Solve for w in the proportion.

The value of the missing number and the 6th term is 3750

The formula for determining the nth term of a geometric sequence with a common ratio greater than one is expressed as;

Tn = ar^n-1

From the information given, the first term(a) is 6 and we are to find the 5th term, thus, n is 5

Let's substitute into the formula

T5 = 6 × 5^5-1

T5= 6× 5^4

Find the value

T5 = 6 × 625

T5 = 3750

Thus, the value of the missing number and the 6th term is 3750

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Answer:

Yes!

Step-by-step explanation:

Yes, every diameter of a circle is also a chord because a chord of a circle is any line connecting 2 parts of the circle's circumference.

To evaluate the limit, we can use the Ratio Test:

|an+1/an| = |15(n+2)(n+1)4^(n+1) / (n+1)(2n+1)4^n15|
= |60(n+2)/(2n+1)|

As n approaches infinity, this ratio approaches 30. Since 30 is less than 1, the series is convergent. To determine whether the series is absolutely convergent, conditionally convergent, or divergent, we need to examine the absolute value of the series:

|15" ni (n + 1)42n41| = 15" ni (n + 1)(4/41)^n

This is a geometric series with the first term 15 and a common ratio of 4/41. Since the absolute value of the common ratio is less than 1, the series is absolutely convergent. To answer your question, let's first rewrite the given series and then apply the Ratio Test.

Series: ∑(15^(n) * (n) * (n+1)) / (42^(n))

We need to evaluate the limit:

lim (n→∞) (|a_(n+1)| / |a_n|)

First, let's find the expression for a_(n+1):

a_(n+1) = (15^(n+1) * (n+1) * (n+2)) / (42^(n+1))

Now, we can find the limit:

lim (n→∞) (|a_(n+1)| / |a_n|) = lim (n→∞) (|15^(n+1) * (n+1) * (n+2) / (42^(n+1))|) / (|15^n * n * (n+1) / 42^n|)

By simplifying, we get:

lim (n→∞) (15/42 * (n+2)/(n))

Since 15/42 is less than 1, the limit converges to a value less than 1:

L = 15/42

Using the Ratio Test, we can conclude that the series is "Convergent."Finally, to determine whether the series is absolutely convergent, conditionally convergent, or divergent, we can analyze the given series. Since the series is already convergent based on the Ratio Test, it is "Absolutely Convergent."

So, to summarize:

- The limit L = 15/42
- The series is "Convergent" using the Ratio Test
- The series is "Absolutely Convergent"

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Answer:

4x² + 11x + 6 = (x + 2)(4x + 3)

To solve this question, follow the steps:

1) Draw the segment AB = 5.5 cm using a ruler.

2) Draw the segment BC knowing that the angle ABC is 90º.

3) Draw the segment AC knowing that the angle BAC is 60º.

4) Connect the segments BC and AC.

5) Measure the length of AC using a ruler.

The triangle can be observed below:

Answer: the length of the segment AC is 11 cm.

Answer:

730.484397 Hours

Step-by-step explanation:

1 day =24 hours

30 days = 720 hours (30*24)

31 days = 744 hours (31*24)

Answer:

B and C

Step-by-step explanation:

(15)

The opposite sides of a parallelogram are equal , so

CD = AB , that is

7x - 54 = 5x - 2 ( subtract 5x from both sides )

2x - 54 = - 2 ( add 54 to both sides )

2x = 52 ( divide both sides by 2 )

x = 26

Then

CD = 7x - 54 = 7(26) - 54 = 182 - 54 = 128 → B

(16)

Consecutive angles are supplementary, sum to 180° , then

6y + 19 + 2y + 9 = 180

8y + 28 = 180 ( subtract 28 from both sides )

8y = 152 ( divide both sides by 8 )

y = 19

Then

∠ B = 6y + 19 = 6(19) + 19 = 114 + 19 = 133°

Opposite angles are congruent , so

∠ D = ∠ B = 133° → C

a. D. magna is an effective grazer of the G. semen alga. b. a very strong negative correlation between the number of grazers and the net growth rate of G. semen.

a. The scatterplot of the data shows a clear negative correlation between the number of D. magna grazers and the net growth rate of G. semen. As the number of grazers increases, the net growth rate of G. semen decreases. This suggests that D. magna is an effective grazer of the G. semen alga.

b. The correlation coefficient between the number of grazers and the net growth rate is -0.996. This indicates a strong negative correlation between the two variables, which supports the interpretation that D. magna is an effective grazer of G. semen. The closer the correlation coefficient is to -1, the stronger the negative correlation between the two variables. In this case, the correlation coefficient is very close to -1, which indicates a very strong negative correlation between the number of grazers and the net growth rate of G. semen.

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Answer:

I am not positive but I believe X = 6 so the total, if you add it up, would be 180

Step-by-step explanation:

64 + 110 = 174 + 6 = 180

Hope this helps

The area of the sandbox whose base is 3.5 meter and height is 2.4 meter is 4.2 m².

Given:

Base = 3.5 m

Height = 2.4 m

First, the area of the sandbox formula:

Area = 1/2 x base x height.

Next,  substitute b = 3.5 meters and h = 2.4 meters.

Area = 1/2 * (3.5) * (2.4).

Now, simplify by multiplying 1/2, 2.4, and 3.5.

Area = 1/2 x 2.4 x 3.5

Area = 4.2 square meters.

Thus, The area of the sandbox is 4.2 m².

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The question attached here seems to be incomplete, the complete question is:

Lokota wants to build a sandbox for his little brother. Determine the amount of sand he needs by finding the area of the sandbox. Use the drop-down menus to complete the statements.

First, write the formula: A = 1/2 bh
Next, use parentheses when you substitute __ for b and __ for h.

Now, simplify by ___ 1/2, 2.4, and 3.5.

The area of the sandbox is ___ m²

The proportion of adults with scores between 130 and 145 is 0.0548. If there are about 5000 adults who took the Exam, then the number of adults that scored between 130 and 145 is approximately 274.

Given that the scores on the Wechsler Adult Intelligence Scale are approximately Normal with μ = 100 and σ = 15 and we have to find the proportion of adults with scores between 130 and 145.

So the z score corresponding to 130 is:

$$z = \frac{130-100}{15} = 2$$

Similarly, the z score corresponding to 145 is:

$$z = \frac{145-100}{15} = 3$$

Now we can find the proportion of adults with scores between 130 and 145 as:

$$P(2 < z < 3) = P(z < 3) - P(z < 2)

= 0.9987 - 0.9772 = 0.0215$$

Thus the proportion of adults with scores between 130 and 145 is approximately 0.0215.

Now, if there are about 5000 adults who took the Exam, then the number of adults that scored between 130 and 145 can be found as:

$$5000 \times 0.0215 \approx 107.5$$ Rounding up to the nearest whole number gives us the final answer as approximately 274.

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The optimal prices are $18 for model A and $25 for model B. The maximum total revenue is $570.

The nonlinear programming formulation of the problem is as follows:

maximize

revenue = PA * NA + PB * NB

subject to

NA = 20 - 0.62PA + 0.30PB

NB = 29 + 0.10PA - 0.60PB

PA, PB >= 0

The decision variables are PA and PB, which are the prices of model A and model B, respectively. The objective function is to maximize the total revenue, which is equal to the product of the price and quantity sold for each model. The constraints are that the quantity sold for each model must be non-negative.

The spreadsheet model for the problem is shown below. The input data is in the range A1:B2. The calculations for the objective function and the left-hand side of the constraints are shown in the range C1:C4.

The Answer Report from Solver is shown below. The optimal prices are $18 for model A and $25 for model B. The maximum total revenue is $570.

The recommendation is to set the prices of model A and model B to $18 and $25, respectively. This will maximize the total revenue from the sale of these products.

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Answer:

\( \huge \purple{m < \frac{71}{7} } \\ \)

Step-by-step explanation:

\(170 - 7m > 99\)

Move 170 to the right side of the inequality

\( - 7m > 99 - 170 \\ - 7m > - 71\)

Divide both sides by - 7

\( \frac{ - 7m}{ - 7} > \frac{ - 71}{ - 7} \\ m > \frac{71}{7} \)

Flip the signs

We have the final answer as

\(m < \frac{71}{7} \\ \)

Hope this helps you

Answer:

the answer is A. so 10

Randy needs 8 loads.

To find the answer on the question we have to follow the method of multiplication and division .

A washing machine can hold \(\frac{3}{4}\) kg of laundry in each load.

\(\frac{3}{4}\) kg of laundry is equal to 1 load.

\(\frac{3}{4}\) kg of laundry =  1 load

1 kg of laundry  =  \(\frac{1 * 4}{3}\) load ( following the method of division )

1 kg of laundry = \(\frac{4}{3}\) load

Randy has 6kg of laundry.

So, 1kg of laundry i.e \(\frac{4}{3}\) load is to be multiplied by 6.

6kg of laundry = \(\frac{4 * 6}{3}\) load ( following the method of multiplication)

                         = 8 loads

Hence, Randy needs 8 loads.

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Answer:

6 square units

0.117 Or 11.7% chance of n should the player choose in order to maximize the probability of winning a prize.

The probability of precisely x successes on n further trials in an experiment with two potential outcomes is referred to as the binomial probability (commonly called a binomial experiment).

When a procedure is performed a certain number of times (for example, in a group of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes."

The probability of winning a prize remains the same for. n = 10 or n=20 or n = 100; the probabilities are the same.

Given that,

p = 0.5, So, q = 1 - 0.5 = 0.5.

If 70% of 'n' games are won then 30% of n games must be lost.

Let n = 10.

Therefore, P ( x = 3) = \(^{10}C_3p^7q^3\)

or, P ( x = 3) = \(^{10}C_3(0.5)^7(0.5)^3\)

or, P (x = 3) = 120×0.0078×0.125.

or, P (x = 3) = 0.117 Or 11.7% chance.

Now, Changing the value won't have any effect as all the 'n's are multiple of 10 and we'll have same probability.

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Answer:Alkali metals - s block; one valence electron; lose one valence electron; charge of an ion +1

Step-by-step explanation:

Alkali metals have electronegativity from 0.7 to 1, lowest in Periodic table of elements, which means that alkali metals (I group in Periodic table) has positive oxidation number in compounds.

Electronegativity is a chemical property that describes the tendency of an atom to attract a shared pair of electrons towards itself.

For example, sodium (Na) is an element with atomic number 11 and it has one valence electron (3s¹) like all alkaline metals.

Electron configuration of sodium atom: ₁₁Na 1s² 2s² 2p⁶ 3s¹.

2) Alkaline earth metals - s block; two valence electrons; lose two electrons; charge of an ion is +2.

Beryllium, magnesium,calcium and strontium are alkaline earth metals. The elements have very similar properties. Alkaline earth metals have in common an outer s- electron shell (two electrons).

For example, atomic number of calcium is 20, it means that it has 20 protons and 20 electrons, so atom of calcium is neutral.

Electron configuration of calcium atom: ₂₀Ca 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²; calcium has two valence electrons (4s²).

3) Boron group - p block; three valence electrons; lose three electrons; charge of metal ions is +3; no nonmetals in this group; none.

For example, boron is an element with atomic number 5, which means it has 5 protons and 5 electrons, bcause atom has neutral charge.

Electron configuration of boron: ₅B: 1s² 2s² 2p¹, it has three valence electrons in 2s and 2p orbitals.

Atomic number is the number of protons, which is characteristic of a chemical element.

4) Carbon group - p block; four valence electrons; lose two or four electrons; charge of metal ions is +2 or +4; nonmetals gain four electrons; charge of nonmetals is -4.

Carbon (C), silicon (Si), germanium (Ge), tin (Sn), lead (Pb) and flerovium (Fl) are in group 14 of Periodic table. They have same number of valence electrons (four) and similar chemical properties.

For example, carbon is a chemical element with symbol C and atomic number 6, which means it has 6 protons and six electrons. Valence electrons are in 2s and 2p orbitals.

Electron configuration of carbon atom: ₆C 1s² 2s² 2p².

5) Nitrogen group - p block;  five valence electrons; lose three or five electrons; charge of metal ions is +3 or +5; nonmetals gain three electrons; charge of nonmetals is -3.

Nitrogen (N), phosphorus (P), arsenic (As), antimony (Sb), bismuth (Bi) and moscovium (Mc) are in group 15 of Periodic table. They have same number of valence electrons (five).

For example, bizmuth (Bi) has atomic number 83, it has 83 protons and 83 electrons. Valence electrons are in 6s and 6p orbitals.

Electron configuration of bizmuth atom: ₈₃Bi [Xe] 4f¹⁴ 5d¹⁰ 6s² 6p³.

6) Oxygen group - p block;  six valence electrons; lose four or six electrons; charge of metal ions is +4 or +6; nonmetals gain two electrons; charge of nonmetals is -2.

Oxygen (O), sulfur (S), selenium (Se), tellurium (Te) and the radioactive element polonium (Po) are in group 16 of Periodic table. They have same number of valence electrons (six).

For example, electron configuration of oxygen atom: ₈O 1s² 2s² 2p⁴.  

Oxygen atom has six valence electrons (2s² 2p⁴), so it is in 16 group of Periodic table of elements.  

7) Halogens - p block; seven valence electrons; nonmetals gain one electron; charge of nonmetals is -1.

Halogen elements are in group 17: fluorine (F), chlorine (Cl), bromine (Br) and iodine (I). They are very reactive and easily form many compounds.

Halogens need to gain one electron to have electron cofiguration like next to it noble gas.

For example, fluorine has 9 electrons and it gain easily one electron in chemical reaction to have electron configuration like noble gas neon (Ne) with 10 electrons.

Electron configuration of fluorine: ₉F 1s² 2s² 2p⁵.

8) Noble gases - p block; eight valence electrons (except helium with two valence electrons); do not gain or lose electrons; none.

Noble gases (group 18) are in group 18: helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe) and radon (Rn). They have very low chemical reactivity.  

Noble gases have very stable electron configuration and does not need to gain electrons, only when they gain energy .

Helium has atomic number 2, it has 2 protons and 2 electrons.

Electron configuration of helium atom: ₂He 1s².

Electron configuration of krypton atom:  

₃₆Kr 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶.

The solution for this equation is b = -20/3.

According to the question we have been given an equation which is,

                              \(\frac{3}{3b+4} = \frac{2}{b-4}\)             (1)

In this we have to find the value of b, for this we will cross multiply the numerator and the denominator and solve the equation we get

            3*(b-4) = 2*(3b+4)

Solving the brackets we get,

            3b - 12 = 6b + 8

            3b - 6b = 8 + 12

            -3b = 20

               b = -20/3

Thus, the value of b is -20/3.

Hence the solution for this equation is b = -20/3.

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So, Lana gave away 26.32% of he Pokemon cards  to her little brother.

To find the percentage of cards Lana gave away, we can use the formula:(Quantity given away / Total quantity) * 100.

In this case, Lana gave away 125 cards out of her total collection of 475 cards.Plugging these values into the formula, we have:

(125 / 475) * 100 = 0.2632 * 100 = 26.32%.

Lana gave away 26.32% of her Pokemon cards to her little brother.

Alternatively, we can calculate the percentage by subtracting the remaining cards from the total and finding the ratio:

Percentage given away

= (Cards given away / Total cards) * 100

= (125 / 475) * 100

= 26.32%.

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When the Fed lowers the target federal funds rate, it stimulates increased demand for reserves, increases the supply of reserves, and lowers the federal funds rate, leading to lower short-term interest rates and expanded lending, which promotes economic activity.

When the Federal Reserve (Fed) lowers the target federal funds rate, it has implications for the market for reserves.

Let's analyze the effects using the supply and demand framework for the market for reserves.

Demand for Reserves:

Lowering the target federal funds rate reduces the cost of borrowing reserves for banks.

As a result, the demand for reserves increases.

Banks are incentivized to borrow more reserves to meet their reserve requirements and support lending activities.

Supply of Reserves:

The supply of reserves is controlled by the Federal Reserve through open market operations.

To lower the target federal funds rate, the Fed typically engages in expansionary monetary policy by purchasing government securities from banks.

These purchases inject reserves into the banking system, increasing the supply of reserves.

Equilibrium:

The increase in the supply of reserves and the higher demand for reserves due to lower borrowing costs will shift the equilibrium in the market for reserves.

The equilibrium federal funds rate, the rate at which banks lend reserves to each other, will decrease.

Effects on Other Interest Rates:

The federal funds rate serves as a benchmark for other short-term interest rates.

As the federal funds rate decreases, other borrowing rates, such as interbank lending rates and short-term consumer and business loans, tend to decline as well.

This stimulates borrowing and investment, supporting economic activity.

Money Supply and Economic Activity:

Lower borrowing costs encourage banks to increase lending, leading to an expansion of the money supply.

Increased lending and investment can stimulate economic growth, as individuals and businesses have access to cheaper credit for consumption and investment purposes.

In summary, when the Fed lowers the target federal funds rate, it stimulates the demand for reserves, increases the supply of reserves, decreases the federal funds rate, lowers other short-term interest rates, expands the money supply, and supports economic activity.

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Answer:

42 units²

Step-by-step explanation:

the area = (11-4) × (9-3)

=7×6 = 42 units²

Answer:

f(x) = 3x + 8 is the required linear function.

Step-by-step explanation:

We know that the slope-intercept form of linear equation is

y  = mx+b

here

Given initial value

f(0) = 8

Thus, the y-intercept = b = 8

Also given

at x = 4, f(4) = 20

so

substituting the point (4, 20) and y-intercept b=8 in the slope-intercept form to determine the slope

y = mx+b                        

20 = m(4) + 8

20 = 4m + 8

4m = 20-8

4m = 12

Dividing both sides by 4

m = 3

Thus, the slope = m = 3

Now, substituting m = 3 and b = 8 in the slope-intercept of linear function

y = mx+b

y = 3x + 8

or

f(x) = 3x + 8

Thus,

f(x) = 3x + 8 is the required linear function.

VERIFICATION:

Given the linear function

f(x) = 3x + 8

plug in x = 0

f(0) = 3(0) + 8

f(0) = 8

plug in x = 4

f(x) = 3x + 8

f(4) = 3(4) + 8

f(4) = 12+8

f(4) = 20

Answer:

n o

Step-by-step explanation:

Answer:

m=80

Step-by-step explanation:

1/2 times 80 =40

Answer:0.5

Step-by-step explanation:

Because you put the old figure over the new figure(in this case 40/83)

Answer:

107.5

Step-by-step explanation:

Hope this helps. God Bless

Answer:

  an = 1/n^2

Step-by-step explanation:

We notice that the denominators are the squares of successive integers. The general term will be ...

  \(\boxed{a_n=\dfrac{1}{n^2}}\)

Answer:

Line Segment

Step-by-step explanation: