3 Cassie wants to determine the length of the shadow that a 60-foot tall telephone pole casts without measuring it. If Cassie's mailbox, which is 42 inches in height, casts a shadow that is 31.5 inches in length, how long is the shadow that the telephone pole casts? A. 43 feet B. 45 feet C. 52 feet D. 55 feet ​

Answer:

  a1 = 1875

Step-by-step explanation:

You want a1 for the geometric series that has r = 2/5, an = 120, and Sn = 3045.

The n-th term of the geometric series with first term a1 and common ratio r is ...

  an = a1·r^(n-1)

The sum of the first n terms of the geometric series is ...

  Sn = a1·(r^n -1)/(r -1)

We can use the expression for an to substitute for r^n in the sum equation:

  [tex]a_n=a_1(r^n)(r^{-1})\\\\r^n=\dfrac{a_n}{a_1r^{-1}}=\dfrac{a_nr}{a_1}\\\\S_n=a_1\dfrac{r_n-1}{r-1}=a1\dfrac{\dfrac{a_nr}{a_1}-1}{r-1}\\\\S_n=\dfrac{a_nr-a_1}{r-1}\\\\a_1=a_nr-S_n(r-1)=a_nr+(1-r)S_n\\\\a_1=(120)\dfrac{2}{5}+(1-\dfrac{2}{5})(3045)=\dfrac{2\cdot120+3\cdot3045}{5}\\\\\boxed{a_1=1875}[/tex]

__

Additional comment

The sum is of the first four terms:

  1875 +750 +300 +120 = 3045

We can also find this by working backward. The previous term is 5/2 times the current term. We need to find the terms that have a sum of 3045.

  120 +300 +750 +1875 +4687.5 +...

Clearly, 5 terms is too many. The sum of the first 4 terms of the backward series is 3045, so we know n=4 and the first term is 1875—the last term of our 4-term backward series.

Substituting for x in an expression means replacing the variable x with a specific value or expression. This is often done to evaluate the expression for that particular value or to simplify the expression.

Substituting 2 for x in the first expression, we get:

[tex]1/2(2) + 4(2) + 6 - 1/2(2) - 2 = 1 + 8 + 6 - 1 - 2 = 12[/tex]

Substituting 2 for x in the second expression, we get:

[tex]2(2) + 2 - 1 = 5[/tex]

One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.

Therefore, the first expression evaluated with x = 2 is 12, and the second expression evaluated with x = 2 is 5. Since they do not have the same value, the correct option is:

Learn more about expressions here:

https://brainly.com/question/14083225

#SPJ1

The given question is incomplete. The complete question is given below:

What will be the result of substituting 2 for x in both expressions below? One-half x + 4 x + 6 minus one-half x minus 2 Both expressions equal 5 when substituting 2 for x because the expressions are equivalent. Both expressions equal 6 when substituting 2 for x because the expressions are equivalent. One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent. One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.

the expression describing all the angles that are coterminal with 8° is: θ = 8° + 360°k, where k is an integer.

How to solve and what is angle?

An angle of 8° has an initial side on the positive x-axis and rotates counterclockwise by 8°.

Any angle coterminal with 8° can be expressed as:

θ = 8° + 360°k

where k is an integer.

Therefore, the expression describing all the angles that are coterminal with 8° is:

θ = 8° + 360°k, where k is an integer.

An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians and are used to measure the amount of rotation or turn between two intersecting lines or planes.

To know more about angle related question visit:

https://brainly.com/question/28451077

#SPJ1

Answer:6^21

Step-by-step explanation:

Answer:

Step-by-step explanation:

To calculate unadjusted cost of goods sold, sum the beginning inventory value and the cost of goods manufactured, then subtract the ending inventory value.

The answer of given Theoretical  Probability Question is  0.1379 , 0.125

Experimental probability of the name Fred being chosen = number of times Fred is chosen / total number of trials

= 17/124

= 0.1379 (rounded to four decimal places)

Theoretical probability of the name Fred being chosen = number of outcomes in which Fred is chosen / total number of possible outcomes

Since there are eight different names in the hat, the total number of possible outcomes is 8. The number of outcomes in which Fred is chosen is 1 (since there is only one Fred in the hat).

Therefore, the theoretical probability of Fred being chosen is:

1/8 = 0.125 (rounded to three decimal places)

If the number of names in the hat were different, both the experimental and theoretical probabilities would change.

To Know more about Probability visit :

https://brainly.com/question/31279414

#SPJ9

Answer:

3/4

Step-by-step explanation:

3/4 is larger because since they have the same denominator (the bottom value), you compare the numerators (the top value). Whichever numerator is bigger gives you the larger fraction.

Answer: 3/4 is larger, this is simply because 3/4 is = 75%

whereas 1/4 = 25%

Answer:

Step-by-step explanation:

yes since they are both divisible by their denominators and equal the same thing

Answer:

yes, they are equivalent

Step-by-step explanation:

2/2 = (2/2)x(4/4) = 8/8 = 1

Answer:

Is the problem -3/4 + 1/2 or 3/4 + 1/2?

I'll just do both then.

-3/4 + 1/2 = -1/4

3/4 + 1/2 = 5/4 or 1 1/4

Step-by-step explanation:

You're welcome.

Answer:

[tex] \frac{3}{4 } + \frac{1}{2} [/tex]

take lcm of denominators i.e. 4and 2

so, the lcm of 4 and 2 is 4.

[tex] \frac{3}{4} + \frac{2}{4} [/tex]

[tex] \frac{3 + 2}{4} [/tex]

[tex] \frac{5}{4} [/tex]

Step-by-step explanation:

hope this will be helpful:)

Answer:

The probability that a randomly selected subject tested negative or did not use marijuana is 0.589.

Step-by-step explanation:

The data set that has the largest range is C. 5, 6, 75, which is calculated as 75 - 5 = 70.

To find the largest range, we need to calculate the difference between the highest and lowest value in each data set and compare them.

A. For 14, 19, 18, 35, 32, 38, 40, we have:

Range = 40 - 14 = 26

B. For 102, 105, 103, 110, we have:

Range = 110 - 102 = 8

C. For 5, 6, 75, we have:

Range = 75 - 5 = 70

D. For 1, 9, 2, 5, 4, 19, 2, 4, 3, we have:

Range = 19 - 1 = 18

Therefore, data set C has the largest range of 70.

Learn more about the range on:

https://brainly.com/question/27206337

#SPJ1

Answer:i don't know the answer

Step-by-step explanation: i don't konw

Answer: A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number is a number that is only divisible by 1 and itself.

Step-by-step explanation:

For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and so on, are prime numbers because they can only be divided by 1 and themselves without any remainder.

However, 4 is not a prime number because it can be divided by 1, 2, and 4, and 6 is not a prime number because it can be divided by 1, 2, 3, and 6.

Answer:

A prime number is a number that can be multiplied by one and itself~
eg- 2,3,5,7,11
Let me know if this helps

Answer:

2/5 of the cookie

Step-by-step explanation:

12 friends need to split 4 cookies

4 cookies needs to divided by 10 people

[tex]\frac{4cookies}{10 people}[/tex] = [tex]\frac{4}{10}[/tex]

simplify: [tex]\frac{4}{10} = \frac{2}{5}[/tex]

Answer:

The probability of winning second prize in a 5/45 lottery is 1 in 8,145. This is calculated by taking the total number of possible combinations (8,145) and dividing it by the total number of possible outcomes (1).

The Answer for the given functions are:

i) f(-3) = -14.

ii) g[f(0)] = -16.

iii) f[h(2)] = 13.

iv)  hᴏf(x) = 3x - 1.

v)  h-1(1) = -3.

Functiοn nοtatiοn is a way οf representing a functiοn using algebraic symbοls. It is a shοrthand way οf expressing a relatiοnship between twο quantities οr variables, where οne variable depends οn the οther.

i) Tο find f(-3), we substitute x = -3 in the expressiοn fοr f(x) and simplify:

f(-3) = 3(-3) - 5 = -9 - 5 = -14

Therefοre, f(-3) = -14.

ii) Tο find g[f(0)], we first evaluate f(0) and then substitute that value intο g(x):

f(0) = 3(0) - 5 = -5

g[f(0)] = g(-5) = 2(-5) - 6 = -10 - 6 = -16

Therefοre, g[f(0)] = -16.

iii) Tο find f[h(2)], we first evaluate h(2) and then substitute that value intο f(x):

h(2) = 2 + 4 = 6

f[h(2)] = f(6) = 3(6) - 5 = 18 - 5 = 13

Therefοre, f[h(2)] = 13.

iv) Tο find hᴏf(x), we substitute f(x) intο the expressiοn fοr h(x) and simplify:

hᴏf(x) = h[f(x)] = f(x) + 4 = (3x - 5) + 4 = 3x - 1

Therefοre, hᴏf(x) = 3x - 1.

v) Tο find h-1(1), we need tο sοlve fοr x in the equatiοn h(x) = 1:

h(x) = x + 4 = 1

Subtracting 4 frοm bοth sides, we get:

x = 1 - 4 = -3

Therefοre, h-1(1) = -3.

To learn more about function notation, Visit

https://brainly.com/question/27915724

#SPJ1

Answer:

Second option [tex]y=\text{log}(2\text{x})+3[/tex]

Solution:

Based on the family of graphs shown in the attached file, the equation could represent the graph is [tex]y=\text{log}(2\text{x})+3[/tex]

This graph is the graph of the function [tex]y=\text{log}(\text{x})[/tex] stretched horizontally by a factor of 2 and translated 3 units upward.

Answer:

B

Step-by-step explanation:

Edge 2023

The simulation suggests that the chef's estimation of 30% broccoli soup orders is reasonable, but actual orders will vary from one set of customers to the next.

The chef's estimation of 30% broccoli soup orders seems reasonable based on the probabilities given, but the actual number of broccoli soup orders will likely vary from one set of 10 customers to the next. To estimate the accuracy of the chef's estimation, she conducts a simulation by shuffling cards representing the soup choices and randomly selecting one for each of the 10 customers. She repeats this process five times.

Based on the simulation results, we can see that the actual number of broccoli soup orders varies quite a bit from the expected value of 1.5. However, this is to be expected due to the random nature of the simulation.

To further estimate the accuracy of the chef's estimation, we could calculate the mean and standard deviation of the results to get a better sense of the distribution of possible outcomes.

Overall, the simulation suggests that the chef's estimation of 30% broccoli soup orders is a reasonable estimate, but the actual number of broccoli soup orders will likely vary from one set of 10 customers to the next.

To learn more about estimation please click on below link        

https://brainly.com/question/30982574

#SPJ1

Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

Answer:

53 in2 is the answer for this question

Answer:

53

Step-by-step explanation:

If you divide the figure into two parts by extending the 4 in side, you get a right triangle and a rectangle.

Area of rectangle:

6*8 = 48 in²

Area of triangle:

1/2*(13 - 8)*(6 - 4) = 1/2 times 5 times 2 = 5 in²

Total area is:

48 + 5 = 53 in²

hope this helps x

Answer:

1/3

Step-by-step explanation:

Answer: D. 9.68

Step-by-step explanation:

145.2 oz/ 15 cups = 9.68 oz per cup

On solving the provided question, we can say that - the value of the simple interest will be $ 881.28.

Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. The interest rate on the loan is known as this percentage.

here,

we have

P = 1360;

R = 5.4 ;

T = 12

so, we get,

SI = 1360 X 5.4 X 12 /100

SI =88128/100

= 881.28

Hence, On solving the provided question, we can say that - the value of the simple interest will be $ 881.28.

To know more about simple interest visit:

https://brainly.com/question/25845758

#SPJ9

Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is used in various fields such as mathematics, statistics, science, and finance to make predictions and analyze data.

Here,

1. The z-score for a sample mean of $75 is calculated as:

z = (75 - 76) / (6 / √(40)) = -2.36

Using a z-table, the probability of a z-score less than -2.36 is 0.0099 (rounded to 4 decimal places).

2. The z-score for a sample mean of $75 is calculated as:

z1 = (75 - 76) / (6 / √(40))

= -2.36

The z-score for a sample mean of $77 is calculated as:

z2 = (77 - 76) / (6 / √(40))

= 0.79

Using a z-table, the probability of a z-score between -2.36 and 0.79 is 0.8669 (rounded to 4 decimal places).

3. The z-score for a sample mean of $77 is calculated as:

z1 = (77 - 76) / (6 / √(40))

= 0.79

The z-score for a sample mean of $78 is calculated as:

z2 = (78 - 76) / (6 / √(40))

= 1.57

Using a z-table, the probability of a z-score between 0.79 and 1.57 is 0.0823 (rounded to 4 decimal places).

4. The standard error of the mean (SEM) is calculated as:

SEM = standard deviation / sqrt(sample size)

SEM = 6 / √(40) = 0.9487

The z-score for a sampling error of $1.50 is calculated as:

z = 1.50 / 0.9487 = 1.58

Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).

To know more about probability,

https://brainly.com/question/30034780

#SPJ1

Answer:

Step-by-step explanation:

To find the utility-maximizing bundle of goods, we need to solve for the values of x and y that maximize U while still satisfying the budget constraint. The budget constraint can be written as:

2x + 4y = 24

or

x + 2y = 12

We can use the method of Lagrange multipliers to solve for the utility-maximizing values of x and y subject to this constraint. The Lagrangian function is:

L = 3x^(2/3)y^(-1/3) + λ(x + 2y - 12)

Taking partial derivatives with respect to x, y, and λ, we get:

dL/dx = 2x^(-1/3)y^(-1/3) + λ = 0

dL/dy = -x^(2/3)y^(-4/3) + 2λ = 0

dL/dλ = x + 2y - 12 = 0

Solving these equations simultaneously, we get:

x = 6

y = 3

So the utility-maximizing bundle is 6 units of x and 3 units of y.

To see if the individual is better off with the government intervention, we can plot the budget line and the indifference curve for the utility-maximizing bundle with and without the limit on x.

Without the limit, the budget line is the same as before (x + 2y = 12), and the indifference curve for the utility-maximizing bundle passes through the point (6, 3) on the graph.

With the limit, the budget line becomes x = 4, since the individual is prohibited from purchasing more than 4 units of x. The corresponding budget line has a slope of -1/2 and intercepts the y-axis at 6.

If we draw the indifference curve for the utility-maximizing bundle of (4,4), which lies on the budget line, we can see that the individual is not better off with the government intervention. This is because the slope of the budget line under the intervention is steeper, so the individual would have to give up more y than x to afford the same amount of utility. Thus, the individual would have to move to a lower indifference curve with lower utility.

Therefore, the individual is not better off with the government intervention.

Answer:

The temperature on the eighth day is 80.

Step-by-step explanation:

Let t = temperature on the eighth day.

[tex] \frac{71 + 80 + 69 + 80 + 73 +77+ 70 + t}{8} = 75[/tex]

[tex] \frac{520 + t}{8} = 75[/tex]

[tex]520 + t = 600[/tex]

[tex]t = 80[/tex]

Note that,
the encrypted message for "OK" is the pair of numbers (616, 2385).
and the final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).

To encrypt a message using RSA, we need to first represent the message as numbers using a suitable encoding scheme. For simplicity, we can use the ASCII code for each character, which is a standard encoding scheme for text.

a) To encrypt "OK", we first convert each letter to its corresponding ASCII code:

"O" = 79

"K" = 75

Next, we use the RSA encryption formula:

C ≡ [tex]M^{e}[/tex] (mod n)

For "O", we have C ≡ 79¹¹ (mod 2911) ≡ 616 (mod 2911)

For "K", we have C ≡ 75¹¹ (mod 2911) ≡ 2385 (mod 2911)

Therefore, the encrypted message for "OK" is the pair of numbers (616, 2385).

b) To encrypt "HELP", we break it up into two blocks:

Block 1: "HE"

Block 2: "LP"

For block 1, we have:

"H" = 72

"E" = 69

Using the RSA encryption formula, we get:

C1 ≡ 72¹¹ (mod 2911) ≡ 738 (mod 2911)

C2 ≡ 69¹¹ (mod 2911) ≡ 1277 (mod 2911)

Therefore, the encrypted message for "HE" is the pair of numbers (738, 1277).

For block 2, we have:

"L" = 76

"P" = 80

Using the RSA encryption formula, we get:

C3 ≡ 76¹¹ (mod 2911) ≡ 1479 (mod 2911)

C4 ≡ 80¹¹ (mod 2911) ≡ 2252 (mod 2911)

Therefore, the encrypted message for "LP" is the pair of numbers (1479, 2252).

The final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).

Learn more about Encrypted Message on:

https://brainly.com/question/30408255

#SPJ1

So the Greatest Common Factor of The given expressions is -63x²y, 9x³y³, and 90x³y is 9x²y.

In mathematics, an expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷, etc.) that represents a value or a quantity. Expressions can be simple or complex, and they can involve arithmetic operations, functions, and algebraic operations. Expressions can be evaluated, simplified, or manipulated using mathematical rules and techniques. They are used in many areas of mathematics, including algebra, calculus, and geometry, as well as in other fields such as physics, engineering, and economics.

Here,

To find the greatest common factor (GCF) of the given terms, we need to factor out any common factors of the coefficients and variables.

-63x²y = (-1) × 3² × 7 × x² × y

9x³y³ = 3² × x³ × y³

90x³y = 2 × 3² × 5 × x² × y

The common factors among these terms are 3², x², and y. Therefore, the GCF of the given terms is:

GCF = 3² × x² × y

= 9x²y

To know more about expression,

https://brainly.com/question/1859113

#SPJ1