Find the 10th term of the geometric sequence whose common ratio is 1/3 and whose first term is 7.

Answer:

Step-by-step explanation:

Write it out

[tex](B+6)/4[/tex]

plug in the value

[tex](1.5+6)/4[/tex]

solve

[tex](1.5+6)/4\\7.5/4\\= 1.875[/tex]

Answer:

the answer is 5

Step-by-step explanation:

(Add 10r to both sides)

-7-7r+10r= 8

Then -7+3r = 8

(Add 7 to both sides)

3r = 8+7

3r = 15

Divide both sides by 3.

r = 5

Answer:1400

Step-by-step explanation:

The exponential function passes through the points (-1,4/5) and (1,20) will be y = 4 × [tex]5^{x}[/tex].

In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

In other meaning, an exponential function is that function above which a variable x has imposed.

Suppose the exponential function as

y = a[tex]e^{bx}[/tex]

Substitute, (-1,4/5)

4/5 = a[tex]e^{-b}[/tex]                             (1)

Substitute, (1,20)

20 = a[tex]e^{b}[/tex]                                (2)

Multiply (1) with (2)

(4/5)20 = a[tex]e^{-b}[/tex] × a[tex]e^{b}[/tex]

4 × 4 = a²

a = 4

Substitute, a = 4 into (2)

20 = 4[tex]e^{b}[/tex]    

[tex]e^{b}[/tex] = 5

Take log on both sides of the above equation,

ln [tex]e^{b}[/tex]  =  ln 5

b = ln 5

Substitute a = 4 and b = ln 5 into y = a[tex]e^{bx}[/tex]

y = 4 e^(x(ln 5)) = 4 e^(ln5^x)

y = 4 × [tex]5^{x}[/tex]

Hence "The exponential function passes through the points (-1,4/5) and (1,20) will be y = 4 × [tex]5^{x}[/tex]".

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1. The volume of the cylinder is 942 m³.

2. The volume of the cone is 33.16 mm.

3. The volume of the sphere is 33.50 in³.

4. The volume of the cuboid is 672 in³.

Volume is defined as how much of a three-dimensional object occupies

a space.

We know the volume of a cylinder is πr²h.

∴ The volume of the given cylinder is = π(5)²×12 m³ = 942 m³.

We know the volume of a cone is = (1/3)πr²h.

∴ The volume of the given cone is = (1/3)π(2)²×8 mm³ = 33.16 mm.

We know the volume of a sphere is (4/3)π×r³.

∴ The volume of the given sphere is = (4/3)×π×(r³) in³ = 33.50 in³.

We know the volume of a cuboid is = (length×width×height).

∴ The volume of the given cuboid is = (7×8×12) in³ = 672 in³.

The volume of the object in figure 8 is the sum of the volume of a cuboid and a pyramid.

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The graph that could be used to find the distance between the points

(-3, -13) and (11, 9) is given as follows:

B. graph of a right triangle with hypotenuse beginning at negative 3 comma negative 13 and ending at 11 comma 9.

What is distance between two points?

The distance between two points in a plane is the length of the line segment separating the two points. Typically, the equation

d=√((x2 - x1)^2 + (y2 - y1)^2) is used to calculate the distance between two points.

Suppose we have a pair of points, with the coordinates given as follows:

[tex](x_1, y_1)[/tex]  and  [tex](x_2, y_2)[/tex].

The two points form a right triangle, in which the sides are given as follows:

[tex]y_2-y_1\\x_2-x_1[/tex]

The distance between these two points is given by the hypotenuse of the right triangle.

Hence, applying the Pythagorean Theorem, the distance is obtained as follows:

[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

In this problem, the coordinates of the points are given as follows:

(−3, −13) and (11, 9).

Hence the correct option is given by option B.

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Answer:

Below

Step-by-step explanation:

y = - x^2 + 5       solve for x

y-5 = - x^2

x^2 = 5-y

x = ± sqrt (5-y)        now switch the x's and y's

y = ± sqrt(5-x)    

Here is a picture:

Answer:

#4 x=70

Step-by-step explanation:

Because this is an Isosceles triangle, we know that the 2 base angles have to be equivalent. So subtract 40 from 180 which leaves you with 140, then divide 140 by 2 because there are 2 base angles. Then arrive at the answer of x=70.

-Hope this helped & Happy Holidays!

Answer:

x = -3

Step-by-step explanation:

If you look at the graph.

x = 4 is a vertical line.  

Another vertical line that would be parallel to this can contain the point (-3, 7) would be the line x = -3

The solution to the parallel lines identification and congruency are;

1) They are not parallel.

2) They are not congruent.

3) They are not congruent.

Parallel lines are defined as lines in a plane that are always the same distance apart. Parallel lines never intersect.

1) Looking at lines m and n , for them to be parallel, it means that they must be the same width all through. However, we see that along the x-axis they are 6 units while going further down, it is not always 6 units as some are 5.5 units. Thus, they are not parallel.

2) No, m is not congruent to p because it is not the same distance from the x and y-axis at similar points.

3) No, n cannot be congruent to p because we see that the distance between the marked points are not congruent.

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The slope of the line perpendicular to 4x - 6y = - 60 is (-3/2).

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is

y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

We know lines perpendicular to each other have slopes that are negative reciprocals of each other.

Given line is 4x - 6y = - 60 ⇒ - 6y = - 4x - 60 ⇒ y = (2/3)x + 10.

Now the line perpendicular to it will have a slope of (-3/2).

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Because AR = AQ, you have an isosceles triangle with triangle RAQ.  This also means ∠ARQ = ∠AQR.

You're also told that RT = QS, so this gives you SAS to show triangle ART = triangle  AQS.

   side: AR = AQ

   angle: ∠ART = ∠AQS

   side: TR = QS

Knowing that the two triangles are congruent gives you that the two top angles are also congruent.  

Hence, the point on the ray is [tex]x > 2[/tex].

What is the number line?

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides

Here given that,

Use the number line to represent the solution to [tex]x + 3 > 5.[/tex]

i.e.,

[tex]x+3 > 5\\\\x > 5-3\\\\x > 2[/tex]

Hence, the point on the ray is [tex]x > 2[/tex].

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The required percent of the coffee left is given as 66.67%.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
24 ounces of coffee Ms. Bobadilla,
And 8 ounces of coffee has been drinking,
Applying the percentage evaluation, in order to calculate the remaining coffee to Ms. Bobadilla.
Percentage of coffee remaining = 24 - 8 / 24 × 100%
Percentage of coffee remaining = 0.6667 × 100%
Percentage of coffee remaining = 66.67%

Thus, the percentage is given as 66.67%.

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The age of the bones when they were discovered is 13439.66 years

What is half-life of an element?

The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value

The decay constant λ is = 0.693/t½

where t½ is the half-life of the element

Given data ,

The radioactive element​ carbon-14 has a​ half-life of 5750 years

So , the value of t½ = 5750 years

Now , the decay constant λ = 0.693 / t½

Substituting the values in the equation , we get

Decay constant λ = 0.693 / t½

Decay constant λ = 0.693 / 5750

Decay constant λ = 1.205 x 10⁻⁴

N=N₀e ^ −λt

where N₀ = Mass of radioactive element initially

N = Mass of radioactive element after time t

Apply natural logarithm on both the sides of the equation , we get

ln N = ln N₀ - λt

Let N0 be 100 then N will be 100 - 80.2 = 19.8

Substituting the values in the equation , we get

ln 19.8 = ln 100 -  1.205 x 10⁻⁴ ( t )

ln [ 19.8 / 100 ] = - 1.205 x 10⁻⁴ ( t )

-1.61948 = -1.205 x 10⁻⁴ ( t )

Therefore , the value of t is

t = -1.61948 / -1.205 x 10⁻⁴

t = 1.343966 x 10⁴

t = 13439.66 years

Therefore , the value of t is 13439.66 years

Hence ,

The age of the bones when they were discovered is 13439.66 years

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340 ft high

d = 400' distance from building to tower

26° from the window to the top of the tower and 20° from the window to the bottom of the tower

Tan 26 = h2/d  

Tan 20 = h1/d  

h2 = 400Tan26

h1 = 400Tan20

on solving the equations,

h=a+b

Tower = 340 ft high

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The required average rate of change in the amount of Kendall's account is $50 per month.

Rate is a measurement to determine the change in one quantity with respect to another quantity.

Given that,

The amount of the end of the 8th month in Kendall's account = $450,

And at the end of the 11th month, the saved amount = $600.

To find the rate of change in saving amount

The increased amount = 600 - 450 = 150.

Since, In 3 months the amount increased by 150.

So, the average rate of change in amount

= 150 / 3.

= 50.

The average rate of change in the amount is $50 per month.

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A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459    , 24.8293 ) .

What is population mean?

A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.

Data: 18

for given data

[tex]$$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$$[/tex]

as population variance is unknown so we used sample variance

[tex]$$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$$[/tex]

Now

[tex]\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$[/tex]

hence 95 % of population mean is

As n=101 which is large so critical value is 1.98397

[tex]$$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$$[/tex]

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A sampling method is simple random sampling.

In statistical analysis, sampling is the procedure by which researchers choose a specific number of observations from a larger population. The sample strategy will depend on the sort of study being done, although it may involve systematic sampling or just plain random sampling.

A selection of participants from a population are chosen at random by the researcher using simple random sampling, a sort of probability sampling. Every person in the population has the same probability of getting chosen. Then, data are gathered from as much of this randomly selected subgroup as feasible.

Since it only uses one random pick and is very simple, this method is the easiest of all the probability sampling techniques.

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Answer:

------------------------------

Equation of line:

Given values can be interpreted as pairs of coordinates of the two points:

Find the slope of the line:

Find the y-intercept, by substituting coordinates of one point:

The equation becomes:

Find the value of y when x = 22:

The relationship between the cone cylinder and sphere is sphere takes up two-thirds of the volume of the cylinder, the cone takes up one-third of the volume of the cylinder.

Answers of blank :

Blank 1 = 1/3

Blank 2 = Three

Blank 3 = Two

Blank 4 = 2/3

Blank 5 = 1/3

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X = 63°

W = 60°

Y = 57° are  the measure of each angle in triangle.

In math, what is a triangle?

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.

W = X - 10

Y = X - 14

X + W + Y = 180    substitute

X + (X - 10) + ( X - 14)

  = 3 X - 24 = 180

3X = 180 + 24.

 X = 204/3

X =  68

W =  58

Y =  54

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The equation of inequality for the given graph will be;

⇒ y < - 4/3x + 5

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The graph is shown in figure.

Now,

Take two points on the graph as;

⇒ (0, 5) and (3, 1)

Hence, The equation of line will be;

⇒ y - 5 = (1 - 5) / (3 - 0)  (x - 0)

⇒ y - 5 = - 4/3x

⇒ y = - 4/3x  + 5

Since, The inequality is shown in figure.

Hence, We get;

⇒ y < - 4/3x + 5

Thus, The equation of inequality for the given graph will be;

⇒ y < - 4/3x + 5

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a) The hypotheses for this study would be the Null hypothesis and Alternative hypothesis.

b) The completed ANOVA summary table would be the Sum of Squares.

c) The calculator would give a p-value of approximately 0.03.

d) The results of the ANOVA test may not be reliable.

(a) The hypotheses for this study would be:

Null hypothesis ([tex]H_0[/tex]): There is no difference in the average lifetime of the four types of batteries.

Alternative hypothesis ([tex]H_1[/tex]): There is a difference in the average lifetime of the four types of batteries.

(b) The completed ANOVA summary table would be:

Sum of Squares (SS) df Mean Squares (MS) F

Between (Factor) 25.7375 3 8.578 3.77

Within (Error) 75 56 1.34

Total 100 59

(c) To find the p-value, you would use the Fcdf function on your calculator. The syntax for this would be Fcdf(F, 10000, df Between, df Within). In this case, the F value is 3.77, the df Between is 3, and the df Within is 56. Plugging these values into the calculator would give a p-value of approximately 0.03.

(d) Based on the p-value, we can reject the null hypothesis and conclude that there is a significant difference in the average lifetime of the four types of batteries. This suggests that the type of battery has an effect on its lifetime. However, it is important to note that this conclusion is based on the assumptions of the ANOVA test, including the assumption of equal variances among the groups. If these assumptions are not met, the results of the ANOVA test may not be reliable.

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The constant of proportionality will be 9.5 when the table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.

Given that,

The table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.

We have to find the constant of proportionality.

We know that,

A collection of consecutively ordered numbers a and b expressed as a/b, where b is never equal to zero, is referred to as a ratio. A statement is considered proportionate when there is equality between two items.

The table displays the proportional relationship between the price for a particular quantity of golf ball cans at a driving range.

Buckets                         3               5             7

Price (dollars)            28.50       47.50      66.50

The constant of proportionality is calculated as,

⇒ 25.8 / 3

⇒ 9.5

Therefore, The constant of proportionality will be 9.5 when the table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.

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Answer:

9.5

Step-by-step explanation:

I took the exam and got it right

The value of [tex]\angle[/tex]ABC=6° was found with the help of the law of cosines.

What is the law of cosines of a triangle?

The lengths of a triangle's sides are correlated with the cosine of one of its angles according to the law of cosines. We can now determine values for distances and angles that are impossible to measure without the aid of trigonometry. When calculating the third side of a triangle given two sides and their enclosed angle, as well as when calculating the angles of a triangle if we know all three sides, the law of cosines is used.

Given values are AB = c = 36 units, BC = a = 42 units, and [tex]\angle[/tex]BCA = 31°.

Now let AB = b, we find b using the law of cosines and quadratic equation:

[tex]c^2 = a^2 + b^2 - 2a b \cos C \\36^2 = 42^2 + b^2 - 2 \cdot \ 42 \cdot \ b \cdot \ \cos 31\degree \\ b > 0 \\ b = 7.22[/tex]

Now, we calculate [tex]\angle[/tex]ABC using the law of cosines:

[tex]\angle ABC=arc cos(\frac{a^{2}+c^{2}-b^{2} }{2ac}) \\\angle ABC=arc cos(\frac{42^{2}+36^{2}-7.22^{2} }{2.42.36}) \\\angle ABC=5.55[/tex]

[tex]\angle[/tex]ABC=6°

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According to the given information The 50 child tickets and 64 adult tickets were sold that day.

The area of mathematics concerned with the characteristics and use of numbers a field of study that concentrates on multiplying, dividing, adding, and subtracting numbers. Mathematical simplifications are made using fractions, decimals, percentages, fractions, square roots, exponents, and other arithmetic operations.

child admission (c)= $5.70

adult admission (a)= $9.80

5.70c + 9.80a = 912.20      (i)

a + c = 114                            (ii)

Set up the equation:

5.70(114 - a) + 9.80a = 912.20

649.8 - 5.7a + 9.80a = 912.20

4.1a = 262.4

a = 64

adult tickets = 64  

Put the value of a in equation (ii) we get,

64 + c = 114

c = 114 - 64

c = 50

child tickets = 50

Therefore , the 50 child tickets and 64 adult tickets were sold that day.

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