest number of students Francisco can teach in each class.

GCF of m and n will give us the number of students that can be divided equally among all the classes. Following the steps to find GCF :

Step 1 :List down all factors of m and n

Step 2 :Identify the common factors of both m and n

Step 3 :Find the largest common factor m and n. We find the factors of m and n below: Suppose m = 36 and n = 72.Therefore, the greatest common factor of m and n is 36.So, the greatest number of students that Francisco can teach in each class is 36.

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Completing the square – can be used to solve any quadratic equation. It is a very important method for rewriting a quadratic function in vertex form. Quadratic formula – is the method that is used most often for solving a quadratic equation.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Any quadratic problem may be solved by completing the square. It is a critical way for expressing a quadratic function in vertex form. The quadratic formula is the most often used method for solving a quadratic problem.

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For the given data, The correct statement is: A refrigerator with 3.75 ft³ of refrigerator space will have 1.5 ft³ of freezer space.

We can compute the refrigerator space ratio for each model by dividing the refrigerator space by the freezer space:

\(\text{For Model A: Space ratio = Refrigerator space / Freezer space} = 15.75 \;ft^3 / 6.3 ft^3 \approx 2.5\)

\(\text{For Model B: Space ratio = Refrigerator space / Freezer space }= 10.25 ft^3 / 4.1 ft^3\approx 2.5\\\\\text{For Model C: Space ratio = Refrigerator space / Freezer space }= 15.25 ft^3 / 6.1 ft^3 \approx 2.5\)

We can use this ratio to compute the freezer space for a particular refrigerator with a known refrigerator space because all refrigerators have the same space ratio of around 2.5.

Now for given statements:

Using the space ratio of 2.5, if a refrigerator has 3.25 ft³ of refrigerator space, the freezer space will be= \(3.25 ft^3 / 2.5 \approx 1.3 ft^3\), not 1.2 ft³. So, statement a is not true.

Using the space ratio of 2.5, if a refrigerator has 3.25 ft³ of refrigerator space, the freezer space will be \(3.25 ft^3 / 2.5 \approx 1.3 ft^3\), not 1.5 ft³. So, statement b is not true.

Using the space ratio of 2.5, if a refrigerator has 3.75 ft³ of refrigerator space, the freezer space will be \(3.75 ft^3 / 2.5 \approx 1.5 ft^3\), not 1.2 ft³. So, statement c is not true.

Using the space ratio of 2.5, if a refrigerator has 3.75 ft³ of refrigerator space, the freezer space wii be\(3.75 ft^3/ 2.5 \approx 1.5 ft^3\) So, statement d is true.

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