Alan found the distance between point A(-8, -4) and point B(3, -4). His worn is shown below. -8 to the y-axis=8 units. 3 to the y-axis=3 units. |-8| - |3| = 5 units from A to B. What error did Alan make? What is the actual distance from point A to point B?

In the given question angle a= 60° and b= 120° by exterior angle theorem

When a triangle's side is extended to make an angle outside the triangle, the external angles of the triangle are formed. We can use the formula below to determine the size of an external angle:

Sum of Measurements of Distant Interior Angles = Measure of Exterior Angle

The two interior angles that are not directly close to the external angle being measured are known as the remote interior angles. Remote internal angles are angles at vertices A and B if we extend the side AB to generate an exterior angle at vertex C in a triangle with vertices A, B, and C.

Measure of Interior Angle at Vertex A + Measure of Interior Angle at Vertex B = 180 degrees, where Measure of Exterior Angle at Vertex C = 180 degrees.

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Answer:

Step-by-step explanation:

To find the instantaneous rate of change function for the given function p = 2 - 3q², we need to find the derivative of the function with respect to q. The derivative gives us the slope of the tangent line to the curve at any point, which is the instantaneous rate of change at that point.

So, we can start by taking the derivative of the given function:

dp/dq = d/dq(2 - 3q²)

dp/dq = 0 - 3(2q)

dp/dq = -6q

Therefore, the instantaneous rate of change function for p = 2 - 3q² is given by:

dp/dq = -6q

This means that the instantaneous rate of change (slope of the tangent line) of the function p with respect to q is -6q at any given point.

Answer:

Step-by-step explanation:

4 *  7= 28

Answer:

28

Step-by-step explanation:

hope i help u:)

As $sqrt-40$ cannot be further simplified in terms of real numbers, the answer is given in simplified form.

A right triangle's hypotenuse (the side that faces the right angle) has a square length that, according to Pythagoras' Theorem, is equal to the sum of the squares of the lengths of the other two sides (the legs). Formally, Pythagoras' theorem asserts that if a right triangle has legs of lengths a, b, and c, and a hypotenuse of length c, then:

[tex]a^2 + b^2 = c^2[/tex]

Pythagoras, an ancient Greek mathematician, is credited with discovering and proving this theorem, therefore it bears his name.

given

The Pythagorean theorem can be used to determine the length of the omitted side. Let x be the length of the side that is missing. The right triangle that results has a hypotenuse that is top-bottom in length and legs that are x and slant in length. This can be expressed as:

x2 + slant2 = (top - bottom)2

$$

To put it simply, we have:

\begin{align*} \s(top - bottom) (top - bottom)

2 &= x 2 + slant 2, top 2 - 2top "cdot bottom + bottom 2 - slant 2," x 2 &= "sqrt" top 2 - 2top "cdot bottom + bottom 2 - slant 2," and "end align"

begin-aligning* x = sqrt((5),2,5,8,and(8),2,-7,2). sqrt = 25 - 80 + 64 - 49; sqrt = 40; sqrt = boxed 2i sqrt 10; end align;

As $sqrt-40$ cannot be further simplified in terms of real numbers, the answer is given in simplified form.

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The option 2 is correct of given question ''All the powers have a value of 1 because the exponent is zero.''

An exponent is a mathematical notation that indicates the number of times a quantity is multiplied by itself. It is written as a superscript number to the right of the quantity being multiplied.

For example, in the expression 5³, 5 is the base and 3 is the exponent. This means that 5 is being multiplied by itself three times: 5 x 5 x 5, which equals 125.

The statement "All the powers have a value of 1 because the exponent is zero" describes what these four powers have in common.

When the exponent is zero, any number (except for 0) raised to the power of 0 equals 1. Therefore, 10⁰  = 1, (-2)⁰ = 1, and any non-zero number raised to the power of 0 equals 1.

There is no fractional value involved in this case, as raising a number to the power of zero does not involve any division.

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Complete question:

Thus, infants are deemed preterm if they arrive on or before 240 days (rounded to the next integer).

The study of chance and uncertainty is covered in the mathematical field of probability. It is a way to gauge how likely something is to happen. Probability can be expressed as a number between 0 and 1, with 0 indicating that an occurrence is impossible, and 1 indicating that an event is certain. Probability is frequently employed in real-world situations to forecast the results of random occurrences like tossing a coin, rolling a die, or drawing cards from a deck. The probability of an occurrence is estimated by dividing the number of possible outcomes by the number of possible ways the event could occur.

given

a. We need to locate the region to the right of 307 under the normal distribution curve in order to determine the likelihood that a pregnancy would last 307 days or longer.

By standardizing the value of 307, we may make use of the standard normal distribution:

(X - mu) / sigma = z

z = (307 - 268) / 15\sz = 2.6

A basic normal distribution table or calculator can be used to determine that a z-score larger than 2.6 has a probability of about 0.0047.

Thus, the likelihood of a pregnancy lasting at least 307 days is roughly 0.0047, or 0.47%.

b. We must determine the gestational period that sets the lowest 3% of pregnancies apart from the others. The value with a cumulative probability of 0.03 to its left is this one.

The z-score for a cumulative probability of 0.03 can be calculated using a conventional normal distribution table or calculator. It is roughly -1.88.

To determine the corresponding length of pregnancy, we can apply the z-score formula:

z = (x - mu)/sigma -1.88 = (x - 268)/15 -28.2 = x - 268 x = 239.8

Thus, infants are deemed preterm if they arrive on or before 240 days (rounded to the next integer).

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Question reads..}[/tex]

[tex]\textsf{Last year 525,398 people walked across the Golden Gate Bridge. This year 650,482}\\\textsf{people walked across the Golden Gate Bridge. How many more people walked}\\\textsf{across the Bridge this year as compared to last year?}[/tex]

[tex]\huge\text{Well when we come across..}[/tex]

[tex]> \textsf{When are comparing two (or more numbers), we are either SUBTRACTING or}\\\textsf{ADDING the numbers, it all depends on how you read the word problem. That is}\\\textsf{we have to read the word problem CAREFULLY so we can know what operation }\\\mathsf{(+,-, \div, \times)}\textsf{ we are doing}[/tex]

[tex]\huge\text{If that is the case, we are doing in this}\\\\\huge\text{word problem..}[/tex]
[tex]> \textsf{We are SUBTRACTING because we are COMPARING \underline{CURRENT year}}\\\textsf{with the \underline{PAST year}}}[/tex]

[tex]\huge\text{What should the equation look like right off the}\\\\\huge\text{top of your head?}[/tex]
[tex]\mathsf{650,482 - 525,398}[/tex]

[tex]\huge\text{Just SOLVE it like a regular basic arithmetic}\\\huge\text{equation}[/tex]
[tex]\mathtt{650,482 - 525,398}[/tex]

[tex]\text{Start with the bigger number (650,482) \& go down however many spaces you} \\\text{have for the smaller number (525,398).}[/tex]

[tex]\rightarrow\mathtt{125,084}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathtt{125,084}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

125,084 more people walked across the Bridge this year, compared to last year.

Step-by-step explanation:

To find how many morepeople walked across the bridge in the current year compared to last year, woth the number of this year being larger than last year's, simply subtract the larger number from the smaller number by hand or using a calculator:

650,482 - 525,398= 125,084.

Therefore, 125,084 more people walked across the Bridge this year, compared to last year.

In case you need to do this subtraction by hand, check the attached image to see the process.

The difference between the balances of Ashley and Fwam after 15 years is given as follows:

$5,650. (Ashley will have $5,650 more than Fwam).

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

Hence Ashley's amount after 15 years is given as follows:

A(15) = 59000 x (1 + 0.03125/365)^(365 x 15)

A(15) = $94,280.

Fwam's amount is given as follows:

F(15) = 59000 x (1 + 0.0275)^(15)

F(15) = $88,630.

Then the difference is of:

94280 - 88630 = $5,650.

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Answer:5650

Step-by-step explanation:

94279.8393-88629.7389=5650.1009

None explains the use of 0.5 for the most conservative sample size. Thus E is the correct one.

A confidence interval is a range of values that is likely to contain the true population parameter, and a wider confidence interval allows for a greater chance of accurately capturing the true population parameter.

The use of 0.5 as an estimate of the sample proportion is most conservative because it produces the widest confidence interval.

A larger sample size is generally used when the confidence interval is wider, as it improves the precision of the estimate.

Using 0.5 as the estimated proportion will produce the widest confidence interval and thus, a larger sample size.

This is why 0.5 is used to calculate the most conservative sample size.

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Graph c is the correct solution of the given inequality.

To solve the inequality 11 <= y - 43, we need to isolate y on one side of the inequality.

Adding 43 to both sides, we get:

11 + 43 <= y - 43 + 43

54 <= y.

Draw a number line and mark any relevant points. For example, if the inequality involves x > 3, mark the point 3 on the number line.

Determine if the inequality is "greater than" (>), "less than" (<), "greater than or equal to" (≥), or "less than or equal to" (≤).

For a "greater than" or "greater than or equal to" inequality, shade the line to the right of the relevant point(s) on the number line. For a "less than" or "less than or equal to" inequality, shade the line to the left of the relevant point(s) on the number line.

If the inequality includes "and," place another shade for the second part of the inequality. The solution is where the two shaded regions overlap.

If the inequality includes "or," draw two separate number lines for each part of the inequality and shade the appropriate regions. The solution is the combination of the two separate shaded regions.

Indicate whether the endpoints are included or excluded, using an open circle for excluded endpoints and a closed circle for included endpoints.

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Answer:

x ≈ 13,6; y ≈ 15,7; z ≈ 26,7

Step-by-step explanation:

I added a photo of my solution

Answer: Answer is below <3

Step-by-step explanation:

Harris should expect to spin a sum that is 10 or greater than 100 times.

Part A:

To predict the number of times Harris will spin a sum less than 10, we need to find the probability of getting a sum less than 10 and multiply it by the total number of spins, which is 500.

The possible outcomes of the first spinner are 1, 2, and 3, and the possible outcomes of the second spinner are 4, 5, 6, 7, and 8.

The minimum sum we can get is 1+4=5, and the maximum sum we can get is 3+8=11.

To get a sum less than 10, we can get:

1+4=5

1+5=6

1+6=7

1+7=8

1+8=9

2+4=6

2+5=7

2+6=8

2+7=9

3+4=7

3+5=8

3+6=9

There are 12 possible outcomes that result in a sum less than 10. So the probability of getting a sum less than 10 is 12/15, or 4/5.

To find the number of times Harris will spin a sum less than 10, we can use the equation:

probability of getting a sum less than 10 × total number of spins = x

So the equation that can be solved to predict the number of times Harris will spin a sum less than 10 is:

C) 12/15 = x/500

Part B:

To find the number of times Harris should expect to spin a sum that is 10 or greater, we can subtract the number of times he will spin a sum less than 10 from the total number of spins:

total number of spins - number of times he will spin a sum less than 10 = number of times he should expect to spin a sum that is 10 or greater

Substituting the values, we get:

500 - (12/15 × 500) = 500 - 400 = 100

So Harris should expect to spin a sum that is 10 or greater than 100 times.

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Answer: THE ANSWER IS 3 BECAUSE I HAD THIS TEST

RATE BRAINLIEST PLEASE

Step-by-step explanation:

The required  average number of people completing voting at any given time as per given 55 people per hour is equals to 27.5.

Average throughput voting facility process = 55 people per hour,

Calculate the average processing time per person ,

⇒ Processing time per person = 1 hour / 55 people

⇒ Processing time per person = 0.01818 hours/person

Average time taken by each person to complete the voting process = 30 minutes  

Convert this to hours by dividing by 60,

⇒ Flow time per person = 30 minutes / 60

⇒ Flow time per person = 0.5 hours/person

Now,

Average number of people in the voting facility using Little's Law,

which states that the average number of items in a system is equal to the average throughput multiplied by the average flow time.

⇒ Average number of people in facility = Average throughput x Average flow time

⇒ Average number of people in facility = 55 people/hour x 0.5 hours/person

⇒ Average number of people in facility = 27.5 people

Therefore, on average there are 27.5 people in the voting facility at any given time.

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The above question is incomplete, the complete question is:

Suppose that a voting facility processes an average of 55 people per hour (throughput) and that, on average, it takes 30 minutes for each person to complete the voting process (flow time).Calculate the average number of people  in the voting facility at any given time.

We can conclude after answering the provided question that Therefore, interest after 19 years, the amount in the account will be $1,418.50.

In mathematics, interest is the sum of money earned but rather owed on an initial investment or loan. You can use either simple or compound interest. Rate of return is computed upon that main fee plus any previously earned interest, whilst simple interest is given as a percent of the initial amt. If you invest $100 at a 5% each year simple interest rate, you will earn $5 through interest every year for four years, for a total of $15.

calculating the future value of an investment is:

[tex]FV = PV x (1 + r)^n\\FV = $500 x (1 + 0.08)^19\\FV = $500 x 2.837\\FV = $1,418.50[/tex]

Therefore, after 19 years, the amount in the account will be $1,418.50.

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Therefore, the slant height of the pyramid is 7.5 cm.

I believe you meant to ask about "height". Height is a measurement of how tall something is, typically referring to the distance from the ground or base to the top of an object. It can be measured in various units, such as feet, inches, meters, or centimeters. People often use height to describe the physical stature of individuals or objects, such as the height of a person, building, or tree.

by the question.

let's start by recalling the formula for the lateral surface area of a pyramid:

[tex]Lateral Surface Area = (1/2) x Perimeter of Base x Slant Height[/tex]

We are given that the lateral surface area is 120 cm2 and the base area is 64 cm2. Since the base is a square, we can find the length of one side by taking the square root of the area:

Side of Base = sqrt(64 cm2) = 8 cm

The perimeter of the base is then 4 times the length of one side:

[tex]Perimeter of Base = 4 x 8 cm = 32 cm[/tex]

Now we can substitute the values we have into the formula and solve for the slant height:

[tex]120 cm2 = (1/2) x 32 cm x Slant Height[/tex]

[tex]Slant Height = (120 cm2) / (16 cm) = 7.5 cm[/tex]

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Minimum and maximum recommended width of the space between 6-inch by 6-inch tiles = 13/6 inches.

An inch is a unit of length in the Imperial system of units, which is primarily used in the United States, Canada, and the United Kingdom. One inch is equal to 1/12 of a foot or 2.54 centimeters. It is commonly used to measure the length or width of objects, such as a piece of paper, a television screen, or a piece of fabric. In the Imperial system, larger units of length, such as feet, yards, and miles, are based on inches.

by the question.

To simplify the expressions for the minimum and maximum recommended widths of the space between 6-inch by 6-inch floor tiles, we can convert the mixed numbers to improper fractions and then find the least common multiple (LCM) of the denominators.

First, let's simplify the minimum recommended width of the space:

[tex]2-2 inch = 2 + 2/12 = 2 + 1/6 = (2*6 + 1)/6 = 13/6 inches[/tex]

Next, let's simplify the maximum recommended width of the space:

[tex]2-1 inch = 2 + 1/12 = 2 + 2/24 = (2*12 + 2)/24 = 26/12 = 13/6 inches[/tex]

We can see that the minimum and maximum recommended widths of the space between the 6-inch by 6-inch tiles are the same, which is 13/6 inches. Therefore, we can simplify the expressions for both.

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Answer:

45∘

Step-by-step explanation:

∠2 = 180∘ - 135∘ = 45∘

∠2 = ∠1 = 45∘

∠1 = ∠4 = 45∘

Answer: Let x be the number of gallons of the first brand (30% pure antifreeze) that needs to be mixed, and let y be the number of gallons of the second brand (80% pure antifreeze) that needs to be mixed. We want to find the values of x and y that satisfy the following conditions:

The total amount of antifreeze mixed is 150 gallons: x + y = 150

The resulting mixture is 40% pure antifreeze: 0.3x + 0.8y = 0.4(150)

We have two equations with two unknowns, so we can solve for x and y. We'll use the first equation to solve for y in terms of x:

y = 150 - x

Substituting this expression into the second equation gives:

0.3x + 0.8(150 - x) = 60

Simplifying and solving for x:

0.3x + 120 - 0.8x = 60

-0.5x = -60

x = 120

Substituting this value back into y = 150 - x gives:

y = 150 - 120 = 30

Therefore, we need to mix 120 gallons of the first brand and 30 gallons of the second brand to obtain 150 gallons of a mixture that contains 40% pure antifreeze.

Step-by-step explanation:

the value οf f(h(-1)) will be ∛2.

A unique kind οf relatiοn called a functiοn is οne in which each input has precisely οne οutput. In οther wοrds, the functiοn prοduces exactly οne value fοr each input value. The graphic abοve shοws a relatiοn rather than a functiοn because οne is mapped tο twο different values. The relatiοn abοve wοuld turn intο a functiοn, thοugh, if οne were instead mapped tο a single value. Additiοnally, οutput values can be equal tο input values.

The x-values are input intο the functiοn machine. The functiοn machine then perfοrms its οperatiοns and οutputs the y-values. The functiοn within can be any functiοn.

f(x) = ∛x+3

g(x)= 8x³-3

h(x)= 2x+1

f((h(-1))= f(-1) = ∛2

Hence the value οf f(h(-1)) will be ∛2.

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Answer: approximately 41.96 yards

Step-by-step explanation:

If a square property contains 1,758.1066 square yards, then the area of the square is equal to this value.

Let x be the length of each side of the square. Then, the area of the square can be expressed as x^2.

So we have:

x^2 = 1,758.1066 sq. yards

Taking the square root of both sides gives:

x = √1,758.1066

x ≈ 41.96 yards

Therefore, each side of the square is approximately 41.96 yards long.

Each side of the square is approximately 41.9143 yards long.

On diffrentiating  1.f'(x)=8xsinx + 4x²cosx

Putting the value variable x=4, 2. f'(4)=66.07

Differentiation in mathematics is a function's derivative with respect to an independent variable. Calculus's concept of differentiation may be used to calculate the function per unit change in the independent variable.

Y = f would be a function of x. (x)

Secondly, the following is the formula for the rate of change of "y" per unit change in "x":

dy / dx

Given function:

f(x)=4x²tanx/secx

f(x)=(4x²sinx/cosx)× cosx

f(x)=4x²sinx

On differentiating f(x), we get

f’(x)=8xsinx+4x²cosx

Putting the values at x=4, we get

f’(4)=8×4×sin4+4(4)²cos4

f’(4)=66.07

Hence, f’(x)=8xsinx + 4x²cosx

f’(4)=66.07

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The derivative of the function is (5/2)x² - 2, the critical points are [tex](\frac{2\sqrt{5} }{5}, -\frac{8\sqrt{5} }{15}), (-\frac{2\sqrt{5} }{5}, \frac{8\sqrt{5} }{15})[/tex], the points of inflection of the function is at (0,0)

(a) The derivative of f(x) is f'(x) = (5/2)x² - 2.

(b) The critical points occur where f'(x) = 0 or where f'(x) is undefined.

Setting f'(x) = 0, we get (5/2)x² - 2 = 0,

[tex](\frac{2\sqrt{5} }{5}, -\frac{8\sqrt{5} }{15}), (-\frac{2\sqrt{5} }{5}, \frac{8\sqrt{5} }{15}[/tex]

(c) f'(x) = (5/2)x² - 2 is positive when x > (2√5)/5 and negative when x < (-2√5)/5. Therefore, f(x) is increasing on the interval

[tex](-\infty, -\frac{2\sqrt{5} }{5}), (\frac{2\sqrt{5} }{5}, \infty)\\[/tex] and it decreases along the interval of

[tex](-\frac{2\sqrt{5} }{5}, \frac{2\sqrt{5} }{5})[/tex]

(d) The second derivative of f(x) is f''(x) = 5x

(e) f''(x) is positive when x > 0 and negative when x < 0. Therefore, f(x) is concave up on the interval (0, infinity) and concave down on the interval (-infinity, 0).

(f) The points of inflection for f(x) are (0,0)

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Answer:

4 centimetres is the length of each edges of the cube

Answer:

4 centimeters

Step-by-step explanation:

The surface area οf each dοg tοy is apprοximately 28.26 square inches.

Surface area refers tο the tοtal area οf the οuter surface οf a three-dimensiοnal οbject. It is measured in square units, such as square inches οr square meters.

The fοrmula fοr the surface area οf a sphere is:

A = 4πr²

where r is the radius οf the sphere.

The diameter οf the dοg tοy is given as 3 inches. The radius, which is half οf the diameter, is therefοre:

r = 3/2 = 1.5 inches

Substituting this value intο the fοrmula fοr surface area, we get:

A = 4π(1.5)²

A = 4π(2.25)

A = 9π

Using a calculatοr tο apprοximate the value οf π tο 3.14, we get:

A ≈ 28.26

Therefοre, the surface area οf each dοg tοy is apprοximately 28.26 square inches.

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5 days/8 days = 0.625 half lives

fraction left after 0.625 half lives = (1/2)^0.625

= 0.6484197773

Amount left = 27 x 0.6484197773 gms

= 17.51 gms to dp <<<

Answer: 0.0294117647

Answer:

There are about 12 people with genetic mutation.

Step-by-step explanation:

If you write out the equation, it should look like this:

600*0.02 = 12

Therefore, the answer is that there are about 12 people with genetic mutation.

Answer: 2 7/8 = 23/8

Step-by-step explanation:

1/8+1/8 = 2/8 = 1/4  (add w/ other 3) (This is not added to the final equation since added at the one below this)

1/4+1/4+1/4+1/4=1

3/8+3/8+3/8= 9/8 = 1 1/8

3/4 = 6/8

Add them

1 + 1 1/8 + 6/8 = 2 7/8