The list represents temperatures for the month of June,
rounded to the nearest degree Fahrenheit. Complete the
frequency table.
93, 85, 97, 79, 104, 88, 92, 94, 97, 87,
78, 95, 101, 93, 97, 99, 87, 103, 90, 95,
102, 97, 99, 91, 95, 92, 101, 89, 99, 98
Temperature (F)
71-80
100
Days

We assume the intensity function is

[tex]f(x) = 50,000(0.975^x) . . . . x[/tex]

Use 200 for x and do the arithmetic.

If the coefficient of x in the objective function is less than the ratio of the coefficient of x in one of the constraint equations to the coefficient of the corresponding decision variable, then increasing the coefficient of x in the objective function will not change the optimal solution.

To determine the maximum amount that the coefficient of x in the objective function can be increased. Let's assume that this ratio is r.

If the current coefficient of x in the objective function is less than r, then the optimal solution will not change if the coefficient of x is increased by any amount.

If the current coefficient of x in the objective function is equal to r, then the optimal solution will not change if the coefficient of x is increased by any amount that does not violate the constraint equation with the smallest ratio.

If the current coefficient of x in the objective function is greater than r, then the optimal solution will change if the coefficient of x is increased by an amount that is greater than or equal to the difference between the current coefficient of x and r.

Therefore, the maximum amount that the coefficient of x in the objective function can be increased without changing the optimal solution depends on the ratio of the coefficient of x to the coefficient of the corresponding decision variable in the constraint equations.

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The initial population of the bacteria culture is 200 bacteria.

The initial population of the bacteria culture can be determined using the equation for exponential growth: P(t)=P0(1+rt), where P(t) is the population after time t, P0 is the initial population, and r is the relative growth rate.

In this case, after 2 hours, the population is 600 and after 8 hours the population is 75,000. Plugging in the values, we get P0 = 600/(1+2*r), or P0 = 600/3. Thus, the initial population of the bacteria culture is 600/3 = 200 bacteria.

Exponential growth is a function of time and rate of growth. It is often used to model population growth or decay, such as in this case. The equation for exponential growth states that the population at any time is equal to the initial population multiplied by the rate of growth at each unit of time.

In this case, the rate of growth (r) is constant over the time period, so the population can be determined by putting in the values for P(t) and P0 and solving for r. Then, using the same equation, the initial population (P0) can be determined.

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For Snowman A:

The initial height of Snowman A is 28 inches, and it decreases by 4 inches per hour. So, the equation for the height of Snowman A in terms of t hours after sunrise is:

A = 28 - 4t

For Snowman B:

The initial height of Snowman B is 46 inches, and it decreases by 7 inches per hour. So, the equation for the height of Snowman B in terms of t hours after sunrise is:

B = 46 - 7t

To find when both snowmen have an equal height, we need to set A and B equal to each other and solve for t:

28 - 4t = 46 - 7t

3t = 18

t = 6

Therefore, both snowmen will have an equal height of 16 inches after 6 hours.

The unit price of the red ribbon is $0.88 per meter.

What is rate ?

A rate is a measure of the speed of something in relation to another quantity or measurement. It is a ratio that expresses how much of one quantity occurs in a given amount of another quantity. In other words, it is a comparison of two different measurements.

To find the unit price of the red ribbon, we need to divide the total cost by the number of units (in this case, meters) in the roll:

Unit price =  cost / Number of units

In this case, the total cost is $7.92 and the number of units is 9 meters. So, we have:

Unit price = $7.92 / 9 meters

Using a calculator or by performing long division, we can simplify this expression to find the unit price:

Unit price = $0.88 per meter

Therefore, the unit price of the red ribbon is $0.88 per meter.

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The outer perimeter of the composite figure is calculated to the nearest hundredth as: 55.70 feet.

The outer perimeter of the composite figure that is shown below which consist of a semicircle and a triangle, can be calculated using the formula below:

Perimeter = 1/2(2πr) + 2(s), where:

s = slant height of the triangle = 20 ft

r = radius of the semicircle = 10/2 = 5 ft

Substitute the values:

Perimeter = 1/2 * (2 * 3.14 * 5) + 2(20)

Perimeter = 55.70 feet

Thus, rounding to the nearest hundredth, the perimeter is calculated as: 55.70 feet.

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Answer:

6 pieces of the original pizza remain.

Step-by-step explanation:

Initially, the pizza was divided into 16 equal pieces. Violet and Sophie each ate 1/8 of the pizza on Friday, so a total of 1/8 + 1/8 = 1/4 of the pizza was eaten on Friday.

This means that 3/4 of the pizza remained after Friday.

The next day, Sophie ate 1/2 of the remaining pizza. So she ate 1/2 * 3/4 = 3/8 of the original pizza.

Therefore, the amount of pizza that remains is 3/4 - 3/8 = 3/8 of the original pizza.

To convert this fraction to a number of pieces, we need to multiply it by the total number of pieces the pizza was divided into:

3/8 * 16 = 6 pieces

Answer: $4.22

Step-by-step explanation:

bananas: 2kg x [tex]\frac{2.10}{5kg}[/tex] = $0.84

mangoes: 3kg x [tex]\frac{2.48}{4kg}[/tex] = $1.86

pineapples: 2kg x [tex]\frac{2.28}{3kg}[/tex] = $1.52

add together:

$4.22

Answer:

120°

Step-by-step explanation:

The sum of the measurement of the interior angles of a parallelogram is 360

t +  2t + t + 2t = 360  Combine like terms

6t = 360  Divide both sides by 6

[tex]\frac{6t}{6}[/tex] = [tex]\frac{360}{6}[/tex]

t = 60

If t = 60, then 2t = 120

Helping in the name of Jesus.

Answer: 240,000= .6x and/or 400,000

Step-by-step explanation:

If 240,000 is 60% of our answer, we can write the equation as...

240,000= .6x

In order to find the answer, (I am unsure if you need it) we would divide both sides by .6.

This would leave us with 400,000.

The measure of angle P = 67.38, calculated the trigonometric function value, we get the same answer.

We have all sides of the triangle, so we can calculate the trigonometric function value of angle P :

sin P = 12/13 ≈ 0.9231

Since △PQR is a right-angled triangle, we can use the cosine or sine or tan rule to find the ∠P

1) Sine

sin ∠P = opposite/ hypotenuse = 12/13

∠P = sin −1 (12/13) = 67.38

(2) Cosine

cos ∠P = adjacent/ hypotenuse = 5/13

∠P = cos−1 (5/13) = 67.38

(3) tan

tan ∠P = opposite/ adjacent = 12/5

∠P = tan−1 (12/5) = 67.38

Hence, as you can see that whichever rule is being used, the answer will always be the exact same.

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The true equations from the given trig. expressions can expressed as;|

From trigonometery tabel the value of the given angles are:

Cos 37 = 0.7986

Sin 53 = 0.7986

Tan 37 = -0.840

Tan 53 =  -0.431

sin 37=-0.644

cos 53 = -0.918

sin37 = -0.644

Sin (90 – θ) = Cos θ

Then we can now be testing the options one after the other by equatiing the terms in right hand side to the one in the left hand sides after doind this we can see that the foirst and the last options are true statement

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According to the question the equation has been solved by using Pythagorean. The left-hand side of the identity simplifies to [tex]cos^2(x)[/tex]

The Pythagorean Theorem can be used to find the correct angled triangle's missing length. The triangle contains three sides: the hypotenuse, this same opposite, which will always be the longest, and the adjacent side, which really doesn't touch the hypotenuse. The Pythagorean equation is: [tex]a^2+b^2=c^2.[/tex]

We can start by using the reciprocal identity for cosecant:

[tex]cos(x) = 1/sin(x)[/tex]

Then, we substitute this into the left-hand side of the identity:

[tex]sin(x)(csc(x) - sin(x)) = sin(x)(1/sin(x) - sin(x))\\= sin(x)/sin(x) - sin^2(x)\\= 1 - sin^2(x)[/tex]

Using the Pythagorean identity for sine and cosine, we know that:

[tex]1 - sin^2(x) = cos^2(x)[/tex]

Thus, the left-hand side of the identity simplifies to [tex]cos^2(x)[/tex], which is equal to the right-hand side of the identity.

Therefore, the identity is verified.

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Answer:

her mistake was in step2.

Step-by-step explanation:

in the parenthesis 4.5^2 would be 20.25 then you would multiply by 2 and get 40.5.

from there you can x by 3.14

value of variable x in the circle is 4unit.

A circle is a two-dimensional form that may be described as a collection of points that are equally spaced out from the centre.

The area of a circle is also an important property, and is given by the formula A = πr^2, where r is the radius. The circle is used in many fields, including mathematics, science, engineering, and art, and is often used to represent concepts such as unity, wholeness, and infinity.

Circles are found in many natural and man-made objects, such as wheels, clocks, planets, and bubbles. They are also used in various applications, such as in navigation, architecture, and computer graphics.

AE=8

CE=12

DE=x

BE=6x

As we know that

AE×CE=DE×BE

8×12=x×6x

96=6x²

x²=16

x=4

Hence, value of variable x in the circle is 4unit.

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A 99% confidence interval for the difference in mean wait times for ambulance and self-transported patients is  (0.15, 3.33) minutes. Since the interval includes 0, we cannot conclude that the difference in mean wait times is statistically significant at a 99% level of confidence.

To estimate the difference between the mean wait times for ambulance-transported patients and self-transported patients, we can use the two-sample t-interval for the difference in means, assuming equal variances:

[tex]$\bar{x}_1 - \bar{x}2 \pm t{\alpha/2, n_1 + n_2 - 2} \times \sqrt{\frac{s_p^2}{n_1}+\frac{s_p^2}{n_2}}$[/tex]

[tex]$\bar{x}1$ and $\bar{x}2$[/tex]where are the sample means, [tex]$s_p$[/tex] is the pooled standard deviation, [tex]$n_1$[/tex] and [tex]$n_2$[/tex] are the sample sizes, and[tex]$t{\alpha/2, n_1 + n_2 - 2}$[/tex] is the critical value from the t-distribution with[tex]$n_1 + n_2 - 2$[/tex] degrees of freedom.

Substituting the given values, we get:

[tex]$\bar{x}_1 - \bar{x}_2 \pm 2.626 \times \sqrt{\frac{8.30^2}{77}+\frac{5.16^2}{73}}$$\implies 6.04 - 4.30 \pm 2.626 \times \sqrt{\frac{8.30^2}{77}+\frac{5.16^2}{73}}$[/tex]

[tex]$\implies 1.74 \pm 1.59$[/tex]

Thus, the 99% confidence interval for the difference between the mean wait times is (0.15, 3.33) minutes.

To determine whether the difference in mean wait times is statistically significant based on the confidence interval, we need to check if the interval contains zero. Since the interval does not contain zero, we can conclude that the difference in mean wait times between ambulance-transported patients and self-transported patients is statistically significant at the 99% confidence level.

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--The given question is incomplete, the complete question is given

"Patients with heart-attack symptoms arrive at an emergency room either by ambulance or self- transportation provided by themselves, family, or friends. When a patient arrives at the emergency room, the time of arrival is recorded. The time when the patient's diagnostic treatment begins is also recorded An administrator of a large hospital wanted to determine whether the mean wait time time between arrival and diagnostic treatment) for patients with heart-attack symptoms differs according to the mode of transportation. A random sample of 150 patients with heart-attack symptoms who had reported to the emergency room was selected. For each patient, the mode of transportation and wait time were recorded. Summary statistics for each mode of transportation are shown in the table below. Mode of Transportation Sample Size Mean Wait Time Standard Deviation (in minutes) of Wait Times (in minutes) 6.04 4.30 8.30 5.16 Ambulance Self 77 73 (a) Use a 99 percent confidence interval to estimate the difference between the mean wait times for ambulance-transported patients and self-transported patients at this emergency room. You may assume that conditions for inference are met. (b) Based only on this confidence interval, do you think the difference in mean wait times is statis- tically significant? Justify your answer."--

it will take 12 months for Muhammad's account balance to surpass Connor's, assuming they continue to deposit amount at the same rate. After 12 months, Muhammad's balance will be $950 ($158 + $59x) and Connor's balance will be $896 ($74 + $66x).

To solve this problem, we can start by finding the monthly difference in their deposits:

Muhammad: $59/month

Connor: $66/month

Since Muhammad's monthly deposit is lower than Connor's, we need to find out how many months it will take for Muhammad's balance to catch up to and surpass Connor's. We can set up an equation to represent this situation:

$158 + $59x = $74 + $66x

where x is the number of months elapsed.

We can simplify and solve for x:

$158 + $59x - $74 - $66x = 0

$84 - $7x = 0

$7x = $84

x = 12

Therefore, it will take 12 months for Muhammad's account balance to surpass Connor's, assuming they continue to deposit money at the same rate. After 12 months, Muhammad's balance will be $950 ($158 + $59x) and Connor's balance will be $896 ($74 + $66x).

the complete question is :

Muhammad has $158 in his bank account and deposits $59 per month into his account. Connor has $74 in his bank account and deposits $66 per month into his account. If Muhammad and Connor continue to deposit money into their accounts at the same rate, how long will it take for Muhammad's account balance to surpass Connor's?

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A statement about the seeds in the remaining packets is best supported by this information include the following: B. Between 50 and 100 seeds will sprout.

Based on the information provided about the packets of tomato seeds, we can logically deduce the following parameters;

Number of packets of tomato seeds = 6 packets.

Number of seeds in each packet = 24 seeds.

Next, we would determine the total number of seeds in six (6) packet by multiplying the number of packets of tomato seeds by the number of seeds in each packet as follows;

Total number of seeds = 6 × 24

Total number of seeds = 144 seeds.

Since 15 seeds sprouted in one packet of 24 seeds, the ratio can be calculated as follows;

Ratio = 15 : 24

Sprouted seeds = 144 × 15/24

Sprouted seeds = 90 seeds.

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Complete Question:

Mari bought 6 packets of tomato seeds. Each packet contained 24 seeds. She planted 1 packet of the seeds, and 15 seeds sprouted.

Which statement about the seeds in the remaining packets is best supported by this information?

No more than 50 seeds will sprout.

Between 50 and 100 seeds will sprout.

At least 100 but no more than 120 seeds will sprout.

All 120 seeds will sprout.

Sin(300°) = -√3 / 2 .

a. True: We need to know the size of the pizza in order to calculate the unit price per square inch. Pi times the radius squared, or approximately 78.5 square inches, is the area of a 10-inch pizza.

b. False: We need to know the price of the entire pizza as well as the price per slice in order to determine if the restaurant would turn a profit by selling the 16-inch pizza by the slice. The cost is not specified in the problem, so we are unable to determine the profit.

c. False: The circumference of a circle is the distance around the edge, which is not directly related to the size of the pizza. To determine if the tray is big enough to hold the personal-sized pizza, we need to know the diameter or radius of the pizza. The radius of the personal pizza is 5 inches, which means the diameter is 10 inches. Therefore, the tray with a circumference of 32 inches is not big enough to hold the personal-sized pizza.

d. False: The area of the large pizza is pi times the radius squared, which is approximately 254.5 square inches. The area of the small pizza is pi times the radius squared, which is approximately 201 square inches. The difference between the areas is 254.5 - 201, which is approximately 53.5 square inches, not 2. Therefore, the statement is false.

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Let's assume that Mr. Paquette has x pencils.

From the problem, we know that for each pencil he has, he also has 3 pens. So the total number of pens he has is 3 times the number of pencils:

Number of pencils = x

Number of pens = 3x

The total number of pencils and pens combined is given as 8, so we can write:

x + 3x = 8

Simplifying, we get:

4x = 8

x = 2

Therefore, Mr. Paquette has 2 pencils and 3x2=6 pens.

The exact volume of the cone is 168π cubic feet and the approximated volume is 528 cubic feet

To find the volume of a cone, we can use the formula:

V = (1/3)πr²h

where r is the radius of the base and h is the height of the cone.

Since the diameter of the base is 12 feet, the radius is half of that, or 6 feet.

Using the given height of 14 feet, we can plug in the values into the formula:

V = (1/3)π(6²)(14)

V = (1/3)π(36)(14)

V = (1/3)π(504)

V = 168π

Therefore, the exact volume of the cone is 168π cubic feet.

If we want to approximate the value using 3.14 for π, we can use a calculator to get:

V ≈ 168 * 22/7

V ≈ 528

Therefore, the approximated volume of the cone is 528 cubic feet

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Glen spends average 1 1/2 times more hours writing the paper than finishing the project, so he spends 9x/(x+y) hours writing the paper and 9y/(x+y) hours finishing the project.

Glen spends a total of 9 hours writing a paper and finishing a project. We can define x as the number of hours he spends writing the paper and y as the number of hours he spends finishing the project. Since Glen spends 1 1/2 times more hours writing the paper than finishing the project, we can set up an equation that states that x = 1.5y. We can then substitute 1.5y for x in the equation for the total number of hours, 9x + 9y, and simplify it to 9(1.5y + y). This simplifies to 13.5y and since y = x/1.5, we can substitute x/1.5 for y and get 13.5(x/1.5). Simplifying this equation, we get 9x, meaning that Glen spends 9x hours writing the paper and 9y/(x+y) hours finishing the project.

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Answer:

x ∈ (0,75; +∞) and x∈ (1; +∞)

Step-by-step explanation:

1) 3 - 4x < 0

-4x < -3 / : (-4)

x > 0,75

x ∈ (0,75; +∞)

2) 2x - 4 > -2

2x > -2 + 4

2x > 2 / : 2

x > 1

x∈ (1; +∞)

the graph οf y=-2sin(-3x) οver the interval [0, 2π] will lοοk like a wave that οscillates 3 times between y=-2 and y=2, with a periοd οf 2π/3. The graph will start at the x-axis at y=0 and be reflected acrοss the x-axis.

In cοmputer science and mathematics, a graph is a cοllectiοn οf vertices (alsο knοwn as nοdes οr pοints) cοnnected by edges (alsο knοwn as links οr lines).

I can help yοu graph the functiοn y=-2sin(-3x) οver the interval [0, 2π].

Tο start, let's analyze the functiοn. The negative sign in frοnt οf the sine functiοn means that the graph will be reflected acrοss the x-axis. The 2 in frοnt οf the sine functiοn means that the amplitude οf the graph will be 2 units.

The argument οf the sine functiοn is -3x, which means that the periοd οf the graph will be 2π/3. This means that the graph will cοmplete 3 full οscillatiοns οver the interval [0, 2π].

Using this infοrmatiοn, we can sketch the graph as fοllοws:

At x=0, the sine functiοn is 0, sο the graph starts at the x-axis at y=0.

As x increases, the sine functiοn οscillates between -1 and 1, sο the graph οscillates between -2 and 2. Since the argument οf the sine functiοn is -3x, the graph cοmpletes οne full οscillatiοn fοr every 2π/3 increase in x.

At x=2π/3, the graph cοmpletes οne full οscillatiοn and returns tο the x-axis at y=0.

As x cοntinues tο increase, the graph repeats the same pattern every 2π/3 units οf x, until it cοmpletes 3 full οscillatiοns at x=2π.

Therefοre, the graph οf y=-2sin(-3x) οver the interval [0, 2π] will lοοk like a wave that οscillates 3 times between y=-2 and y=2, with a periοd οf 2π/3. The graph will start at the x-axis at y=0 and be reflected acrοss the x-axis.

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52,437 rounded to the nearest thousand is 53,000.

When we round a number to the nearest thousand, we want to find the closest multiple of 1,000 to the given number. To do this, we need to look at the digit in the hundreds place, which is the third digit from the right in the number.

In the case of 52,437, the digit in the hundreds place is 4. If this digit were less than 5, we would round down to the nearest thousand, but since it is 5 or greater, we need to round up. When we round up, we increase the value of the digit in the thousands place by 1 and replace all the digits after that with zeros.

In this case, the digit in the thousands place is 2, so we need to increase it to 3. The digits after the thousands place are already zeros, so we don't need to change them. Therefore, when we round 52,437 to the nearest thousand, we get:

52,437 rounded to the nearest thousand = 53,000

So 52,437 rounded to the nearest thousand is 53,000.

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El ángulo -3π / 4 está en el tercer cuadrante del plano cartesiano.

The greatest number of wristbands that can be made from a rectangular piece of paper that measures 18 centimeters by 85 centimeters is 36.

To calculate the greatest number of wristbands that can be made from a rectangular piece of paper that measures 18 centimeters by 85 centimeters, we need to divide the width of the paper by the width of each wristband, and then divide the length of the paper by the length of each wristband, and then multiply the two numbers together. The result will be the greatest number of wristbands that can be made from the paper.

Using the dimensions given in the question, and assuming that each wristband measures 1.5 centimeters by 22 centimeters (which is a typical size for a wristband), we can calculate the number of wristbands as follows:

Width of paper = 18 centimeters

Width of each wristband = 1.5 centimeters

Number of wristbands in width = (18 / 1.5) = 12

Length of paper = 85 centimeters

Length of each wristband = 22 centimeters

Number of wristbands in length = (85 / 22) ≈ 3.86 (round down to 3)

Total number of wristbands = (12 x 3) = 36

Therefore, the greatest number of wristbands that can be made from a rectangular piece of paper that measures 18 centimeters by 85 centimeters is 36.

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