Answer: 50 uk pounds
Step-by-step explanation:
Step-by-step explanation:
See image below
Help please & thanks
The function f(t)=−5t^2+20t models the approximate height of an object t seconds after it is launched. Which of the following equations correctly shows the quadratic formula being used to determine the number of seconds it will take for the objects to be at a height of 18 feet after launch?
The equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.
What is trigοnοmetric equatiοns ?Trigοnοmetric equatiοns are equatiοns that invοlve trigοnοmetric functiοns such as sine, cοsine, tangent, etc. These equatiοns usually invοlve finding values οf the unknοwn angle(s) that satisfy the given equatiοn. They can be sοlved using algebraic techniques οr by using the prοperties οf trigοnοmetric functiοns.
Accοrding tο the given infοrmatiοn:
The given functiοn is [tex]f(t) = -5t^2 + 20t[/tex], which mοdels the height οf an οbject in feet as a functiοn οf time in secοnds.
Tο find the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch, we need tο sοlve the equatiοn [tex]-5t^2 + 20t = 18[/tex].
Tο sοlve this quadratic equatiοn using the quadratic fοrmula, we first identify the values οf a, b, and c frοm the general fοrm οf a quadratic equatiοn, [tex]ax^2 + bx + c = 0[/tex].
In this case, a = -5, b = 20, and c = -18. Substituting these values intο the quadratic fοrmula, we get:
[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]
Plugging in the values οf a, b, and c, we get:
[tex]t = (-20 \± \sqrt{+(20^2 - 4(-5)(-18)})) / 2(-5)[/tex]
Simplifying this expressiοn, we get:
[tex]t = (-20 \± \sqrt{(400 - 360))} / (-10)[/tex]
[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]
[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]
[tex]t = 2 \± 0.632[/tex]
Therefοre, the twο pοssible values οf t are:
t = 2 + 0.632 = 2.632 secοnds
t = 2 - 0.632 = 1.368 secοnds
Therefοre, the equatiοn that cοrrectly shοws the quadratic fοrmula being used tο determine the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch is:
[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]
[tex]t = (-20 \± \sqrt{(20^2 - 4(-5)(-18))}) / 2(-5)[/tex]
[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]
[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]
t = 2 ± 0.632
Therefοre, the equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.
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If Julie drives from York to corby via Derby. How many miles will she drive
Julie will have driven a total distance of 289 miles if she travels from York to Corby via Derby.
Starting from York, Julie needs to travel to Derby. The distance between York and Derby is given as 89 miles. So, we know that Julie will have driven 89 miles once she reaches Derby.
Next, Julie needs to travel from Derby to Corby, but the given information is a bit tricky here. The distance from Derby to Corby is not given directly. Instead, we are given two distances - Derby to Dory and Dory to Corby.
To find the distance from Derby to Corby, we need to add the distances between Derby and Dory, and Dory and Corby. From the question, we know that the distance between Derby and Dory is 127 miles and the distance between Dory and Corby is 73 miles. Adding these two distances gives us the total distance from Derby to Corby, which is 200 miles.
Finally, we can add up the distances traveled between each location to find the total distance traveled by Julie. Adding the distances of each leg of the journey, we get:
89 miles (York to Derby) + 200 miles (Derby to Corby via Dory) = 289 miles
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Complete Question:
If Julie drives from York to Corby via Dory how many miles will she have driven?
York 89
Derby 127 73
Corby
the length of a rectangle is 3 in longer than its width. if the perimeter of the rectangle is 50 in, find its length and widths
First, re-read the problem until you understand it and can put it into your own words. I re-wrote it like this: "Find the area of a rectangle by first finding the length (L) and the width (W)." [note that I added "find L and W," but that is how I'm going to solve the problem; I could also have said that we will need the formulas, P=2L+2W and A=LW, but you knew that already, right?).
Translate the problem:
"The length of a rectangle is 3 ft longer than its width" means
L = 3 + W (eq1)
"the perimeter of the rectangle is 30 ft" means
P = 50 (eq2)
So, now the math is easy, just find L and W so we can compute the area:
P = 50 = 2L + 2W (eq3; from eq2 and the formula for P)
50 = 2(3+W) + 2W (use eq1 to substitute for L)
50 = 6 + 2W + 2W (distribute)
50 = 6 + 4W (collect terms)
44 = 4W (subtract 6 from both sides)
11 ft = W (divide both sides by 4)
Use the easiest equation (either eq1 or else eq3) to find L:
L = 3 + W (eq1)
L = 3 + 11
L = 14 ft
What is the area (A)?
A = L*W
A = (14 ft) x (11 ft)
A = 154 sq ft
Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
The discount percentage is different, the amount that Lisa pays will also be different.
What exactly is the discounted method?The act of estimating the present value of a future payment or series of cash flows that will be received in the future is referred to as discounting. A discount rate (also known as a discount yield) is the rate at which future cash flows are discounted back to their present value.
We need to know what percentage of the regular ticket price Lisa saves with her railcard. We cannot calculate the exact amount Lisa pays for the ticket without this information.
Assuming Lisa receives a 1/3 discount with her railcard, we can calculate the cost of her ticket as follows:
Discounted price = Regular price minus discount amount
Normal price x Discount percentage = Discount amount
Discount rate = 1/3 = 33.33% (rounded to two decimal places)
Discount amount = £24.90 multiplied by 33.33% = £8.30 (rounded to two decimal places)
Price after discount = £24.90 - £8.30 = £16.60 (rounded to two decimal places)
As a result, if Lisa receives a 1/3 discount with her railcard, she will pay£16.60 for the ticket. However, if the discount percentage is different, Lisa's payment will be different as well.
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Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
the classification of student class designation (freshman, sophomore, junior, senior) is an example of a) a categorical random variable. b) a discrete random variable. c) a continuous random variable. d) a parameter.
The classification of student class designation (freshman, sophomore, junior, senior) is an example of a categorical random variable. The correct option is A.
What is a random variable?A random variable is a numerical or categorical quantity whose value is unknown but whose behavior can be forecast based on data that has been measured or observed. Random variables are typically used to represent quantities that fluctuate over time or are subject to chance occurrences.
The types of random variables are as follows:
i) Categorical random variable: This type of variable contains categorical data or data that are descriptive in nature. It is used to classify items or events into categories, which can be named or identified. For example, a set of data that includes categories like gender, eye color, or country of origin.
ii) Discrete random variable: This type of variable takes on discrete values, which means it can only take on whole numbers. For example, the number of cars sold at a dealership on any given day is a discrete random variable because it can only take on integer values.
iii) Continuous random variable: This type of variable takes on continuous values, which means it can take on any value within a given range. For example, the temperature in a room can take on any value between a certain minimum and maximum value.
Therefore, the correct option is A.
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a school pays 1,852 for 150 shirts . this includes the 25$ flat-rate shipping costs. c. what are the initial value and rate of change of the function? what does each on represent
Therefore, the initial value of the function is $1,852 and the rate of change is $12.18 per shirt. The initial value represents the cost of the shirts before any were purchased,
What is function?In mathematics, a function is a rule that assigns to each element in a set called the domain, a unique element in another set called the range. In other words, a function is a mathematical object that takes an input and produces a specific output, according to a specific set of rules or operations.
by the question.
et the initial value be represented by a and the rate of change by r.
The given information can be represented by the following equation:
a + 150r = 1,852
Since the flat-rate shipping cost is $25, the cost of the 150 shirts alone would be:
a + 150r - 25 = 1,827
The initial value, a, represents the cost of the shirts before any shirts were purchased. In this case, it would be the cost of the shirts if no shirts were purchased plus the flat-rate shipping cost of $25.
So, a = 1,827 + 25 = 1,852.
The rate of change, r, represents the increase in cost for each additional shirt purchased. In this case, it would be the cost of one shirt.
So, r = (1,852 - 25)/150 = 12.18.
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In △PQR
how many degrees is m∠Q?
Answer:
105 degrees
Step-by-step explanation:
sum of angles in triangle is 180 degrees
11x-5+6x+5+x = 180
simplify this to get 18x=180
180/18 = 10 = x
plug in 10 for x
11(10) - 5
110-5
105
i do not understand how to answer this question
a. Hence proved that the sum of fractions [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
b. The value will be 7 for the expression
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
What is square root?Square rοοt οf a number is a value, which οn multiplicatiοn by itself, gives the οriginal number. The square rοοt is an inverse methοd οf squaring a number. Hence, squares and square rοοts are related cοncepts.
Suppοse x is the square rοοt οf y, then it is represented as x=√y, οr we can express the same equatiοn as x² = y. Here, ‘√’ is the radical symbοl used tο represent the rοοt οf numbers. The pοsitive number, when multiplied by itself, represents the square οf the number. The square rοοt οf the square οf a pοsitive number gives the οriginal number.
Here,
a. [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
Using (a + b)(a - b) = a² - b²
⇒ [tex]${\frac{1 \cdot \sqrt{1}-\sqrt{2}}{\sqrt{1}+\sqrt{2}\cdot \sqrt{1 }-\sqrt{2}}+{\frac{1 \cdot \sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}\cdot \sqrt{1}-\sqrt{2}}}+{\frac{1 \cdot \sqrt{3}-\sqrt{4}}{\sqrt{3}+\sqrt{4}\cdot \sqrt{3}-\sqrt{4}}}$[/tex]
⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{1-2}+{\frac{ \sqrt{2}-\sqrt{3}}{2-3}+{\frac{\sqrt{3}-\sqrt{4}}{3-4}}$[/tex]
⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-\sqrt{4}}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]
⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}}-{\sqrt{3}+2}$[/tex]
⇒ [tex]$ -1+2}$[/tex]
⇒ 1
a. Hence proved that the sum of fractions [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
B. This will be done with the same process,
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}} \cdot \cdot \cdot -{\sqrt{63}+8}$[/tex]
There, will be same roots of every number until - 8
So,
⇒ [tex]$ -1+8}$[/tex]
= 7
b. The value will be 7 for the expression
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
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3
The ratio of desktop computers to laptop computers sold by
a mail-order company last week was 8 to 3. What could be
the numbers of computers sold by the company last week?
A
B
C
D
448 desktops, 168 laptops
448 desktops, 165 laptops
440 desktops, 168 laptops
400 desktops, 165 laptops
using the ratio given, the number of computers could be sold by the company last week is: A. 448 desktops, 168 laptops.
How to Calculate Ratios?To find the actual numbers of desktop and laptop computers sold, we need to choose a common factor for the ratio 8:3.
Let's assume that the total number of computers sold is 33x (where x is a positive integer). Then, the ratio 8:3 corresponds to 8x desktops and 3x laptops. We can check which of the given options satisfies this condition:
A. 8x = 448, 3x = 168 --> This satisfies the condition, as 8:3 = 448:168
B. 8x = 448, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 448:165
C. 8x = 440, 3x = 168 --> This does not satisfy the condition, as 8:3 is not equal to 440:168
D. 8x = 400, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 400:165
Therefore, the answer is option A: 448 desktops and 168 laptops could be the numbers of computers sold by the company last week.
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Based on the following sorted 20 values for age, what are the possible split points?
{20, 22, 24, 26, 28, 31, 32, 33, 35, 40, 42, 43, 45, 47, 49, 50, 52, 53, 55, 57}
Multiple Choice
a {20, 21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49. 5, 51, 52, 54, 56}
b {21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49, 51, 52. 5, 54, 56, 57}
c {0, 21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49, 51, 52. 5, 54, 56}
d {21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49. 5, 51, 52. 5, 54, 56}
Based on the following sorted 20 values for age, the possible split points are {20, 21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49. 5, 51, 52, 54, 56} (option a).
Option A suggests that the split points are {20, 21, 23, 25, 27, 29.5, 31.5, 32.5, 34, 37.5, 41, 42.5, 44, 46, 48, 49.5, 51, 52, 54, 56}. Notice that every split point falls between two consecutive ages in the original list. For example, the first split point is 20 because it is between 20 and 22. The second split point is 21 because it is between 20 and 22 as well.
Option B suggests that the split points are {21, 23, 25, 27, 29.5, 31.5, 32.5, 34, 37.5, 41, 42.5, 44, 46, 48, 49, 51, 52.5, 54, 56, 57}. Notice that the only difference between this option and Option A is that the last split point is 57 instead of 49.5.
Option C suggests that the split points are {0, 21, 23, 25, 27, 29.5, 31.5, 32.5, 34, 37.5, 41, 42.5, 44, 46, 48, 49, 51, 52.5, 54, 56}. Notice that the first split point is 0, which is not a possible age in the original list.
Option D suggests that the split points are {21, 23, 25, 27, 29.5, 31.5, 32.5, 34, 37.5, 41, 42.5, 44, 46, 48, 49.5, 51, 52.5, 54, 56}. Notice that the only difference between this option and Option A is that the split point after 49 is 49.5 instead of 49.5.
In summary, the correct answer is Option A because it provides all the possible split points that fall between the ages in the original list. When working with split points, it's important to consider the specific context and criteria for dividing the data.
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Charles is 10 years old what is the best estimate of the length of his shoe
Answer:
Size 3 ♀️
Step-by-step explanation:
In the US, the average shoe size for 10-Year-Old is USA Size 3.
-Jul 12, 2020
an inner city revitalization zone is a rectangle that is twice as long as it is wide. the width of the region is growing at a rate of 32 m per year at a time when the region is 220 m wide. how fast is the area changing at that point in time?
The area is changing at a rate of 28,160 m²/year at that point in time.
The area of the rectangular region is given by:
A = lw
Where l is the length of the rectangular region and w is the width of the rectangular region.
The width of the rectangular region is given to be 220 m. Therefore, we have the width w = 220 m. The length l of the rectangular region can be found knowing that it is twice as long as it is wide. Therefore, the length of the rectangular region is given by:
l = 2w
l = 2 x 220
l = 440
Therefore, the length l of the rectangular region is 440 m.
At the given point in time, the width of the rectangular region is growing at a rate of 32 m per year. Therefore, we have the rate of change of the width dw/dt to be 32 m per year. We need to find how fast the area of the rectangular region is changing at that point in time. Therefore, we need to find the rate of change of the area of the rectangular region dA/dt.
A = lw
dA/dt = w dl/dt + l dw/dt
dA/dt = 220 d/dt(2w) + 440 dw/dt
dA/dt = 220 x 2 dw/dt + 440 dw/dt
dA/dt = 880 dw/dt
Substitute the value of dw/dt to get:
dA/dt = 880 x 32
dA/dt = 28,160 m²/year
Therefore, the area of the rectangular region has a rate of change of 28,160 m² per year at that point in time.
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suppose we are interested in estimating the difference in survival rate between the control and treatment groups using a confidence interval. explain why we cannot construct such an interval using the normal approximation. what might go wrong if we constructed the confidence interval despite this problem?
We cannot construct an interval using the normal approximation of survival rate between control and treatment groups because the samples must be random, independent, and their sample sizes must be sufficiently large.
What is the normal approximation?The normal approximation is valid when the sample sizes are large enough to ensure that the sampling distribution of the mean of the variable is approximately normal.
The central limit theorem applies to the distribution of the sample mean when the sample size is large enough, according to the normal approximation.
As a result, the mean difference between the two groups must have a normal distribution. The normal distribution may not be an accurate representation of the underlying distribution of the difference between the two population means in the absence of this requirement, causing the confidence interval to be inaccurate. It will lead to incorrect inferences about the difference in the survival rates of the two groups.
The confidence interval constructed despite this problem will lead to incorrect inferences about the difference in the survival rates of the two groups. This would make it difficult to draw any conclusions based on the findings of this experiment.
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Please help, this is due in 10 minutes, im giving 35 points for it.
The scientific and standard notation and clue obtained from the clue sheet are;
1. Name starts with; J
2. Difference = 145 million miles = Weight = 145 lbs
3. Height: 5 ft, 6 in
4. I. 2.54 × 10⁸ miles corresponding to letter I
II. 0.0005825 corresponds to letter G
III. 5.0432 × 10⁶ corresponds to letter N
IV. 1.547 × 10³ corresponds to letter R
V. 4.977 × 10⁻² corresponds to letter W
VI. 1.3 × 10¹⁰ light years away; corresponds to letter D
VII. 5.04 × 10⁻⁵ corresponds to letter A
The suspects hubby is DRAWING
What is the scientific notation of presenting numbers?Scientific notation is a format used to express very large or very small numbers such that they are much easier to work with. The scientific notation format is; a × 10ⁿ, where; a is the coefficient, which is a number between 1 and 10 (10 excluded), and n is an integer.
1. G = (6.07 × 10⁷)/(7.035 × 10³) ≈ 8628.29
J = (6.03 × 10⁻³)/(5.05 × 10⁻⁷) ≈ 11940.59
Therefore; J > G
The suspects name starts with J
2. The distance the telescope in the laboratory allows the viewer to see = 1.5 × 10⁹ miles away
The distance the other telescope a few hours away allows the viewer to see = 1.355 × 10⁹ miles away
The difference between the distances = (1.5 - 1.355) × 10⁹ miles = 1.45 × 10⁸ miles
The difference in the distance is 1.45 × 10⁸ miles = 145 million miles
The suspect weight is 145 lbs
3. The numbers are;
Feet; 532.063 × 10³ = 5.32063 × 10⁵
Inches; 5,030,045 = 5.030045 × 10⁶
The height of the suspect is 5 feet 6 inches (5'6'') = 5.5 feet
Height; = 5 ft, 6 in
4. I. The difference in distances between Earth and Saturn can be found as follows;
The difference in the distances = (1000 - 746) million miles = 254 million miles apart
Scientific notation is the expression of numbers in the form consisting of a number between 1 and 10, multiplied by 10 raised to a power
254 million miles = 2.54 × 10⁸ miles
The corresponding letter from the code cracker is; I
II Standard notation is the expression of numbers in the standard form without the use of exponents or special symbols
The number 5.825 × 10⁻⁴ in standard notation is; 0.0005825
The corresponding letter from the code cracker is; G
III. The number 504.32 × 10⁴ in scientific notation can be obtained by moving the decimal point two places to the left followed by increasing the index of 10 by 2 as follows;
504.32 × 10⁴ = 5.0432 × 10⁶
The corresponding letter from the code cracker is; N
IV. The sum of the numbers 1.202 × 10³ and 3.45 × 10² can be obtained by expressing both numbers to the same power of 10 as follows;
1.202 × 10³ + 3.45 × 10² = 12.02 × 10² + 3.45 × 10² = 15.47 × 10²
15.47 × 10² = 1.547 × 10³
Therefore; 1.202 × 10³ + 3.45 × 10² = 1.547 × 10³
The corresponding letter from the code cracker is; R
V. The difference of the numbers can be obtained as follows;
5.023 × 10⁻² - 4.6 × 10⁻⁴ = 502.3 × 10⁻⁴ - 4.6 × 10⁻⁴ = 497.7 × 10⁻⁴
497.7 × 10⁻⁴ = 4.977 × 10⁻²
Therefore; 5.023 × 10⁻² - 4.6 × 10⁻⁴ = 4.977 × 10⁻²
The corresponding letter from the code cracker is; W
VI. 13 billion light years = 13 × 10⁹ light years = 1.3 × 10¹⁰ light years
The distance a standard telescope can allow to be seen is 1.3 × 10¹⁰ light years away
The corresponding letter from the code cracker is; D
VII. 0.0000504 in scientific notation is; 5.04 × 10⁻⁵
The corresponding letter from the code cracker is; A
IGNRWDA
The suspects favorite hubby is DRAWING
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Find the value of the expression x+|x| if x=7, 10, 0, -3, -8. write the expression without the absolute value symbol for these values of x: x≤0
The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.
What does the expression mean?When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The value of a function, given the value(s) assigned to its argument, is the sum that the function assumes for these input values (s).
For x =7,x+|x| =7+|7| =14
For x =10,x+|x|= 10+|10| =20
For x = 0,x+|x| =0+|0| =0
For x = -3, x + |x| = -3 + |-3| = 0
For x = -8, x + |x| = -8 + |-8| = 0
The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.
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please help
this is all the information i have!
New points of graph A'B'C'D' are A'(-2, -2), B'(-2, 0), C'(-4, 0), D'(-4, -1)
Define the term Translation?In graph theory, the term "translation" refers to a type of operation that moves all the vertices and edges of a graph by a fixed distance in a given direction. Specifically, a translation of a graph involves shifting every vertex a certain distance horizontally and/or vertically, without changing the shape or connectivity of the graph.
Translation: 4 left and 2 down
Start with a point at its original location and then move it 4 units to the left and 2 units down. This can be done by subtracting 4 from the x-coordinate and subtracting 2 from the y-coordinate of the point or shape.
Given points in a graph ABCD are, A(2, 0), B(2, 2), C(0, 2), D(0, 1)
Subtract 4 from the x-coordinate and subtract 2 from the y-coordinate, resulting in a new points of graph A'B'C'D' are A'(-2, -2), B'(-2, 0), C'(-4, 0), D'(-4, -1)
The figure shown in below diagram.
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5 x _ = -35
Topic: Multiplying and Dividing Integers
Given:
5× ______ = - 35
• -35/5
• -7
Answer:5 x -7 = -35
Answer:
The answer is 7
Step-by-step explanation:
Divide each term in 5x=-35 by 5 and simplify.x=−7
Y= 1/3x-9
Write the equation of a line PERPENDICULAR to
point (-6, 10).
that passes through the
The equation of the line perpendicular to y = 1/3x - 9 that passes through the point (-6, 10) is y = -3x - 8.
The given equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
So, we can see that the slope of the given line is 1/3.
A line perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line.
The negative reciprocal of 1/3 is -3.
Now, we have the slope of the perpendicular line and a point that it passes through. We can use point-slope form to find the equation of the line.
Point-slope form, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values we have
y - 10 = -3(x - (-6))
y - 10 = -3(x + 6)
y - 10 = -3x - 18
y = -3x - 8
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The given question is incomplete, the complete question is:
Write the equation of a line perpendicular to y = 1/3x - 9 that passes through the point (-6, 10)
The blueprint of a triangular patio has side lengths 3.5 in., 3.5 in., and 5.25 in. If the shorter sides of the actual patio are each 10.5 ft long, how long is the third side?
The length of the third side of the actual patio is 15.75 feet.
What is similarity of triangle?In order to solve issues requiring proportional connections between the sides of two triangles, it is crucial to understand the idea of triangle similarity. If the matching sides and angles of two triangles are identical, then two triangles are said to be similar. When referring to similarities, the symbol is used.
Let us suppose the length of third side = x.
Given that, blueprint of a triangular patio has side lengths 3.5 in., 3.5 in., and 5.25 in.
Thus, the blueprint and the actual patio form two similar triangles.
The sides of the similar triangles are equal in ratio thus,
3.5/5.25 = 10.5/x
3.5x = 5.25 * 10.5
x = (5.25 * 10.5) / 3.5
x = 15.75
Hence, the length of the third side of the actual patio is 15.75 feet.
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ABCD is a quadrilateral in which BD = 15 cm., perpendiculars from A and Con BD are 6 cm and 8 cm respectively. Calculate the area of the quadrilaterals
The area of the quadrilateral is 161.24 cm².
How to deal with quadrilateral?We can see that we can divide the quadrilateral into two triangles: ABD and CBD. We know that the height of ABD is 6 cm and the height of CBD is 8 cm. We also know that BD is 15 cm. To find the area of each triangle, we need to find the base of each triangle. We can do this using the Pythagorean theorem.
For triangle ABD:
AB² = AD² + BD²
AB² = (6 cm)² + (15 cm)²
AB² = 261 cm²
AB = [tex]\sqrt(261) cm[/tex]
For triangle CBD:
BC² = CD² + BD²
BC² = (8 cm)² + (15 cm)²
BC² = 289 cm²
BC = 17 cm
Now we can find the areas of the triangles:
Area of ABD =[tex]\frac{1}{2}[/tex] * AB * 6 cm
Area of ABD = [tex]\frac{1}{2}[/tex] * [tex]\sqrt(261) cm[/tex] * 6 cm
Area of ABD = 93.24 cm^2
Area of CBD = [tex]\frac{1}{2}[/tex] * BC * 8 cm
Area of CBD = [tex]\frac{1}{2}[/tex] * 17 cm * 8 cm
Area of CBD = 68 cm²
Finally, we can find the area of the quadrilateral by adding the areas of the triangles:
Area of ABCD = Area of ABD + Area of CBD
Area of ABCD = 93.24 cm² + 68 cm²
Area of ABCD = 161.24 cm²
Therefore, the area of the quadrilateral is 161.24 cm².
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11. Figure EFGH is a parallelogram. Find the length of Line FG.
The length οf line FG is 12 cm, If Figure EFGH is a parallelοgram.
What is parallelοgram?A parallelοgram is a type οf quadrilateral with twο pairs οf parallel sides. The οppοsite sides οf a parallelοgram are equal in length and parallel tο each οther.
Since EFGH is a parallelοgram, we knοw that the οppοsite sides are parallel and equal in length. Therefοre, the length οf line FG is equal tο the length οf line EH.
We can find the length οf EH by using the Pythagοrean theοrem οn right triangle EFG:
[tex]EF^2 + FG^2 = EG^2[/tex]
Since EF = 5 cm, EG = 13 cm, and angle FEG is a right angle (as οppοsite angles in a parallelοgram are equal), we can sοlve fοr FG:
[tex]FG^2 = EG^2 - EF^2[/tex]
[tex]FG^2 = 13^2 - 5^2[/tex]
[tex]FG^2 = 144[/tex]
[tex]FG = \sqrt{(144)[/tex]
[tex]FG = 12 cm[/tex]
Therefοre, the length οf line FG is 12 cm.
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The interest rate of an auto
loan is 4%. Express this
number as a decimal.
Answer: 0.04
Step-by-step explanation:
In order to get 4% as a decimal, you must divide 4 by 100.
4/100 = 0.04
Thus, the answer to your question is 0.04
If P(A)=0. 3, P(B)=0. 2, and P(A∩B)=0. 1, find the probability
a. P(
)
b. P(A∪B)
c. P(
∩B)
d. P(A∩
)
e. P(
∪B)
P(∅) = 0, P(A∪B) = 0.4 , P(A∩B) = 0.1 ,Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').and P(A∪B) = 0.4. are the required solutions ofgiven probability check .
a. The probability of an empty set is always zero. Therefore, P(∅) = 0.
b. The probability of the union of two events, A and B, is given by the formula P(A∪B) = P(A) + P(B) - P(A∩B). Substituting the values given in the question, we get:
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.3 + 0.2 - 0.1
= 0.4
Therefore, P(A∪B) = 0.4.
c. The probability of the intersection of A and B is given by the formula P(A∩B). Substituting the values given in the question, we get:
P(A∩B) = 0.1
Therefore, P(A∩B) = 0.1.
d. The probability of the intersection of A and the complement of B is given by the formula P(A∩B'). The complement of B is the set of all outcomes that are not in B. Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').
e. The probability of the union of A and B is given by the formula P(A∪B). Substituting the values given in the question, we get:
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.3 + 0.2 - 0.1
= 0.4
Therefore, P(A∪B) = 0.4.
In probability theory, the union of two events A and B is the set of outcomes that belong to either A or B or both. The intersection of two events A and B is the set of outcomes that belong to both A and B. The complement of an event A is the set of outcomes that do not belong to A. These concepts are fundamental in probability theory and are used extensively in solving various problems.
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Smoothie Activity
6. Using the relative frequency table, create a segmented bar graph by employee type using technology or by hand. If using Excel technology the columns may need to be switched after inserting the chart. Click on the chart and the "Chart Design" ribbon will pop up. Then select "Switch Row/Column." (10 points)
By answering the presented question, we may conclude that I used the following procedures to produce this graph.
What is graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph contains vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.
I used the following procedures to produce this graph:
I classified the personnel as full-time, part-time, and temporary.
I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."
I used the following procedures to produce this graph:
I classified the personnel as full-time, part-time, and temporary.
I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."
I made the segmented bar graph using these percentages.
The graph was made using Excel technology. You may make a similar graph with Excel or any other software that supports segmented bar graphs.
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Una pintura incluyendo su marco tiene 25 cm de largo y 10 cm de ancho cuánto es el area del marco, si este tiene 4cm de ancho?
216 cm2 is the size of the rectangle border.
the translation of the question is
A painting including its frame is 25 cm long and 10 cm wide, what is the area of the frame if it is 4 cm wide?
What is a rectangle's area?
When the dimensions of a rectangle with length and width are multiplied, the area of the rectangle is determined as follows:
A = lw.
The total area is therefore given by:
A = 25 x 10 = 250 cm².
The white region's size is shown by:
A = (25 - 2 x 4) x (10 - 2 x 4) is equal to 17x 2 and 34 cm2.
Hence, the border's area is as follows:
216 cm2 = 250 cm2 - 34 cm2.
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A $2,000 investment was made 16 years ago into an account that earned quarterly
compounded interest. If the investment is currently worth $6,883.55, what is the
annual rate of interest?
Answer:
We can use the formula for compound interest to solve the problem:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, we know that P = $2,000, A = $6,883.55, n = 4 (quarterly compounding), and t = 16. We can solve for r by rearranging the formula as follows:
r = n[(A/P)^(1/nt) - 1]
Substituting the values, we get:
r = 4[(6,883.55/2,000)^(1/(4*16)) - 1] = 0.0522 or 5.22%
Therefore, the annual interest rate is approximately 5.22%
Write in the standard form of a conic if possible, and identify the conic section represented by r = 6/(cos x + 3sin x)
The standard form of a conic section represented by r = 6/(cos x + 3sin x) is r^2 = 6(x + 3y) and the represented equation is a line.
The equation r = 6/(cos x + 3sin x) is in polar form, where r represents the distance from the origin to a point (x, y) in the plane, and x is the angle that the line connecting the origin to (x, y) makes with the positive x-axis. To determine the standard form of the conic represented by this equation, we need to convert it to Cartesian coordinates.
Using the trigonometric identity cos x = x/r and sin x = y/r, we can rewrite the equation as:
r = 6/(x/r + 3y/r)
Multiplying both sides by r, we get:
r^2 = 6(x + 3y)
This is the standard form of a conic section in Cartesian coordinates, namely an equation of a line. Therefore, the conic represented by the equation r = 6/(cos x + 3sin x) is a line in the Cartesian coordinate system.
In summary, to determine the standard form of a conic represented by an equation given in polar form, we can use trigonometric identities to rewrite it in Cartesian coordinates.
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Find the total amount and total interest after six months if the interest is compounded every quarter. Principal =₹10 000 Rate of interest =20% per annum.
Answer:I=(PxRxT)/100
I=(10000x20x1)/100x2
I=200000/200
I=1000
Step-by-step explanation:
I NEED HELP ON THIS ASAP!!
a) Graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380
b) The maximum profit of $5200 achieved.
Define the term selling profit?Selling profit is the profit that a business makes on the sale of its products or services. It is the difference between the selling price and the cost of product.
a) Let x be the number of boards of mahogany sold and y be the number of boards of black walnut sold. Then, the constraints of the problem can be represented by the following system of inequalities:
x ≥ 0 (non-negative constraint)
y ≥ 0 (non-negative constraint)
x ≤ 260 (maximum number of mahogany boards available)
y ≤ 320 (maximum number of black walnut boards available)
x + y ≤ 380 (maximum number of boards that can be sold)
To graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380 on a coordinate plane and shade the feasible region that satisfies all of the constraints. The feasible region is the area that is bounded by these lines and includes the origin (0, 0).
b) The profit function P(x, y) can be defined as follows:
P(x, y) = 20x + 6y
To maximize the profit, we need to find the values of x and y that satisfy all of the constraints and maximize the profit function P(x, y).
One way to do this is to use the corner-point method. We can evaluate the profit function at each of the corners of the feasible region and find the corner that gives the maximum profit.
The corners of the feasible region are (0, 0), (0, 320), (260, 0), and (120, 260).
P(0, 0) = 0
P(0, 320) = 6(320) = 1920
P(260, 0) = 20(260) = 5200
P(120, 260) = 20(120) + 6(260) = 4720
Therefore, the maximum profit of $5200 can be achieved by selling 260 boards of mahogany and 0 boards of black walnut.
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How do you do this I need help please
Answer:
30,000 grams
Step-by-step explanation:
multiply the 30KG by 1,000 (that is the conversion) and you get 30,000g
Answer:
hi I'm really sorry I can't help