pls help me with both of them

Pls Help Me With Both Of Them

Answers

Answer 1

The year that saw 164 billion dollars being spent on advertising, given the function for the advertising would be c. 1994

The dimensions of the rectangle, given the area of the rectangle would be:

Length : 12. 8 meters Width : 6.9 meters

How to find the year ?

The function is given by y = 0.93x² + 2.2x + 130, where y is the amount of money spent (in billions of dollars) and x is the number of years since 1990. We need to find the value of x when y = 164.

164 = 0.93x² + 2.2x + 130

0.93x² + 2.2x + 130 - 164 = 0

0.93x² + 2.2x - 34 = 0

x = 2.5

Now, we'll find the year by adding the value of x to 1990:

Year = 1990 + 2.5 = 1992.5

= 1994 which is the closest year in options

How to find the dimensions of the rectangle ?

The area of the rectangle is given by:

Area = width × length

91 = (x + 2)(2x + 3)

91 = 2x² + 3x + 4x + 6

91 = 2x² + 7x + 6

2x² + 7x - 85 = 0

When solved differently:
x = 4.9

x = -3.5

Using the positive values:

Width = x + 2 ≈ 4.9 + 2 = 6.9 meters

Length = 2x + 3 ≈ 2(4.9) + 3 ≈ 9.8 + 3 = 12.8 meters

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Related Questions

based solely on statistical probability from demographic studies, which individual has the greatest likelihood of being a smoker?

Answers

Based solely on statistical probability from demographic studies, the individual who has the greatest likelihood of being a smoker is a male aged between 18 to 24 years old.

According to demographic studies, men are more likely to smoke than women. Besides, the smoking rate increases with age, which means individuals aged between 18 to 24 have a higher likelihood of being a smoker than people of other ages.

Therefore, based solely on statistical probability from demographic studies, a male aged between 18 to 24 years old has the greatest likelihood of being a smoker.

It is important to note that statistical probability from demographic studies only shows what is likely or probable to happen but does not guarantee the actual occurrence of the event.

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For what values of a are the following expressions true?
(PLease help ASAP)
|a +5| = −5−a
|a +5 |=a +5

Answers

The equation |a + 5| = −5 − a is not true for any value of a, while the equation |a + 5| = a + 5 is true for values of a greater than or equal to -5.

The absolute value of a number is defined as the distance of the number from zero on a number line. Thus, |a + 5| is equal to the distance of (a + 5) from zero on a number line. Since distance is always non-negative, |a + 5| is always non-negative.

On the other hand, the expression −5 − a is always negative, since the sum of a negative number (-5) and any number (a) is always negative.

Therefore, for the equation |a + 5| = −5 − a to be true, the absolute value of (a + 5) would have to be negative, which is impossible since absolute value is always non-negative.

For the equation |a + 5| = a + 5 to be true, a must be greater than or equal to -5, because when a is greater than or equal to -5, (a + 5) is already non-negative, so the absolute value of (a + 5) is equal to (a + 5).

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What are the coordinates of the vertices of the figure after a reflection across y=2:
G (-3,3), H (-2,5), I (1,1)

Answers

Answer:

G (-3,-1)

H (-2,-3)

I (1,1)

Step-by-step explanation:

After a reflection across y=2, the y-coordinates of the vertices will change sign while the x-coordinates remain the same. Thus, the new coordinates of the vertices will be:

G (-3,-1)

H (-2,-3)

I (1,1)

Answer:

G (3,3) , H (2,5), I (-1,1)

Step-by-step explanation:

Since it’s flipped over the Y-Axis, the X-Axis numbers remain the same.

WRONG!!

didnt read the question correctly, so the vertices are incorrect lol.

1 point question at position 8 a stockout occurs when customer orders for a product exceed the amount of inventory kept on hand. suppose specialty toys management decides to order 15,000 units. using the demand distribution calculated earlier, what is the probability of a stockout? use 4 decimal places.

Answers

The probability using the demand distribution of a stockout is given as 0.6293.

a. profit if 15000 units are sold $120,000b. if there is demand for 15,000 units but orders only 18000 units profit is $87,000c. if there is demand for 18,000 units but orders only 24000 units profit is $78,000.

Out-of-stock situations, commonly referred to as stockouts, occur when a company runs out of a product that a client is prepared to purchase. Stockouts have a direct influence on customer satisfaction and are a major reason for bad reviews, additional expenses, and lost revenue or, worse, customers.

Let X = no of demand for the toy

μ =20,000

P(10000 < X < 30000) = 0.90

X follows  normal distribution

z=x−μ​/σ

P(10000 < X < 30000)=0.90

P((10000−20000​)/σ) < (x−20000​)/σ < (30000−20000​)/σ )=0.90

as probability is 0.90, the z-score =1.645.

(30000−20000)​/σ =1.645

10000​/σ=1.645

σ=10000​/1.645

σ=6079

1.P(X>15,000)

=P(Z> (15000−20000​)/6079)

=P(Z> −0.82)

=P(Z< 0.82)

=0.5+0.1293

=0.6293

2. P(X> 24000)

=P(Z> (24000−20000​)/6079)

=P(Z> 0.66)

=0.5−0.2454

=0.2546

3.Expected profit = (profit per unit )*(no of sold units) + (loss per unit )*(of units unsold)

profit = $8

loss = -$11

a. profit if 15000 units are sold =(8)(15000) + (-11)(0) = $120,000

b. if there is demand for 15,000 units but orders only 18000 units profit is (8)(15000) + (-11)(3000) = $87,000

c. if there is demand for 18,000 units but orders only 24000 units profit is (8)(18000)+(-11)(6000)= $78,000.

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Complete question:

(a) What is the expected profit if all 15,000 units are sold? type your answer...

(b) Suppose there is demand for 15,000 units, but Specialty Toys orders 18,000 units? What is the expected profit? type your answer...

(c) Suppose there is demand for 18,000 units, but Specialty Toys orders 24,000 units? What is the expected profit? type your answer... 15 3 points Based on what you know about the distribution of demand, the probability of stock-outs, and the expected profit, how many units of Weather Teddy do you recommend that Specialty Toys purchase?

suppose 60% of american adults believe martha stewart is guilty of obstruction of justice and fraud related to insider trading. we will take a random sample of 20 american adults and ask them the question. then the sampling distribution of the sample proportion of people who answer yes to the question is: group of answer choices

Answers

Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading.

We will take a random sample of 20 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is a binomial distribution.

What is a binomial distribution?

A binomial distribution is a statistical distribution that represents the likelihood of one of two outcomes in a sequence of independent trials. Binomial distributions can be used to model a variety of phenomena, including flipping coins, rolling dice, and performing multiple independent experiments.

The probability of getting k successes in n trials in a binomial distribution with probability of success p and probability of failure q is given by the following formula:P (k) = nCk * p^k * q^(n-k)Where nCk is the binomial coefficient, which represents the number of ways to select k items from a set of n items without regard to order.

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1. Divide and simplify. **Please show all work to receive full credit 1/x+4 ÷ x-3/ x²+7x+12​

Answers

After dividing and simplifying we get (x-3)/(x+3)

What is division?

One of the four fundamental operations of arithmetic, or how numbers are combined to create new numbers, is division. The additional operations are addition, subtraction, and multiplication.

At a fundamental level, counting the instances in which one number is contained within another is one interpretation of the division of two natural numbers. There is no requirement that this quantity be an integer. For instance, if there are 20 apples and they are divided equally among four people, each person will get 5 apples (see picture).

The integer quotient, which is the quantity of times the second number is entirely contained in the first number, and the remainder are both produced by the division with remainder or Euclidean division of two natural numbers.

1/(x+4) divide by  [tex](x-3)/(x^2 + 7x +12)[/tex]

Simplify : [tex]x^2 +7x +12[/tex]

[tex]x^2 + (3+4)x + 12[/tex]

[tex]x^2 + 3x +4x + 12[/tex]

[tex]x(x + 3) + 4(x + 3)[/tex]

[tex](x+3)(x+4)[/tex]

[tex]1/(x + 4) x (x-3)/(x+3)(x-4)[/tex]

After dividing and simplifying we get the following answer;

[tex]= (x-3)/(x+3)[/tex]

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Name 2 figures for which all cross sections taken at a particular orientation
are congruent.

Answers

Answer: Rectangular prism & Cylinder

Step-by-step explanation: In geometry, a rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The line segment joining the two centers is the axis, that denotes the height of the cylinder.

if the number of degrees of freedom for a chi-square distribution is 25, what is the standard deviation? round to four decimal places. standard deviation

Answers

The standard deviation for a chi square distribution for given degree of freedom is 7.0711.

The chi-square distribution is parameterized by the number of degrees of freedom (df). As the number of degrees of freedom increases, the shape of the distribution becomes more symmetrical and approaches a normal distribution.

The standard deviation (σ) of a chi-square distribution with k degrees of freedom is given by the formula:

σ = sqrt(2k)

Therefore, for a chi-square distribution with 25 degrees of freedom:

σ = sqrt(2(25)) = sqrt(50) ≈ 7.0711

Rounding this to four decimal places gives a standard deviation of approximately 7.0711.

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Grace plans on going to the amusement park this Friday. It costs $10.00 to enter the park, and then $2.50 for every ride that Grace goes on. What will be the total cost if Grace goes on 7 rides?

Answers

Answer: 27.50

Step-by-step explanation: 2.50 X 7 =17.50 + 10 = 27.50

What is the weight of a 48 kg girl on Earth? Round the answer to the nearest whole number.

___N

Answers

Answer:

remember, in order to calculate the weight on earth, we need to multiply the mass of the object with the force of Gravity (9.8 m/s^2 on earth)

so, her weight would be:

48 x 9.8 = 470.4 >>>>>>> Will be 470 if we round it to the nearest whole number.

Step-by-step explanation: Hope this helps. Mark me brainliest!! :)))

Answer: 470

Step-by-step explanation:

Find m∠AZJ using the figure below

Answers

In Linear pair, 52°  is the value ∠AZJ .

What is Linear pairs?

When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair's total angles are always equal to 180 degrees.

                                   A pair of adjacent angles is said to be a linear pair if the total of the two angles' (measured) angles is 180°. This means that a linear pair of angles always adds up to 180°. The linear pair of 30°, for instance, is 150°; the linear pair of 70°, 110°; etc.

∠JZF or ∠HZG

Linear pairs form supplementary angles.

 ∠AZJ = ∠AZH - ∠HZA

           = 90° - 38°

  ∠AZJ = 52°

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what is the probability that a senior nutrition major and then a sophomore non-nutrition major are chosen at random? express your answer as a fraction or a decimal number rounded to four decimal places.

Answers

Answer: 60%

Step-by-step explanation:

As mentioned earlier, we need to know the number of senior nutrition majors and sophomore non-nutrition majors to calculate the exact probability. Without this information, we cannot provide a specific answer to the question.

However, we can provide a general formula for computing the probability, assuming that the selections are made without replacement and the population of students is large enough to assume independence:

Probability of selecting a senior nutrition major and then a sophomore non-nutrition major = (Number of senior nutrition majors / Total number of students) × (Number of sophomore non-nutrition majors / (Total number of students - 1))

Once we have the values for the number of senior nutrition majors and sophomore non-nutrition majors, we can substitute them into this formula to obtain the probability, which will be a decimal number rounded to four decimal places.

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WILL MAKE U BRAINLIST! HELPS PLS AND SHOW ALL STEPS

Answers

Answer:

................

Step-by-step explanation:

.................

The area of the patio is enter your response here ​, so the cost of concrete is ​$ enter your response here. The area of the garden is enter your response here ​, so the cost of soil is ​$ enter your response here. The total area of the deck is enter your response here ​, so the cost of wood is ​$ enter your response here. ​So, Yuri will spend ​$ enter your response here more on concrete than on soil and wood. ​(Type integers or​ decimals. )

Answers

Yuri will spend $ X more on concrete than on soil and wood.

When answering questions on Brainly, it is important to be factually accurate, concise, and professional.

It is also important to provide a step-by-step explanation of how you arrived at your answer.

The question is asking about the cost of materials for a patio, garden, and deck.

Let's break down the information we have.

Area of the patio = enter your response

Here

Cost of concrete = $ enter your response

Here

Area of the garden = enter your response

here

Cost of soil = $ enter your response

here

Total area of the deck = enter your response

here

Cost of wood = $ enter your response

here

Yuri will spend $ enter your response here more on concrete than on soil and wood.

To find the cost of each material, we need to multiply the area by the cost per unit area.

For example, the cost of concrete would be the area of the patio multiplied by the cost of concrete per unit area.

Let's call the cost per unit area for concrete C, the cost per unit area for soil S, and the cost per unit area for wood W.

Area of patio = P

Cost of concrete = C

Area of garden = G

Cost of soil = S

Total area of deck = D

Cost of wood = W

Yuri will spend X more on concrete than on soil and wood.

To find the values of P, C, G, S, D, and W, we need to use the information given in the question.

However, some values are missing.

We can use the given information to create equations that will help us find these values.

For example, we know that the total area of the deck is the sum of the area of the patio and the area of the garden, so we can write:

D = P + G

Similarly, we can write an equation for the cost of each material.

For example, the cost of concrete is the area of the patio multiplied by the cost per unit area for concrete, so we can write:

C = P * C

Similarly, we can write equations for the cost of soil and wood:

S = G * W, W = D * W

Now we have three equations and three unknowns: P, G, and D. We can solve this system of equations to find these values.

Let's solve for P and G first.

We'll use the equation

D = P + G

to eliminate G from the equations.

C = P * CS = G * WP = D - G

Substitute P = D - G into the first two equations.

C = (D - G) * CW = D * W - G * W

Now we have two equations and two unknowns: D and G.

We can solve for these values.

We'll use the equation

W = D * W - G * W

to eliminate W from the equations.

C = (D - G) * CS = G * SD = P + G = 2G - (W / C)

Substitute D = P + G into the first two equations.

C = P * C + G * CS = G * SW = P + G - DC = P * C + (D - P) * C + (W / C) * C = 2P * C + W

We can now solve for P, G, and D.

P = (C + S + W / C) / 2G = (S + W / C) / 2D = P + G = (C + S + W / C) / 2 + (S + W / C) / 2P = enter your response

here

C = enter your response

here

S = enter your response

here

W = enter your response

here

G = enter your response

here

D = enter your response

here

Now we can find the value of X, which is the difference between the cost of concrete and the combined cost of soil and wood.

X = C - (S + W)X = enter your response.

The area of the patio is enter your response here ​, so the cost of concrete is ​$ enter your response here. The area of the garden is enter your response here ​, so the cost of soil is ​$ enter your response here. The total area of the deck is enter your response here ​, so the cost of wood is ​$ enter your response here.

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Question:

Yuri bought a new house. The diagram shows the layout of his backyard. Yuri is designing improvements that he wants to make. Yuri plans to fill the patio with concrete, the garden with a special soil mixture, and the remaining areas that surround the hot tub with a wood deck. The table shows the costs associated with each project. How much more will Yuri spend on concrete than on soil and wood?

now fit a logistic model with a single explanatory variable mcat scores. why is the null deviance the same as that from part a.?

Answers

The MCAT scores variable can predict some of the variation in the response variable.

The logistic regression model is a type of regression analysis that is widely used in various fields. A logistic model can be fitted using the glm() function in R. Now fit a logistic model with a single explanatory variable, MCAT scores.In logistic regression, the null deviance is the deviance for a model that has only the intercept. The null deviance will always be equal to the residual deviance if the model has only the intercept.The null deviance is calculated based on the difference between the saturated and null models' likelihoods. It is the amount of variation in the response variable that cannot be explained by the model when no predictor variables are used. When the single predictor variable MCAT scores is added to the null model, it reduces the null deviance by 11.59. This is significant because it indicates that the MCAT scores variable can predict some of the variation in the response variable.

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Which of the contexts below represents exponential growth?

A town's population shrinks at a rate of 8.1% every year.
A taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile.
A town's population grows at a rate of 4% every year.
A radioactive compound decays at a rate of 5% per hour.

Answers

The exponential function [tex]P(t) = P0 \times 1.04^t[/tex] represents the exponential growth of Option C: A town's population grows at a rate of 4% every year.

What is an exponential function?

The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The context that represents exponential growth is "A town's population grows at a rate of 4% every year."

Exponential growth occurs when a quantity grows at an increasing rate over time, which is exactly what is happening with the population of the town.

As the population grows, the growth rate also increases, resulting in an exponential increase over time.

Let P(t) be the population of the town after t years, where t is a positive integer.

The exponential function that models the population growth is -

[tex]P(t) = P0 \times (1 + r)^t[/tex]

where P0 is the initial population, r is the growth rate as a decimal, and t is the time in years.

In this case, the growth rate is 4% per year, which can be written as a decimal as r = 0.04.

Therefore, the exponential function for the town's population growth is -

[tex]P(t) = P0 \times (1 + 0.04)^t[/tex]

Simplifying the expression, we get -

[tex]P(t) = P0 \times 1.04^t[/tex]

This function can be used to calculate the population of the town after a given number of years, assuming the growth rate remains constant.

In contrast, the other contexts represent either a steady decrease (town's population shrinking at a rate of 8.1% per year and the radioactive compound decaying at a rate of 5% per hour) or a linear increase (taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile).

Therefore, the exponential growth is displayed by town's population growing 4% every year.

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This is parallelograms practice and I don’t get it at all!! Please help me guys

Answers

Step-by-step explanation:

p-grams have equal opposite side lengths

soooo  

 5x+7   =  27  

               x = 4

then 22x = 22(4) = 88  units      ( this is also AB length)

The ratio of ounces to pounds is 16:1. A veterinarian is treating a dog that weighs 46 pounds. To calculate the correct amount of medicine, the vet must convert the dog's weight
ounces. Which ratio shows the conversion to ounces?

Answers

The correct option is c: 46lb x (16 oz / 1lb). Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.

Explain about the unit conversion?

The same attribute is expressed using a unit conversion, but in a different measurement unit. For example say, time can be mentioned in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Measurements are frequently offered in one set of measurements, like feet, but are required in another set, like chains. A conversion factor is a mathematical equation that facilitates an equal exchange of feet for chains.

Given data:

ratio of ounces to pounds = 16:1

16 ounce / 1 pound

Let the weight of dog in ounce be 'x'.

weight of dog in pounds = 46 pounds.

ratio : x ounce /  46 pounds

Equating both ratios:

16 ounce / 1 pound = x ounce /  46 pounds

Cross multiplying:

x = 16*46  ounce

x = 736 ounce

The correct option is c: 46lb x (16 oz / 1lb)

Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.

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Complete question is-

The ratio of ounces to pounds is 16:1. A veterinarian is treating a dog that weighs 46 pounds. To calculate the correct amount of medicine, the vet must convert the dog's weight

ounces. Which ratio shows the conversion to ounces?

The full question is attached.

15. Anna has $2.00 in change, including 5 quarters. What is the maximum number of dimes she can have? A 2 C 7 B 5 D 9​

Answers

Answer:

To solve the problem, we need to first determine the value of the quarters Anna has. Since there are 5 quarters, we have:

5 quarters = 5 x $0.25 = $1.25

Thus, Anna has $2.00 - $1.25 = $0.75 left. We can find the maximum number of dimes she can have by dividing this amount by the value of a dime, which is $0.10. Therefore:

$0.75 ÷ $0.10 = 7.5

Since Anna cannot have a fraction of a dime, we round down to the nearest whole number to get a maximum of 7 dimes. Therefore, the answer is option B, 5.

A publisher reports that 75% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 250 found that 69% of the readers owned a particular make of Car. Find the value of the test statistic. Round your answer to two decimal places

Answers

Rounded to two decimal places, the value of the test statistic is 0.41.

The value of the test statistic to compare the publisher's reported percentage of 75% and the marketing executive's claim that the actual percentage is different can be found by using the formula z = (p1 - p2)/(sqrt[p*(1-p)*((1/n1)+(1/n2))]), where p is the pooled proportion, p1 is the proportion of the publisher's readers owning the particular make of car, p2 is the proportion of the random sample owning the particular make of car, n1 is the total number of the publisher's readers, and n2 is the total number of the random sample.

In this case, p = [tex](75% + 69%)/2 = 72%, p1 = 75%, p2 = 69%, n1[/tex]is unknown, n2 = 250. Thus, the test statistic is z =[tex](75%-69%)/(sqrt[72%(1-72%)((1/n1)+(1/250))]) = 0.41.[/tex]

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There is an amoeba (a single-celled animal) on a dish.



After one hour, the amoeba divides to form two amoebas.

One hour later, each amoeba divides to form two more.

Every hour, each amoeba divides to form two more.



Write an expression for the number of amoebas after `24` hours.

Answers

An expression for the number of amoebas after 24 hours is 1 × 2²⁴ = 16,777,216

How do amoebas develop?

Single-celled creatures knοwn as amοebas reprοduce asexually. An amοeba begins tο reprοduce when its genetic material dοubles, twο nuclei are fοrmed, and it begins tο alter shape by develοping a thin "waist" in the centre. Typically, this prοcedure gοes οn until the cells are finally divided intο twο.

Amοeba reprοduce typically asexually thrοugh a prοcess called binary fissiοn. The cell splits intο twο daughter cells οf equal size fοllοwing the replicatiοn οf its genetic material by mitοtic divisiοn.

a. It is given that an amοeba divides tο fοrm twο amοebas after οne hοur sο there are 2 amοebas after 1 hοur.

b. It is given that οne hοur later, each οf the twο amοebas divides tο fοrm twο mοre amοebas sο there are 2×2=4 amοebas after 2 hοurs.

c. The number οf amοebas is dοubling after each hοur since each amοeba divides intο twο amοebas every hοur. This means that the number οf amοebas after 6 hοurs can be fοund by multiplying the οriginal number οf amοebas, which was 1, by 2 six times. The number οf amοebas after 6 hοurs is then 1 × 2⁶ = 2⁶= 64 amοebas.

d. Using the same pattern frοm part (c), the number οf amοebas after 24 hοurs is 1 × 2²⁴ = 2²⁴ = 16,777,216 amοebas.

Expression = 1 × 2²⁴ = 16,777,216

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a wooden artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees. how long ago was the artifact made?

Answers

The artifact was made about 3102.5 years ago.

An artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees, how long ago was the artifact made?

Carbon dating is used to estimate the age of organic materials, and it is used to determine the age of an artifact in this situation. The method used to estimate the age of an artifact based on its carbon-14 content is known as carbon dating. Carbon-14 has a half-life of 5,730 years. As a result, the amount of carbon-14 present in an object can be used to determine how long it has been since the object was last in contact with the atmosphere, and therefore how long it has been since it was alive.

Let C0 be the amount of carbon-14 present in living trees and C1 be the amount of carbon-14 present in the wooden artifact. After 5,730 years, C1 will have decayed to 1/2 of C0. After 2(5,730) = 11,460 years, C1 will have decayed to 1/4 of C0. After 3(5,730) = 17,190 years, C1 will have decayed to 1/8 of C0. After 4(5,730) = 22,920 years, C1 will have decayed to 1/16 of C0. After 5(5,730) = 28,650 years, C1 will have decayed to 1/32 of C0.

We'll have to solve the following equation to find the age of the artifact.

C1 = (70/100) * C0

Substitute the value of C0 into the equation and solve for t,

t = ln(0.7) / ln(1/2) = 3102.5 years

The artifact was made about 3102.5 years ago.

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a state's license plates consist of 4 letters followed by 5 digits. how many possible license plates can be issued using this condition?

Answers

In the following question, among the conditions given, There are 26^4 x 10^5 possible license plates that can be issued using this condition.

Hence, This is because the license plates consist of 4 letters and 5 digits. There are 26 possible letters that can be used in the first four places, so the total possible combinations of 4 letters is 26^4. There are 10 possible digits that can be used in the last five places, so the total possible combinations of 5 digits is 10^5. Multiplying these two together gives the total number of possible license plates: 26^4 x 10^5.

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There are a total of $26^4 × 10^5$ possibilities, which simplifies to 26,000,000,000 (twenty-six billion) possibilities. Therefore, with this condition, twenty-six billion license plates can be issued.

A state's license plates consist of 4 letters followed by 5 digits.

How many possible license plates can be issued using this condition?

When designing a license plate, the condition provided in the question suggests that a license plate should consist of 4 letters followed by 5 digits.

Therefore, we can count the total number of license plates in two phases.

The number of choices for each segment must be taken into account separately for the letters and the numbers.

When considering the letter possibilities, there are 26 options for each position since there are 26 letters in the alphabet.

For the first 4 positions, there are a total of $26^4$ = 456,976 possibilities.

Similarly, for the last 5 positions,

there are 10 options for each position since there are 10 digits.

There are $10^5$ = 100,000 possibilities for the last 5 positions.

The entire plate's total number of combinations is obtained by multiplying these numbers.

There are a total of $26^4 × 10^5$ possibilities

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how many ways are there to put 23 identical objects into 7 distinct containers so that no container is empty?

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This problem is a classic example of applying the stars and bars combinatorial method.

To solve this problem, we need to distribute 23 identical objects into 7 distinct containers so that none of the containers is empty. Let's start by assuming that each container has at least one object. This means we have distributed 7 objects, leaving 16 objects to be distributed.

We can now use the stars and bars method to distribute these 16 objects. Imagine placing all 16 objects in a line, and placing 6 dividers between them to separate them into 7 groups (one for each container). Each group will then receive the objects that are to the left of the divider.

For example, if we have the sequence OO|OOO|O|OOO|OO|OO|O, this corresponds to 2 objects in the first container, 3 objects in the second container, 1 object in the third container, and so on.

The number of ways to place the 6 dividers in the sequence of 16 objects is the same as the number of ways to choose 6 positions out of 16 to place the dividers. This can be computed using the formula for combinations:

$${16 \choose 6} = \frac{16!}{6!(16-6)!} = 8008$$

Therefore, there are 8008 ways to distribute 23 identical objects into 7 distinct containers so that no container is empty.

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a jar contains 21 brown and 19 blue marbles. a marble is drawn at random. what is the theoretical probability of drawing a blue marble?

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19/40 because there are in total 40 marbles and 19 of them are blue.

The theoretical probability of drawing a blue marble from a jar containing 21 brown and 19 blue marbles is 19/40, or 0.475.

To calculate this, divide the number of blue marbles by the total number of marbles in the jar. 19 divided by 40 equals 0.475, or 19/40. This means that there is a 47.5% chance of drawing a blue marble from the jar.

The probability of drawing a specific marble from the jar can be expressed using the formula P(A) = n(A)/n(T).

In this example, the probability P(A) is the chance of drawing a blue marble, n(A) is the number of blue marbles (19) and n(T) is the total number of marbles in the jar (40). Therefore, P(A) = 19/40 = 0.475.

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COFFEE A national coffee chain makes and serves 4 billion cups of coffee in a year. If the average cup of coffee costs $3.15, how much money does the coffee chain make in a year? Write your answer in scientific notation.

Answers

Answer: 1.26 × 10 to the 10th power

Step-by-step explanation:

The perimeter of a rectangular garden is 43. 8 feet. Its length is 12. 4 feet what is its width

Answers

The width of the rectangular garden is 9.5 feet.

Given that the perimeter of a rectangular garden is 43.8 feet and its length is 12.4 feet.

Let's assume the width of the rectangular garden be "w".

Now we need to find the width of the garden.

Solution: Perimeter of a rectangular garden is given by the formula: P = 2(l + w)

where l = length and w = width.

Substituting the given values in the above formula,

we get43.8 = 2(12.4 + w)

We can solve for "w" by simplifying the above equation.

43.8 = 24.8 + 2w43.8 - 24.8 = 2w19 = 2w

Dividing both sides by 2,we get

w = 9.5 feet.

Therefore, the width of the rectangular garden is 9.5 feet.

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Sasha had 30 minutes to do a three-problem quiz. She spent 8 3/4

minutes on questions A and 5 1/2

minutes on question B. How much time did she have left for question C?

Answers

add 8 3/4 and 5 1/2 to get 14 1/4. subtract 14 1/4 from 30. Sasha has 15 3/4 min left for question C.

how long will it take for $500 to amount to $850 at 10% simple interest? question 37 options: 7 years 5 years 3.5 years 10 years none of these

Answers

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 850\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years \end{cases} \\\\\\ 850 = 500[1+(0.1)(t)] \implies \cfrac{850}{500}=1+0.10t\implies \cfrac{17}{10}=1+0.10t \\\\\\ \cfrac{17}{10}-1=0.10t\implies \cfrac{7}{10}=0.10t\implies \cfrac{7}{(10)(0.10)}=t\implies 7=t[/tex]

Mrs. Garcia is ordering pizza for students in the Homework Club. A large two-topping pizza is 20% off the regular price of $15. Mrs. Garcia wants to know the sale price. Which equation can be used to find the sale price, s, of the pizza

s = 0.8(15) s = 0.1(15) S = 0.115 S=0.8 15

Regular Price 100% $15

Sale Price 80% $ ?

Discount 20%​

Answers

The equation that can be used to find the sale price, s, of the pizza is S = 0.8(15).

What is sale price?

It is the final amount paid for a product or service and is often lower than the original asking price.

This equation uses the percentage discount of 20%, which can be represented as 0.8, to find the sale price.

To calculate the sale price, the equation multiplies the regular price of $15 by the discount, 0.8.

0.8*15 =12

Therefore, the sale price of the pizza is $12.

The other equations are not correct because they do not take into account the percentage discount of 20%.

S = 0.1(15) does not consider the discount of 20%, as it is multiplying the regular price of $15 by 0.1, which is equivalent to 10%, not 20%.

Similarly, S = 0.115 is incorrect because it is multiplying the regular price of $15 by 1.15, which is equivalent to 115%, not 20%.

Lastly, S=0.8 15 is incorrect because it is not multiplying the regular price of $15 by the discount of 20%, which is 0.8.

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