Given: EFGH is a square
Find the length of FH.

Answer:

\(\sqrt{202}\) units or 14.2 units (rounded to the nearest tenth)

Step-by-step explanation:

To find the distance between a pair of two points, use the distance formula  \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\). Substitute the x and y values of (-1,-2) and (8,9) into the formula and simplify:

\(d = \sqrt{(-1-8)^2+(-2-9)^2} \\d = \sqrt{(-9)^2+(-11)^2} \\d = \sqrt{81+121} \\d= \sqrt{202}\)  

So, as an exact answer, the distance is \(\sqrt{202}\) units.

(To find the decimal approximate of that answer, enter it into a calculator. This would make the decimal approximate 14.2 units, when rounded to the nearest tenth.)  

Answer:

14.2

Step-by-step explanation:

All you need to do is plug the coordinates into the distance formula.

√(x2 - x1)² + (y2 - y1)²

√[8 - (-1)]² + [9 - (-2)]²

√(9)² + (11)²

√81 + 121

√202

= 14.2

Answer:blue

Step-by-step explanation:

Answer:

you just multiply the values inside the parentheses. 11 x -4 x 12, so its -44 x 12, being -528

Step-by-step explanation:

Answer:

The one that makes a circle

Step-by-step explanation:

The probability that the coin will land heads up on the first flip, tails up on the second flip, and tails up on the third flip is (1/8).

If we toss a coin, we have two possible outcomes: head or tail. Now:

P(E) = Favourable outcomes / Total outcomes

      = 1/2

As per the question, we need heads on the first throw and tails on the next two throws. We know that for independent events:

P(A∩B∩C) = P(A)*P(B)*P(C)

Let A be the event of getting head on the first throw and B and C be events of getting tails on the second and third throws of dice respectively.

P(A) = P(B) = P(C) = 1/2

So, P(A∩B∩C) = (1/2)*(1/2)*(1/2) = 1/8

So, the Required probability is (1/8)

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Using the Pythagorean Theorem, it is found that:

a) The hypotenuse is of 9.49 cm.

b) The new area of the triangle is of 30 cm².

The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle with the length of the hypotenuse h, according to the following equation:

\(h^2 = l_1^2 + l_2^2\)

For this problem, the sides are given as follows:

3 cm and 9 cm.

Hence the hypotenuse is given by:

h² = 3² + 9²

h = sqrt(3² + 9²)

h = 9.49 cm.

The hypotenuse is of 9.49 cm.

The area of a right triangle of sides a and b is given by half the multiplication of the sides, as follows:

A = 0.5ab.

For this problem, we have that:

Then:

A = 0.5 x 5 x 12 = 30 cm².

The new area of the triangle is of 30 cm².

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Answer:

1:4

Step-by-step explanation:

so we are comparing the arc lengths to get the ratio of DE:BC

\( \beta \div 360 \times 2 \times \pi \times r\)

to get arc length BC as

\( \beta \times \pi \times r \div 90\)

and for DE as

\( \beta \times \pi \times r \div 360\)

so divide DE by BC where beta pi r will cancel out. and you remain with 1/4 Wich will translate to 1:4

I'm sorry, but there seems to be some confusion in your question. The first part mentions a sequence 22n+12no while the second part mentions a sequence 40n+sin(n) In=1. It is unclear how these two sequences are related.

Without further information, it is impossible to determine whether the sequence converges or what its limit would be. Could you please provide more context or clarify your question?
Hi! Based on the given information, the sequence is:

In = 40n + sin(n), where In = 1.

(i) To determine if the sequence converges, we need to analyze the behavior of the sequence as n approaches infinity. The term 40n grows without bound as n increases, while the sin(n) term oscillates between -1 and 1. Since the 40n term dominates the behavior of the sequence, it does not converge.

(ii) Since the sequence does not converge, it does not have a limit as n approaches infinity.

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The normal curve with a mean of 0 and standard deviation of 1 is called (D)  the z-value.

Therefore, the normal curve with a mean of 0 and standard deviation of 1 is called (D)  the z-value.

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The trigonometric functions sine and cosecant have a positive sign.

In this problem we must determine what trigonometric functions associated with a vector of the form (x, y) have a positive sign. This can be done by computing on each function:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

If we know that x = - 12 and y = 5, then the values of the trigonometric functions are, respectively:

sin θ = 5 / √[(- 12)² + 5²]

sin θ = 5 / 13

cos θ = - 12 / √[(- 12)² + 5²]

cos θ = - 12 / 13

tan θ = - 5 / 12

sec θ = - 13 / 12

csc θ = 13 / 5

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Answer:

  y=x+5

Step-by-step explanation:

The equation is given in slope-intercept form, so we can read the slope from the equation. It is the x-coefficient, -1.

The slope of the perpendicular line will be the opposite reciprocal of this value:

  -1/-1 = 1

The new y-intercept will be ...

  b = y -mx = (4) -(1)(-1) = 5

Then the slope-intercept equation of the perpendicular line is ...

  y = x +5

wdym “What are the values of each Halloween icon”?

Answer:

Length & Breadth could be : 4 meters , 5 meters

Step-by-step explanation:

Border, ie perimeter measurement of Rectangle = 2 ( Length + Breadth )

So, 2 (Length + Breadth) = 18

Length + Breadth = 18 / 2

Length + Breadth  = 9

So, sum of length & breadth must be = 9.

(L, B) = (2,5) ; (2,8) ; (2,9) and (3,5) ; (3,8) ; (3,9) don't satisfy this condition. (4,5) ; (4,8) also don't.

(L, B) = (4,5) satisfy it. As sum 4 + 5 = 9.

Answer:

22.5

Step-by-step explanation:

A=1/2 times base times height

Answer:

22.5

Step-by-step explanation:

The probabilities for each particular color are:

We assume that all the colors have the same probability of being randomly selected, then the probability of randomly selecting a particular color is eqal to the quotient between the nmber of balloons with that color and the total number of balloons.

The total number is 21, and we will get:

Probability of red:

p = 5/21

Probability of blue:

q = 3/21

Probability of green:

k = 4/21

Probability of yellow:

J = 4/21

Probability of purple:

n  = 5/21

If these are all the possible outcomes in the sample space, then the probabilities should add up to 1. let's check that:

5/21 + 3/21 + 4/21 + 4/21 + 5/21 = (5 + 3 + 4 + 4 + 5)/21 = 21/21 =1

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Answer:

27 is 30% of what number?

D. 90

Step-by-step explanation:

You're welcome.

Answer:

a

Step-by-step explanation:

Answer:

x < -1

Step-by-step explanation:

Hope this helps you :)

You can use either a numerical (integer or floating-point) variable or a Boolean variable to store the value of a logical expression.

Numerical Variable: You can use a numerical variable, such as an integer or floating-point variable, to store the result of a logical expression. In this case, the logical expression would be evaluated and assigned a numerical value, typically 0 or 1, representing false or true, respectively. For example, if you have a logical expression "x > 5", you can assign the result to a numerical variable like "result = (x > 5)", where the value of "result" would be 0 if the expression is false and 1 if it is true.

Boolean Variable: Alternatively, you can use a Boolean variable to directly store the truth value of a logical expression. A Boolean variable can only have two possible values: true or false. In this case, the logical expression would be evaluated and directly assigned to the Boolean variable. For example, if you have a logical expression "x > 5", you can assign the result to a Boolean variable like "isGreaterThanFive = (x > 5)", where "isGreaterThanFive" would be true if the expression is true and false if it is false.

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The Z score for the proportion of consumers who purchased milk chocolate, given a sample of 97 individuals where 52% purchased milk chocolate, is approximately -3.87.

To calculate the Z score, we need to compare the observed proportion (52%) with the expected proportion (79%) and account for the sample size. The formula for calculating the Z score for proportions is: Z = (p - P) / sqrt((P * (1 - P)) / n), where p is the observed proportion, P is the expected proportion, and n is the sample size.

Substituting the given values into the formula, we have: Z = (0.52 - 0.79) / sqrt((0.79 * (1 - 0.79)) / 97). Simplifying the equation further, we get: Z = (-0.27) / sqrt(0.1621 / 97).

Calculating the expression inside the square root, we have sqrt(0.1621 / 97) ≈ 0.040. Substituting this value back into the equation, we find: Z ≈ (-0.27) / 0.040 ≈ -6.75.

Rounding the Z score to two decimal places, we get approximately -3.87.

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The symbol ∪ represents the "union of events" in the context of probability and set theory.

The symbol ∪ indicates the union of events. This option corresponds to choice (d) in your given list. The union of events refers to the occurrence of at least one of the events in question. In other words, it combines the outcomes of two or more events into a single set, without any repetitions. This concept is essential in understanding probability theory, as it helps to analyze the likelihood of different events happening together or separately.

This means that it represents the set of all outcomes that belong to either one or both of the events being considered. For example, if event A represents rolling an even number on a die and event B represents rolling a number greater than 4, then the union of events A and B would be the set of outcomes {2, 4, 5, 6}. It is important to note that the union of events is different from the intersection of events, which represents the set of outcomes that belong to both events being considered. The sample space, on the other hand, represents the set of all possible outcomes of an experiment. Finally, the symbol ∑ represents the sum of probabilities of events, not the symbol ∪.

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Swinging an arc on either side of the segment is the correct next step when bisecting a segment using a compass.

We have,

When bisecting a segment using a compass, Jessica's next step after placing the compass on one endpoint and opening it to a width larger than half of the segment is to swing an arc on either side of the segment.

Here's a step-by-step explanation:

- Jessica starts by placing the compass on one endpoint of the segment.

- She opens the compass to a width larger than half of the segment. This ensures that the arcs she will create will intersect on both sides of the segment.

- Keeping the compass width unchanged, Jessica pivots the compass around the endpoint, drawing arcs on both sides of the segment.

- The arcs will intersect at two points.

- Finally, Jessica can connect these two points with a straight line to find the midpoint, which is the point where the segment is bisected.

- By swinging the arcs on either side of the segment, Jessica ensures that the midpoint is accurately determined, as it is the point equidistant from both endpoints.

Therefore,

Swinging an arc on either side of the segment is the correct next step when bisecting a segment using a compass.

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Answer:

Step-by-step explanation:

He collected a total of 225 stamps. If 88​% of the stamps he collected were​ foreign, how many other stamps did he​ collect?

28=9x-8

36=9x

x=4

:) hope it helps!

Answer:

There's no answer choices but I can give you an example.  

Step-by-step explanation:

Hopefully this helps.  

The equivalent expression to 7×7² is C. (7³)¹.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An exponential expression 7×7².

Now, We know 7×7² = 7¹⁺² = 7³.

It can also be written as (7³)¹.

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Answer:

c) l x - 5 l - 4

Step-by-step explanation:

when you're graphing functions whatever is inside the paranthesis, square root or absolute value determines whether you go left or right, if its a negative you go to the right, if its positive you go to the left. So the opposite of what you would expect it to go

in this instance its - 5, so you go 5 units to the right

and the number outside determines if you go up or down, in this question its - 4 so you go down 4 units

Answer:

-15

Step-by-step explanation:

I think

The total number of cupcakes in the order is 50.

Since you are giving away 3 cupcakes, that is indeed 60% of your order.

If you are giving away 3 cupcakes to your friends and that is 60% of your order, then the total number of cupcakes you ordered is 5.

To find the total number of cupcakes, we can use the concept of percentages.

If 3 cupcakes represent 60% of the order, then we can set up the following proportion:

3/60% = x/100%

To solve for x, we can cross-multiply:

0.6x = 300

Multiplying both sides by 10 gives:

x = 50

Therefore, the total number of cupcakes in the order is 50.

And since you are giving away 3 cupcakes, that is indeed 60% of your order.

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