Elena wonders how much water it would take to fill her cup. She drops her pencil in her cup and notices that it just fits diagonally. (See the diagram.) The pencil is 13 cm long and the cup is 12 cm tall. How much water can the cup hold? Explain or show your reasoning.

Answer:

Step-by-step explanation:

If the temperature of a person follows a normal distribution, we know that approximately 95% of the observations fall within 2 standard deviations of the mean. Since we are given that we want to find the probability of the temperature being within 2.42 standard deviations of its mean, we can use the standard normal distribution and the z-score formula.

The z-score formula is given by:

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation. In this case, we want to find the probability that the temperature is within 2.42 standard deviations of the mean, so we can set:

z = 2.42

Since the normal distribution is symmetric, we can find the area to the right of the mean (z = 0) and double it to get the total probability. Using a standard normal distribution table or calculator, we find that the area to the right of z = 2.42 is approximately 0.0074. So the area to the left of z = 2.42 is approximately 0.9926.

Doubling this area gives us the total probability:

P(z < 2.42 or z > -2.42) = 2 * P(z < 2.42) = 2 * 0.9926 = 0.9852

Therefore, the probability that the temperature of a randomly selected person will be within 2.42 standard deviations of its mean is 0.9852, or approximately 0.9852 with four decimal places.

Answer:

To find the probability of a value between 50 and 70 in a normal distribution with mean 40 and standard deviation 15, we need to first standardize the values using the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

For the lower bound of 50:

z = (50 - 40) / 15 = 0.67

For the upper bound of 70:

z = (70 - 40) / 15 = 2

Using a standard normal distribution table or a calculator with a built-in normal distribution function, we can find the probabilities corresponding to these z-scores:

P(0 < z < 0.67) = 0.2514

P(0 < z < 2) = 0.4772

To find the probability of a value between 50 and 70, we can subtract the probability of the lower bound from the probability of the upper bound:

P(50 < x < 70) = P(0 < z < 2) - P(0 < z < 0.67)

P(50 < x < 70) = 0.4772 - 0.2514

P(50 < x < 70) = 0.2258

Therefore, the probability of a value between 50 and 70 in this normal distribution is 0.2258 or about 22.58%.

Answer:    c=2πr

Step-by-step explanation:

because im just that guy

Answer:

c=62.8

Step-by-step explanation:

diameter=20

radius=10

c=2πr

c=2×22/7×10

c=62.8

Answer:

36π

Step-by-step explanation:

To find the volume of the sphere we have to use the equation: [tex]\frac{4}{3}[/tex]πr³

To work our answer out we have to distribute the values we are given into the question...

We can ignore π for now as we will add it at the end

Now we have to solve what we are given...

Now we can put π into our answer...

Hope this helps, have a lovely day! :)

$73,394.49 is the present value of $80,000 that is due in 4 years at a 4% interest rate.

Compound interest is interest that is accrued on both the principal and the prior interest. It is frequently referred to as "interest over the interest" as a result. Here, the interest that has already accrued is added to the principal, and the resulting amount acts as the new principal for the following period.

Hence, compound interest is the sum of interest on the principal and interest on earlier interest.

Using the formula below, it is possible to determine the present value of $80,000 payable in 4 years at a 4% rate of interest compounded quarterly:

PV = FV / (1 + r/n) ^(nt)

such that:

Present Value, or PV, is the term.

FV stands for future value.

The annual number of compounding periods is n, and the interest rate is r.

The number of years is t.

To solve this problem, we have:

FV = $80,000

r = 4% = 0.04

n = 12 (as compounding is done monthly)

t = 4

Adding these values to the formula provides the following results:

PV = 80,000 / (1 + 0.04/12) ^ (12 × 4)

PV = 80,000 / (1.003333) ^48

PV = 80,000 / 1.090777

PV = 73,394.49

As a result, $73,394.49 is the present value of $80,000 that is due in 4 years at a 4% interest rate.

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Answer:

A

Step-by-step explanation:

Using suitable identities, the following mathematical expressions are evaluated:

a) 972 is evaluated as 1000 - 28

b) 102 x 105 is evaluated as = 10710

Mathematical evaluation refers to the process of finding the numerical value of a mathematical expression or equation using mathematical operations and rules. The evaluation involves substituting values for variables and simplifying the expression or equation until a final answer is obtained.

In more complex cases, mathematical evaluation may involve multiple steps and the use of various identities and formulas to simplify the expression or equation before arriving at the final answer

The given values are evaluated as follows:

a) 972 can be evaluated using the following identity:

972 = 1000 - 28

b) 102 x 105 can be evaluated using the following identity:

102 x 105 = (100 + 2) x 105 = 100 x 105 + 2 x 105 = 10500 + 210 = 10710

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The fraction of the water bottles that has at least 24 ounces is 1/4.

A box plot is a graph that is used to show the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%

24 represents the third quartile of the dataset. The third quartile represents 75% of the dataset. A third quartile value of 24 means that at most 3/4 (75%) of the dataset has a value that is at most 24 and 1/4 or 25% of the dataset has a value that is at least 24.

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Answer:

Step-by-step explanation:

x² + 4x-21

x²-5x-2

x² + 3x + 7

x² + 4x-21

x²-5x-2

x² + 3x + 7

x²-x-1

x²-x-1

The coordinates of the vertices from of the image of triangle ABC are A'(x, y) = (0, - 1), B'(x, y) = (- 1, - 1) and C'(x, y) = (- 0.5, - 4).

Herein we find the representation of a triangle on a Cartesian plane, which is generated by three non-colinear points set on the plane mentioned above. The image of the triangle can be found by applying the following rigid transformation formulas:

x' = Ox + (x - Ox) · cos θ - (y - Oy) · sin θ

y' = Oy + (x - Ox) · sin θ + (y - Oy) · cos θ

Where:

If we know that (Ox, Oy) = (- 2, 0), θ = 180°, A(x, y) = (- 4, 1), B(x, y) = (- 3, 1) and C(x, y) = (- 3.5, 4), then the resulting coordinates of the triangle are, respectively:

xA' = Ox + (xA - Ox) · cos θ - (yA - Oy) · sin θ

xA' = - 2 + [- 4 - (- 2)] · cos 180° - (1 - 0) · sin 180°

xA' = 0

yA' = Oy + (xA - Ox) · sin θ + (yA - Oy) · cos θ

yA' = 0 + [- 4 - (- 2)] · sin 180° + (1 - 0) · cos 180°

yA' = - 1

xB' = Ox + (xB - Ox) · cos θ - (yB - Oy) · sin θ

xB' = - 2 + [- 3 - (- 2)] · cos 180° - (1 - 0) · sin 180°

xB' = - 1

yB' = Oy + (xB - Ox) · sin θ + (yB - Oy) · cos θ

yB' = 0 + [- 3 - (- 2)] · sin 180° + (1 - 0) · cos 180°

yB' = - 1

xC' = Ox + (xC - Ox) · cos θ - (yC - Oy) · sin θ

xC' = - 2 + [- 3.5 - (- 2)] · cos 180° - (4 - 0) · sin 180°

xC' = - 0.5

yC' = Oy + (xC - Ox) · sin θ + (yC - Oy) · cos θ

yC' = 0 + [- 3.5 - (- 2)] · sin 180° + (4 - 0) · cos 180°

yC' = - 4

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Answer:

The solutions to the given system of equations are:

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=-x^2+4\\y=2x+1\end{cases}[/tex]

To solve the given system of equations, substitute the second equation into the first equation:

[tex]\implies 2x+1=-x^2+4[/tex]

Add x² to both sides:

[tex]\implies x^2+2x+1=4[/tex]

Subtract 4 from both sides:

[tex]\implies x^2+2x-3=0[/tex]

Factor the quadratic equation:

[tex]\implies x^2+3x-x-3=0[/tex]

[tex]\implies x(x+3)-1(x+3)=0[/tex]

[tex]\implies (x-1)(x+3)=0[/tex]

Apply the zero product property:

[tex](x-1)=0 \implies x=1[/tex]

[tex](x+3)=0 \implies x=-3[/tex]

Substitute the found values of x into the second equation and solve for y:

[tex]x=1 \implies y=2(1)+1=3[/tex]

[tex]x=-3 \implies y=2(-3)+1=-5[/tex]

Therefore, the solutions to the given system of equations are:

The distance KT and angle of elevation of the pole's top, K, with respect to the ground, D, are;

KT is about 6.2 cm

DN = 30 m

The angle of elevation of K from D is  0.23°

The angle created between a horizontal line and the line of sight of a viewer gazing up at an object is known as the angle of elevation.

The two vertical poles are MT and NK

The height of MT = 8 cm

The height of NK = 12 cm

From the top of the pole MT, point T, to the top of the pole NK, point K, there is a 40-degree elevation difference.

The poles' height differences are 12 cm - 8 cm, or 4 cm.

The distance KT can be found as follows;

Therefore;

sin(40°) = 4/KT

KT = 4/(sin(40°)) ≈ 6.2

The distance KT is approximately 6.2 cm

According to the information in the question, the distance is DN = 30 m.

The base of the poles MT and NK is on the same level ground as point D.

ND=30m

Hence, the trigonometric ratio for tangent may be used to get the angle of elevation,, of the top of the pole NK, (point K), from D as follows;

tan(θ) = NK/ND

tan(θ) = (12 cm)/(30 m) = 0.12/30 = 0.004

θ = arctan(0.004) ≈ 0.23°

K is elevated from d at an angle of roughly 0.23°.

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The total number of miles driven by the two brothers is 2,220 miles.

Average speed is the ratio of total distance and time. It measures how fast an object is moving with respect to time.

Average speed = distance / time

In order to determine the formula for distance from the formula of average speed, multiply both sides of the equation by time.

Distance = time x average speed.

The distance that Kevin covered  = 65 x 12 = 780 miles

The distance that Jeffery covered  = 60 x 24 = 1440 miles

The total distance is the sum of the distance covered by Kevin and the distance covered by Jeffery.

Total distance = 1440 + 780 = 2,220 miles

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Therefore , the solution of the given problem of expressions comes out to be Q = Q0 e(ln(0.9)/24)t this is the formula for the block's mass at any moment t.

Calculations such as joining, random subdivision, variable multiplier, and elimination are required. They would accomplish the following if they were united: An  algorithm, some information, and a mathematical equation. Numerical information, formulas, elements, and arithmetic operations like additions, erasures, errors, and categories are all included in a declaration of truth. Words and phrases can be evaluated and analysed.

Here,

Let's write Q for the radioactive material's mass at any moment t. (t). We can write: Because the substance decays at a rate proportional to its mass.

=> -kQ = dQ/dt

where k is a measure of ratio. This first-order differential equation can be solved by separating the variables, and it is separable:

=>-k dt Equals dQ/Q

By combining both parts, we obtain:

=>Q = -kt + C, where

where C is the integration constant. We can use the original assumption that the material has a mass of Q grammes at time t = 0 to determine C:

=> ln(Q) = C

When we add this to the prior solution, we obtain:

=> Q = -kt + ln, where (Q0)

where Q0 is the starting mass of the material.

=> 0.9Q0 = Q(24) = Q0 e^(-k*24)

After finding k, we obtain:

=> k = ln(0.9)/(-24) (-24)

Using this value of k as a substitute in the preceding equation, we obtain:

=> (ln(0.9)/24)t - ln(Q) + ln (Q0)

If we simplify, we get:

=> Q = Q0 e(ln(0.9)/24)t

This is the formula for the block's mass at any moment t.

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Answer:

Step-by-step explanation:

The formula for average rate of change of a function f(x) over an interval [a, b] is given by:

Average rate of change = [f(b) - f(a)] / (b - a)

In this case, we are given the function f(x) = 10 and the interval [2, 3]. So, a = 2 and b = 3. Substituting these values, we get:

Average rate of change = [f(3) - f(2)] / (3 - 2)

= [(10 x 3 - 4) - (10 x 2 - 4)] / (3 - 2)

= (30 - 20) / 1

= 10

Therefore, the average rate of change of the function f(x) = 10 from [2, 3] is 10.

Answer:

a^2-ac/a-b + b^3-b^2*a/b+c + bc-c^2/a-c

Step-by-step explanation:

The condition that proves congruent of two given triangles ΔDEF ∼ ΔJKL would be option (a) DE : JK = 3:1 but ratio value in option is given wrong.

In this case triangle in congruent when two sides and one angle of first triangle is equal to two sides and one angle of second triangle.

we have given proof two triangles congruent by the postulate of SAS.

Since two corresponding sides of these triangles are congruent and one  angle is also congruent. So  to prove both the triangles congruent.

∠EDF ≅ ∠KJL will complete the SAS property to prove both the triangles are congruent.

DE : JK

= 21 : 7

= 3 : 1

So, DE: JK = 3:1 is answer.

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If one borrowed $2,500 for 2 years and paid interest of $155, the interest rate charged was 3.053%.

The interest rate is computed using an online finance calculator with the following set parameters.

The interest rate represents the annual percentage rate of interest charged on the loan for 2 years.

N (# of periods) = 2 years

PV (Present Value) = $2,500

PMT (Periodic Payment) = $-0

FV (Future Value) = $-2,655

Results:

I/Y = 3.053%

Total Interest = $155.00

Thus, for this loan, the interest rate was 3.053%.

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Answer:180 square inches

Step-by-step explanation:

18*6+9*8=180

There are 6 possible outcomes for each roll of the cube, since there are 6 letters on the cube. Out of the 6 letters, there are 3 consonants (S, L, V) and 3 vowels (O, E, D).

To find the probability of rolling two consonants, we need to multiply the probability of rolling a consonant on the first roll (3/6) by the probability of rolling a consonant on the second roll (also 3/6), since the rolls are independent events.

(3/6) * (3/6) = 9/36 = 1/4

Therefore, the probability of rolling two consonants is 1/4, which can also be expressed as 25%.

Therefore, y = 7x + 2/5, 7x + 5 = y, and y = 7x + 4 are the equations that depict a line parallel to y = 7x + 3.

A mathematical statement known as an equation demonstrates the equality of two expressions or values by separating them with an equal symbol. The values on either side of the equal symbol in an equation are equal and can be used to find the value of an unknown variable. For instance, the equation "2x + 3 = 7" states that "2x + 3" equals the number "7".

given

Since parallel lines have identical slopes, the equation of a line that is perpendicular to y = 7x + 3 will have the same slope as 7.

Any equation of the form y = 7x + b, where b is a constant, will therefore indicate a line parallel to y = 7x + 3.

y = 3x + 7: This line's slope, 3, is less than 7, so it is not parallel to the line y = 7x Plus 3.

y = 7x + 2/5: This line is parallel to y = 7x + 3 because it has the same slope as that equation.

7x + 5 = y: This equation is parallel to y = 7x + 3 because y = 7x + 5 has the same slope as it.

y = 7 + 3x is not parallel to y = 7x + 3 because it has the same slope as the solution y = 3x + 7, which does not equal 7.

Therefore, y = 7x + 2/5, 7x + 5 = y, and y = 7x + 4 are the equations that depict a line parallel to y = 7x + 3.

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The complete question is:-  Choose all the equations below that represent a line parallel to

y=7x+3

y=3x+7 y=7x+2/5

7x+5=y

y=2x+3

y=4+7x y=3-7x

y+7x=3 y=7+3x

Check the picture below.

[tex]52=(4y-4)+(3y)\implies 52=76-4\implies 56=7y \\\\\\ \cfrac{56}{7}=y\implies \boxed{8=y} \\\\\\ \stackrel{\measuredangle W}{4y-4}\implies 4(8)-4\implies \text{\LARGE 28}[/tex]

The missing description in radical form is ∛64.

In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;

bⁿ

Where:

the variables b and n represent numerical values or an algebraic expression.

Based on the information about the rational exponent form, we have the following:

64^{1/3} = 4

∛64 = 4.

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Answer:

34,900,000

Step-by-step explanation:

349 ×  [tex]10^{5}[/tex]

[tex]10^{5}[/tex] = 100,000

349 x 100000 = 34,900,000

So, the answer is 34,900,000

The z-scοre is prefer tο have cοmpared tο yοur cοmpetitοrs fοr the time it tοοk yοu tο cοmplete the race is -2.50.

When a value is given a Z-scοre, it shοws hοw far οff frοm the standard deviatiοn it is. The amοunt οf standard deviatiοns a given data pοint is abοve οr belοw the mean is represented by the Z-scοre, alsο knοwn as the standard scοre. The level οf variability within a particular data cοllectiοn is effectively reflected in the standard deviatiοn.

We knοw that ,

=> z=(x-µ)/σ

If we have z scοre less it means we cοmplete the race in less time as cοmpare tο οthers.

Sο, z scοre -2.50 is least as per given all the οptiοns. sο ,we wοuld yοu prefer -2.50 cοmpared tο οur cοmpetitοrs fοr the time it tοοk yοu tο cοmplete the race.

Hence the z-scοre is -2.50.

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At 4.0 megabits per second, Able Cable provides the fastest average downloading speed.

To find out which company offers the fastest mean downloading speed, we need to calculate the mean download speed for each provider and then compare the results.

The mean download speed for CityNet is:

(3.6 + 3.7 + 3.7 + 3.6 + 3.9) / 5 = 3.7 megabits per second

The mean download speed for Able Cable is:

(3.9 + 3.9 + 4.1 + 4.0 + 4.1) / 5 = 4.0 megabits per second

The mean download speed for Tel-N-Net is:

(3.9 + 3.7 + 4.0 + 3.6 + 3.8) / 5 = 3.8 megabits per second

Therefore, Able Cable offers the fastest mean downloading speed at 4.0 megabits per second.

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The number of slides per hour that Ibragim believes he will be able to process w weeks from now is represented by the following calculation: 65 + 2w.

Number is an abstract concept used to describe a quantity or amount. It can refer to a countable quantity of objects, or it can refer to an abstract concept such as size, direction, or position. In mathematics, number is used as a way of measuring and describing a quantity or amount. It is used to represent quantities in equations and formulas, to compare quantities, and to measure and compare distances. Number is also used to represent relationships between different objects, such as in geometry where angles, lines, and points are all represented by numbers.


This equation shows that Ibragim's slides per hour processing speed will increase by 2 for each week that passes. For example, if Ibragim practises for 4 weeks, his slides per hour processing speed will have increased from 65 to 73. This is because 65 + (2 x 4) = 73. Therefore, if Ibragim practises for w weeks, then the number of slides per hour he believes he will be able to process will be 65 + 2w.

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The expression 65 + 2w represents the number of slides per hour that Ibragim believes he will be able to process w weeks from now. This expression can be used to calculate the number of slides per hour that Ibragim believes he will be able to process after any number of weeks of practice.

Number is an abstract concept used to describe a quantity or amount. It can refer to a countable quantity of objects, or it can refer to an abstract concept such as size, direction, or position. In mathematics, number is used as a way of measuring and describing a quantity or amount. It is used to represent quantities in equations and formulas, to compare quantities, and to measure and compare distances. Number is also used to represent relationships between different objects, such as in geometry where angles, lines, and points are all represented by numbers.


The number of slides per hour that Ibragim believes he will be able to process w weeks from now is given by the expression 65 + 2w. In this expression, 65 represents the number of slides per hour that Ibragim can currently process, and 2w represents the number of slides per hour that Ibragim believes he can increase his processing speed by each week.

For example, if Ibragim believes he will be able to process slides at a rate of 100 per hour after 6 weeks of practice, then the expression would be 65 + 2(6) = 77. This means that Ibragim believes he will be able to process 77 slides per hour after 6 weeks of practice. In general, if w represents the number of weeks of practice, then the expression 65 + 2w represents the number of slides per hour that Ibragim believes he will be able to process w weeks from now.

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Complete questions as follows-