If Allison needs 13 inches of cloth for sewing project, then Allison will need to buy 33.02 centimeter of cloth.
The length of cloth that Allison needs to buy is = 13 inches ,
The conversion factor is ⇒ 1inch = 2.54 centimeter,
Allison needs 13 inches of cloth, and we know that 1 inch is the same as 2.54 centimeters.
So, to convert 13 inches to centimeters we multiply it by the conversion factor of 2.54 centimeters per inch,
Which is written as;
⇒ (13 inches) × (2.54 centimeters per inch)
⇒ 33.02 centimeters
Therefore, Allison needs to buy 33.02 centimeters of cloth for her sewing project.
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Suppose that 40% of voters in Okeechobee county support a proposed property tax. Consider the sampling
distribution of the sample proportion of supporters with sample size n = 135. Determine the mean and
standard deviation of the sampling distribution of p. Round solutions to four decimal places, if necessary.
The mean of the sampling distribution of p is 0.40 and the standard deviation of the sampling distribution of p is 0.0409.
What is standard deviation?Standard deviation is a measure of how spread out the values in a data set are from the mean. It is calculated by taking the square root of the variance of the data set. It is a commonly used measure to assess the variability in a data set.
The mean of the sampling distribution of p is 0.40, which is the same as the proportion of supporters in the population of Okeechobee County. This is due to the fact that the sample proportion estimates the population proportion. The standard deviation of the sampling distribution of p is equal to the square root of the product of p (0.40) and q (1-p, or 0.60) divided by the sample size (135). In this case, the standard deviation of the sampling distribution of p is 0.0409.
The mean and standard deviation of the sampling distribution of p can be used to understand what values of p are likely when samples of size n = 135 are drawn from the population of Okeechobee County. If a sample is drawn from the population, the sample proportion of supporters is likely to be close to 0.40, which is the mean of the sampling distribution of p. Furthermore, most of the sample proportions of supporters are likely to be within two standard deviations (or 0.0818) of the mean. This means that the sample proportion of supporters is likely to be between 0.3182 and 0.4818 when samples of size n = 135 are drawn from the population.
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A rectangular field bordering a river is to be enclosed with 600 m of fencing. No fence is needed along the riverbank. What equation represents the maximum area enclosed by the fence?
The equation that represents the maximum area enclosed by the fence is 600x - 2x².
What is the maximum area?
Any rectangle's maximal surface area requires a minimum length-to-breadth ratio. Hence, in this scenario, the length must equal the ceiling (perimeter / 4) and the width, of the floor (perimeter /4). Therefore a rectangle with a given perimeter has a maximum area equal to the ceiling(perimeter/4) and the floor(perimeter/4)
Here, we have
Given: A rectangular field bordering a river is to be enclosed with 600 m of fencing. No fence is needed along the riverbank.
We have to find the equation that represents the maximum area enclosed by the fence.
The sum of the sides NOT along the river x + x + y = 600, and the area equals xy.
This makes the two equations: 2x + y = 600, and A = xy.
To find the largest area, we need to find A as a function of x or y. I suggest solving the first equation for y and replacing that in the second equation.
y = 600 - 2x. and A(x) = x(600-2x)
We now need to maximize A(x) = 600x - 2x²
Hence, the equation that represents the maximum area enclosed by the fence is 600x - 2x².
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5. A car costs $22,000. After a down payment of $4,000, the balance will be paid off in 48 equal monthly payments with the interest of 12% per year on the unpaid balance. Find the amount of each payment. 6. A car costs $22,000. After a down payment of $4,000, the balance will be paid off in 60 equal monthly payments with the interest of12%per year on the unpaid balance. Find the amount of each payment.
7. A car costs $22,000. After a down payment of $4,000, the balance will be paid off in 72 equal monthly payments with the interest of 12% per year on the unpaid balance. Find the amount of each payment.
8. (Bad credit): A car costs $22,000. After a down payment of $4,000, the balance will be paid off in 48 equal monthly payments with the interest of 18% per year on the unpaid balance. Find the amount of each payment.
The equal monthly payments for a car costs $22,000 with a down payment of $4,000 based on each scenario are:
Interest of 12% with 48 equal monthly payments = $621.92.Interest of 12% with 60 equal monthly payments = $505.01.Interest of 12% with 72 equal monthly payments = $383.63.Interest of 18% with 48 equal monthly payments = 704.26Let's discuss each scenario we have.
5. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.
The amount of the down payment is $4,000.
The total cost of the car is $22,000.
Hence the balance is:
Balance = Total cost of the car − Down payment
Balance = $22,000 − $4,000 = $18,000
Now we can calculate the amount of each payment.
The payment is to be made in 48 equal monthly installments.
The interest rate is 12% per year.
We need to convert this into the monthly interest rate by dividing by 12.
Hence:
Monthly interest rate = 12% / 12 = 1% = 0.01
Let x be the amount of each monthly payment. Then the equation that represents the above conditions is given by:
18000=x(1−(1+0.01)−48)/0.01
Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:
18000=x(1−(1+0.01)−48)/0.01x
=18000/28.95x
≈621.92
Hence the amount of each equal monthly payment is approximately $621.92.
6. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.
The amount of the down payment is $4,000.
The total cost of the car is $22,000.
Hence the balance is:
Balance = Total cost of the car − Down payment
Balance = $22,000 − $4,000 = $18,000
Now we can calculate the amount of each payment.
The payment is to be made in 60 equal monthly installments.
The interest rate is 12% per year.
We need to convert this into the monthly interest rate by dividing by 12.
Hence:
Monthly interest rate = 12% / 12 = 1% = 0.01
Let x be the amount of each monthly payment.
Then the equation that represents the above conditions is given by: 18000=x(1−(1+0.01)−60)/0.01
Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:
18000=x(1−(1+0.01)−60)/0.01x
=18000/35.643x
≈505.01
Hence the amount of each payment is approximately $505.01.
7. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.
The amount of the down payment is $4,000.
The total cost of the car is $22,000.
Hence the balance is:
Balance = Total cost of the car − Down payment
Balance = $22,000 − $4,000 = $18,000
Now we can calculate the amount of each payment.
The payment is to be made in 72 equal monthly installments.
The interest rate is 12% per year.
We need to convert this into the monthly interest rate by dividing by 12.
Hence:
Monthly interest rate = 12% / 12 = 1% = 0.01
Let x be the amount of each monthly payment.
Then the equation that represents the above conditions is given by:
18000=x(1−(1+0.01)−72)/0.01
Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:
18000=x(1−(1+0.01)−72)/0.01x
=18000/46.869x
≈383.63
Hence the amount of each payment is approximately $383.63.
8. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.
The amount of the down payment is $4,000.
The total cost of the car is $22,000.
Hence the balance is:
Balance = Total cost of the car − Down payment
Balance = $22,000 − $4,000 = $18,000
Now we can calculate the amount of each payment.
The payment is to be made in 48 equal monthly installments.
The interest rate is 18% per year.
We need to convert this into the monthly interest rate by dividing by 12.
Hence:
Monthly interest rate = 18% / 12 = 1.5% = 0.015
Let x be the amount of each monthly payment.
Then the equation that represents the above conditions is given by:
18000=x(1−(1+0.015)−48)/0.015
Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:
18000=x(1−(1+0.015)−48)/0.015x
=18000/25.525x
≈704.26
Hence the amount of each payment is approximately $704.26.
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The circle graph describes the distribution of preferred music from a sample of 400 randomly selected middle school students.
a circle graph titled preferred music, with five sections labeled rock 13 percent, hip hop 25 percent, pop 35 percent, classical 13 percent, and jazz 14 percent
Which of the following conclusions can we draw from the circle graph?
Pop is the preferred music for 35 students.
Jazz is the preferred music for 56 students.
Together, Hip Hop, Rock, and Jazz are the preferred music for less than half the students.
Together, Hip Hop and Pop are the preferred music for 260 students.
Cοnclusiοn that can be drawn frοm the circle graph is 'Pοp is the preferred music fοr 140 students.'
Cοrrect οptiοn is A.
What is percentage?In math, a percentage is a number οr a ratiο that can be expressed as a fractiοn οf 100. If we need tο calculate the percentage οf a number, divide that number by whοle and multiply by 100. Therefοre, percentage means οne part per hundred.
Given,
Tοtal number οf students = 400
By circle graph five sectiοns labeled rοck 13 percent, hip hοp 25 percent, pοp 35 percent, classical 13 percent, and jazz 14 percent
Number οf students preferring pοp music
= 35%
= (35/100) × 400
= 35 × 4
= 140
Number οf students preferring classical music
= 13%
= (13/100) × 400
= 13 × 4
= 52
Number οf students preferring jazz music
= 14%
= (14/100) × 400
= 14 × 4
= 56
Number οf students οf pοp and classical tοgether = 140 + 52 = 192
Number οf students οf classical and jazz tοgether = 52 + 56 = 108
Hence, the οnly cοnclusiοn that is true is, Pοp is the preferred music fοr 140 students.
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Giving 50 points
Solve for x.
x² = 144
Enter your answers in the boxes. Enter the smaller answer first.
x = and x =
Answer:
x = -12 and x = 12.
Step-by-step explanation:
To solve for x, we need to take the square root of both sides of the equation:
x² = 144
√(x²) = √144
since sqaure root gives both positive and neagtive value, so
x = ±12
So the solutions for x are x = -12 and x = 12.
Identify the tax rate (in rand) used to calculate a person's payable tax, if
the person's annual taxable income is R450 090.
The tax rate used to calculate a person's payable tax in South Africa is not a fixed rate, but rather a combination of different rates that apply to different income brackets
As of the 2021/2022 tax year, the tax rates for individuals in South Africa are as follows:
For taxable income up to R216,200: 18% of taxable income
For taxable income between R216,201 and R337,800: R38,916 plus 26% of taxable income above R216,200
For taxable income between R337,801 and R467,500: R70,532 plus 31% of taxable income above R337,800
For taxable income between R467,501 and R613,600: R110,739 plus 36% of taxable income above R467,500
For taxable income between R613,601 and R782,200: R163,335 plus 39% of taxable income above R613,600
For taxable income above R782,200: R229,089 plus 41% of taxable income above R782,200
Based on the above tax rates, if a person's annual taxable income is R450,090, their payable tax would be calculated as follows:
18% of the first R216,200 = R38,916
26% of the amount above R216,200 up to R337,800 = R26,890
31% of the amount above R337,800 up to R450,090 = R34,754
Total payable tax = R38,916 + R26,890 + R34,754 = R100,560
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Sydney went bowling and
had the following scores:
101, 115, 78, 87 and 99.
Find the mean range,
variance, and standard
deviation
The mean score is 96.
The variance is 160.
The standard deviation is approximately 12.65.
To find the mean (average) of the scores, we add them up and divide by the total number of scores:
Mean = (101 + 115 + 78 + 87 + 99) / 5 = 96
So the mean score is 96.
We deduct the lowest score from the highest score to determine the range:
Range = highest score - lowest score = 115 - 78 = 37
So the range is 37.
To find the variance, we need to find the squared difference between each score and the mean, then add up all those squared differences and divide by the number of scores.
The formula for variance is:
Variance = [tex]\frac{\sum(x_i - \bar x)^2}{n}[/tex]
where
Σ represents the sum of,
[tex]x_i[/tex] is the ith score,
n is the number of scores,
[tex]\bar x[/tex] is the mean.
Using the formula, we get:
Variance = [(101 - 96)² + (115 - 96)² + (78 - 96)² + (87 - 96)² + (99 - 96)²] / 5
= (25 + 361 + 324 + 81 + 9) / 5
= 800 / 5
= 160
So the variance is 160.
We take the square root of the variance to calculate the standard deviation:
Standard deviation = √160 ≈ 12.65
So the standard deviation is approximately 12.65.
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Q3 Calculate the surface area of question 3 a)
Answer:
2520 m²
Step-by-step explanation:
You want the surface area of the irregular prism shown.
PerimeterThe perimeter of the base (shaded front face) is the sum of the lengths of the horizontal edges and the lengths of the vertical edges. That sum is ...
2(20 m) +2(20 m) = 80 m
Lateral areaThe lateral area of the prism is the sum of the unshaded rectangle areas. That total area is the product of the perimeter of the base and the distance between bases:
LA = Ph = (80 m)(25 m) = 2000 m²
Base areaThe area of each of the two bases can be found several ways. We find the height of the middle step to be (20 m -7 m -6 m) = 7 m, so the bottom step fits nicely into the space not used by the middle step. (This is shown in the attachment.)
That is, the base area can be computed as the area of a rectangle 13 m high and 20 m wide:
Base area = WH = (20 m)(13 m) = 260 m²
Surface areaThe total surface area of the prism is the sum of the lateral area and the area of the two bases:
SA = LA +2·B = (2000 m²) +2(260 m²) = 2520 m²
The surface area of the prism is 2520 square meters.
Simplify the following algebraic expression.
The algebraic expression is simplified to 13. Option A
What are algebraic expressions?These are expressions that are made up of terms, variables, constants and coefficients.
They are also made up of arithmetic operations like subtraction, division, multiplication, bracket, and parentheses.
The square root of a number is defined as the factor that when multiplied by itself gives the original number.
The symbol for square root is '√'. The square root of a number is the opposite of squaring a number.
From the information given, we have that;
√169
Now, let's determine the square root
13
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Help please <3 :) Im struggling
The square based pyramid has a surface area of is 224 mm²
Drawing the net of the pyramidGiven that
A square based pyramid
The shapes in the net of a square based pyramid are
1 square 4 trianglesThe shape's net is attached
Calculating the surface area of the netTo determine the surface area, we use
Area = l² + 2hl
Where
l = length of the square base = 8 mm
h = slant height = 10 mm
By substitution, we have
Area = 8² + 2 * 10 * 8
Evaluate
Area = 224
Hence, the surface area is 224 mm²
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Every plane contains at least three____ points
Answer:
3
Step-by-step explanation:
in a three - dimensional scenario a plane consists of three points and also they are not on the same line.
consider a model in which only industry is used to predict delay. at a level of significance, test for any positive autocorrelation in the data.
In order to test for any positive autocorrelation in the data, you would use the Pearson correlation coefficient. This measures the strength and direction of a linear relationship between two variables. The level of significance that you set depends on the size of your dataset, but generally should be 0.05 or less.
To test for positive autocorrelation, you need to compare the Pearson correlation coefficient with the critical value of the correlation coefficient. The critical value is determined by the level of significance you have set. If the Pearson correlation coefficient is greater than the critical value, then you can conclude that there is a significant positive autocorrelation.
It is important to keep in mind that a positive correlation does not necessarily mean that there is a cause and effect relationship between the two variables. It only means that the two variables move in the same direction.
In conclusion, if the Pearson correlation coefficient is greater than the critical value, then you can conclude that there is a significant positive autocorrelation.
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For the right triangles below, find the exact values of the side lengths b and d.
If necessary, write your responses in simplified radical form.
The side of the right triangle can be found as follows:
b = 4√2 units
d = 7√3 / 2 units
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's use trigonometric ratios to find the side of the right triangle as follows;
Let's find b as follows:
sin 45 = opposite / hypotenuse
sin 45° = b / 8
cross multiply
b = 8 sin 45
b = 8 × √2 / 2
b = 8√2 / 2
b = 4√2 units
Let's find d as follows:
sin 60° = d / 7
cross multiply
d = 7 sin 60
d = 7 × √3 / 2
d = 7√3 / 2 units
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due in 5 minutes -3x-24≤-36
Answer:
x ≥ 4
Step-by-step explanation:
Who has a better bating average 12 to 15 or 9 to 10
in essence, which of the two fractions is the larger one, well, let's put both with the same denominator by multiplying each other by the other's denominator.
[tex]12:15\qquad 9:10\hspace{5em}\cfrac{12}{15}\qquad \cfrac{9}{10} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{12}{15}\cdot \cfrac{10}{10}\implies \cfrac{120}{150} ~~ \bigotimes\hspace{9em}\cfrac{9}{10}\cdot \cfrac{15}{15}\implies \cfrac{135}{150} ~~ \textit{\LARGE \checkmark}[/tex]
Answer:9/10
Step-by-step explanation:
90% average vs 80% average
100 people are tested for disease. 30 people have the disease; 70 people are not diseased. So, prevalence is 30%: Calculate the following: The sensitivity and specificity . The positive and negative predictive values. The probability of the correct diagnosis.
Sensitivity 67% specificity 86%
Positive predictive values 67% Negative predictive values 86%
Probability of the correct diagnosis 80%
The following can be calculated from the data given:1. Sensitivity and Specificity2. Positive and Negative Predictive Values.3. The probability of the correct diagnosis1. Sensitivity and Specificity:Sensitivity is the proportion of positive cases correctly identified by a screening test or diagnosis test. Sensitivity = Number of true positives / (Number of true positives + Number of false negatives) = 20 / (20 + 10) = 20 / 30 = 67%Specificity is the proportion of negative cases correctly identified by a screening test or diagnosis test. Specificity = Number of true negatives / (Number of true negatives + Number of false positives) = 60 / (60 + 10) = 60 / 70 = 86%2. Positive and Negative Predictive Values.Positive Predictive Value (PPV) is the proportion of positive test results that are true positives.Positive predictive value (PPV) = Number of true positives / (Number of true positives + Number of false positives) = 20 / (20 + 10) = 20 / 30 = 67%.Negative Predictive Value (NPV) is the proportion of negative test results that are true negatives.Negative predictive value (NPV) = Number of true negatives / (Number of true negatives + Number of false negatives) = 60 / (60 + 10) = 60 / 70 = 86%.3. Probability of the correct diagnosisThe probability of correctly diagnosing a diseased individual would be the proportion of true positives and true negatives among the total tested.Probability of correctly diagnosing a diseased individual = (Number of true positives + Number of true negatives) / (Number of true positives + Number of false positives + Number of true negatives + Number of false negatives) = (20 + 60) / (20 + 10 + 60 + 10) = 80 / 100 = 80%.
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PLEASE SHOW WORK!!!!!!!!!
The correct option is ([tex]H) i.e. a² > b².[/tex]
What is an inequality?
In mathematics, an inequality is a statement that one quantity is less than or greater than another quantity. Inequalities are used to compare values and express relationships between them.
For all integers a < 0 and b < 0, the following inequality must be true:
[tex]H. a² > b²[/tex]
This can be proved as follows:
If a and b are both negative, then a² and b² are both positive. Since a < 0 and b < 0, we have a < b or b < a, which implies that[tex]a² > b² or b² > a².[/tex]
If a and b are both negative and equal (i.e., a = b < 0), then a² = b², which implies that a² > b² and b² > a² are both false.
None of the other inequalities (F, G, J, K) must be true for all such a and b. For example:
F. a/b > 1 is not necessarily true, since a and b could both be negative and have the same absolute value (e.g., a = b = -1), in which case a/b = 1.
G. ab > 2 is not necessarily true, since a and b could both be negative and have absolute values less than 2 (e.g., a = b = -1), in which case ab = 1 < 2.
J. [tex]a²b³ > 0 is[/tex] not necessarily true, since a and b could both be negative and have different absolute values (e.g., a = -2 and b = -1), in which case[tex]a²b³ = -8 < 0.[/tex]
K. [tex]a^{4} b² > 0[/tex] is not necessarily true, since a and b could both be negative and have the same absolute value (e.g., a = b = -1), in which case [tex]a^{4} b² = 1 > 0[/tex]. However, if we add the condition that a and b have different absolute values, then K would be true, since [tex]a^{4} b²= (|a|)² |b|² > 0.[/tex]
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fsThe cuboid below is made of lead and has a mass of 339 g. Calculate its density, in g/cm³. If your answer is a decimal, give it to 1 d.p.
The density of the lead cuboid is approximately 11.3 g/cm³.
What is density?
Density is a physical property of matter that describes how much mass is contained within a certain volume. It is defined as the amount of mass per unit of volume, and is typically measured in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).
The formula for density is:
density = mass / volume
where mass is the amount of matter in an object, and volume is the amount of space that the object occupies.
The volume of the cuboid can be calculated using the formula V = lwh, where l, w, and h are the length, width, and height of the cuboid, respectively.
Given that the length (l) of the cuboid is 5cm, the width (w) is 3cm, and the height (h) is 2cm, we can calculate the volume as:
V = lwh = 5cm x 3cm x 2cm = 30 cm³
The density (ρ) of an object is defined as its mass (m) per unit volume (V), or ρ = m/V.
Given that the mass of the cuboid is 339 g and its volume is 30 cm³, we can calculate the density as:
ρ = m/V = 339 g / 30 cm³ ≈ 11.3 g/cm³ (to 1 decimal place)
Therefore, the density of the lead cuboid is approximately 11.3 g/cm³.
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What is the answer to this equation -4. 3+1. 2n=10. 1
The value of the n for the given algebraic equation is=12.
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added to a variable before being multiplied by it.
The given algebraic expression is
-4.3+1.2n=10.1
Add 4.3 on both sides
1.2n=10.1+4.3
1.2n=14.4
divide 1.2 into both sides
n = 14.4÷1.2
n = 12
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A company makes steel rods shaped like cylinders. Each rod has a diameter of 8 centimeters and a height of 20 centimeters. How much steel will the company need to make 146 rods? For your calculations, do not round any intermediate steps, and use the 3.141592654 button on a calculator. Round your answer to the nearest hundredth.
Step-by-step explanation:
The volume of each steel rod can be calculated using the formula for the volume of a cylinder:
V = πr^2h
where r is the radius of the cylinder (half the diameter), and h is the height.
In this case, the diameter is 8 cm, so the radius is 4 cm. The height is 20 cm. Therefore, the volume of each steel rod is:
V = π(4 cm)^2(20 cm) = 320π cm^3
To find out how much steel is needed to make 146 rods, we can multiply the volume of one rod by the number of rods:
Total volume = 146 rods x 320π cm^3/rod
Total volume = 46,720π cm^3
We can use a calculator to approximate the value of π to 3.14 and then calculate the total volume:
Total volume ≈ 46,720 x 3.14 cm^3
Total volume ≈ 146,748.8 cm^3
Rounding to the nearest hundredth, the company will need approximately 146,748.8 cubic centimeters of steel to make 146 rods.
Hugo is traveling in Toronto, Canada. His weather app shows the temperature is 25°C. Hugo writes the equation 25 559(F232) to find the temperature in degrees Fahrenheit, F. What is the temperature in degrees Fahrenheit?
The temperature in degrees Fahrenheit is approximately 77.4°F.
What are the differences between the Celsius and Fahrenheit temperature scales?There are two widely used temperature scales in the world: Celsius and Fahrenheit. The freezing and boiling temperatures of water serve as the foundation for the Celsius scale, commonly referred to as the centigrade scale. According to this scale, the freezing point of water is 0°C, while the boiling point is 100°C.
On the other hand, a German physicist by the name of Daniel Gabriel Fahrenheit created the Fahrenheit scale. While it makes use of different reference points, this scale is similarly based on the freezing and boiling points of water.
The formula of the conversion is given by equation:
25 = 559/9 * (F - 32).
We can solve for F as follows:
25 = 559/9 * (F - 32)
25 * 9/559 = F - 32
F = 25 * 9/559 + 32
F ≈ 77.4
Therefore, the temperature in degrees Fahrenheit is approximately 77.4°F.
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help would be appreciated
The graph that shows the given transformation is option A.
How to identify the graph of the transformation?We can see the graph of f(x) on the top of the given image, and we want to identify the graph of the transformation f(4x), this will be an horizontal compression of the function.
So we should look for a graph that looks like the first one, but its compresed on the horizontal axis. The vertical axis is not changed, remember that.
The only one that shows that is graph A, so that is the correct option.
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Write the 5 number summary for the set of data.
42,58,67,55,40,69,66,51,46,48,68
minimum ___
quartile 1__
quartile 2___
quartile3___
Maximum____
The 5 number summary for the given dataset (40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69) is: Minimum: 40, Q1: 47, Median (Q2): 55, Q3: 66.5, Maximum: 69.
What is statistics ?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of quantitative methods to gather, describe, and draw inferences from data, which can be used to make decisions, predictions, or conclusions about a population or a phenomenon.
To find the 5 number summary, we need to find the minimum, maximum, and the three quartiles of the given dataset:
The minimum value is 40.
To find the quartiles, we first need to sort the data in ascending order:
40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69
The median (quartile 2) is the middle value of the dataset, which is 55.
Quartile 1 (Q1) is the median of the lower half of the dataset, which includes the values 40, 42, 46, 48, and 51. The median of this lower half is (46+48)/2 = 47.
Quartile 3 (Q3) is the median of the upper half of the dataset, which includes the values 58, 66, 67, 68, and 69. The median of this upper half is (66+67)/2 = 66.5.
The maximum value is 69.
Therefore, the 5 number summary for the given dataset is:
Minimum: 40
Q1: 47
Median (Q2): 55
Q3: 66.5
Maximum: 69
Therefore, the 5 number summary for the given dataset (40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69) is: Minimum: 40, Q1: 47, Median (Q2): 55, Q3: 66.5, Maximum: 69.
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In the diagram below, \triangle EFD\sim \triangle GHD△EFD∼△GHD. Which ratio is equivalent to tan FF?
The equivalent ratio to tan F in right angles triangle, △EFD is tan F = DE / DF.
Explain about the similar triangles?Identical triangles differ in size but have the same shape. Corresponding angles are identical in similar triangles. Similar triangles have corresponding sides that have the same ratio. The ratio of a square of any two of their corresponding sides to any identical triangle's area is the same.For the stated question:
△EFD∼△GHD
So, in right angles triangle, △EFD
Sin Ф = perpendicular / hypotenuse.
Sin E = DF / EF
And,
The ratio is equivalent to tan F = perpendicular / base
tan F = DE / DF
Thus, the equivalent ratio to tan F in right angles triangle, △EFD is tan F = DE / DF.
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The complete question is attached:
What is the equation of the graph below?
On a coordinate plane, a curve crosses the y-axis at y = 1 and then completes one cycle at 360 degrees.
y = sine (x + 90 degrees)
y = cosine (x + 90 degrees)
y = sine (x + 45 degrees)
y = cosine (x + 45 degrees)
Answer:
y = sine (x + 90 degrees)
Step-by-step explanation:
y = cosine(x) is a curve that crosses the y-axis at y = 1 and completes one cycle at 360 degrees.
sine(x) have the same curve than cosine(x), but translated 90° to the right respect cosine(x)
f(x + c) translates f(x) horizontally c units to the left.
Then, sine(x + 90) is equivalent to cosine(x)
The volumes of two similar prisms are 27 cm' and 1 cm. The surface area of the larger prism is 153 cm².
a.) What is the scale factor?
b.) What is the ratio of their areas?
c.) What is the ratio of their volumes?
d.) What is the surface area of the smaller prism?
Answer: a) To find the scale factor, we need to find the ratio of the corresponding lengths of the two prisms, since the volumes of two similar prisms are proportional to the cube of the scale factor. Let x be the scale factor.
(volume of larger prism) / (volume of smaller prism) = (x³) = 27/1
x³ = 27
x = 3
Therefore, the scale factor is 3.
b) The ratio of the areas is equal to the square of the scale factor. Let A1 and A2 be the areas of the larger and smaller prisms, respectively.
(A1) / (A2) = (scale factor)²
A2 = A1 / (scale factor)²
A2 = 153 / 9
A2 = 17 cm²
Therefore, the ratio of their areas is 9:1.
c) The ratio of the volumes is equal to the cube of the scale factor.
(volume of larger prism) / (volume of smaller prism) = (scale factor)³
(volume of smaller prism) = (1 cm³) * (scale factor)³
(volume of smaller prism) = 27 cm³
Therefore, the ratio of their volumes is 27:1.
d) To find the surface area of the smaller prism, we can use the same ratio as in part (b) to find that the surface area of the smaller prism is equal to the surface area of the larger prism divided by the square of the scale factor.
(surface area of smaller prism) = (surface area of larger prism) / (scale factor)²
(surface area of smaller prism) = 153 / 9
(surface area of smaller prism) = 17 cm²
Therefore, the surface area of the smaller prism is 17 cm².
Step-by-step explanation:
What is the acceleration of a bus his speech changes from 126M/S to 3097 m/s over a period of three seconds
The acceleration of a bus his speech changes from 126M/S to 3097 m/s over a period of three seconds is 990. 3 m/s^2
What is acceleration?Acceleration is can be defined as the rate of change of the velocity of an object with respect to time.
It is also defined as the rate at which velocity changes with time, that is, in both speed and direction.
Accelerations are vector quantities because they are known to have both magnitude and direction.
The orientation of an object's acceleration is determined by the configuration of the net force acting on that object.
The formula for acceleration is given as;
Acceleration = change in velocity/time
Substitute the values
Acceleration = 3097 - 126 (m/s)/3 s
Divide the values
Acceleration = 990. 3 m/s^2
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A dessert has been through and yoghurt inside altogether. The mess of the desert is 165 g. The ratio of the mass of the fruit to the mass of the yoghurt is 2:3 what is the mass of the yoghurt? 99g
If The ratio of the mass of the fruit to the mass of the yoghurt is 2:3 the mass of the yogurt is 99 g,
Let's assume the mass of the fruit is 2x and the mass of the yogurt is 3x, where x is a common factor.
According to the problem, the total mess of the desert is 165 g, so we can write an equation:
2x + 3x = 165
Simplifying this equation, we get:
5x = 165
x = 33
Therefore, the mass of the fruit is:
2x = 2(33) = 66 g
And the mass of the yogurt is:
3x = 3(33) = 99 g
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Find the center and radius of the circle
x2 + 2x - 1 + y2+ 4y = 3
Answer:R=3\\
(a,b)=(1,2)
Step-by-step explanation:
[tex](x-a)^{2}+(y-b)^{2}=R^{2}\\(a,b)-center\\R-radius\\x^{2} + 2x - 1 + y^{2}+ 4y = 3\\(x+1)^2=x^{2}+2x+1\\(y+2)^{2}=y^{2}+ 4y+4\\x^{2} + 2x - 1 + y^{2}+ 4y = (x+1)^2-1+(y+2)^2-4-1=(x+1)^2+(y+2)^2-6=3\\(x+1)^2+(y+2)^2=9\\R=3\\(a,b)=(1,2)[/tex]
Which linear function can be used to model the line on the graph?
Option (a) [tex]y=\frac{3x}{2} -5[/tex] can be used as a the model line on the graph for the Linear function.
What is Linear function?A linear function in mathematics is one that has either one or two variables but no exponents. It is a function with a straight line as its graph.
A straight line on the coordinate plane is described by a linear function.
Option (a) [tex]y=\frac{3x}{2} -5[/tex] satisfy with all point as below,
If we take, x = 0, we get y = -5
If we take, x = 2, we get y = -2
If we take, x = 4, we get y = 1
If we take, x = 6, we get y = 4
If we take, x = 8, we get y = 7
So, here we see all the value are match according to the graph.
Therefore, [tex]y=\frac{3x}{2} -5[/tex] can be used as a the model line on the graph for the Linear function.
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