A teacher recorded unit 4 test scores from her class.

58, 64, 66, 70, 71, 75, 77, 80,
84, 85, 87, 90, 93, 95, 96.

Find the percentile rank of a score of 71 on this street -

Victor is in the 60th percentile, what was his score?

Answer:

  761.25 miles

Step-by-step explanation:

  (2.625 mi/trip)(2 trip/day)(5 day/week)(29 weeks) = 2.625×2×5×29 mi

  = 761.25 miles in 29 weeks

The perimeter of the rectangle is 2(sqrt(82) + 4) units.

what is perimeter?

Perimeter is the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. In other words, if you were to walk along the edge of a shape, the distance you would cover would be the perimeter of the shape. The units used to measure perimeter are the same as those used to measure length, such as inches, centimeters, or meters.

Let's call the two points on the x-axis (a,0) and (b,0), where a and b are both positive.

Since the rectangle has an area of 54 square units, we know that:

length x width = 54

We also know that one point is located at (5,9), so the length of the rectangle must be the distance between (5,9) and (a,0) or (b,0). Similarly, the width must be the distance between (5,9) and (a,0) or (b,0).

Let's first find the length. The distance formula gives us:

length = sqrt((5-a)^2 + 9^2) or sqrt((5-b)^2 + 9^2)

Next, let's find the width. Again, using the distance formula, we have:

width = sqrt((a-b)^2 + 0^2)

Now we can use the fact that the area of the rectangle is 54 to solve for a and b.

54 = length x width

54 = sqrt((5-a)^2 + 9^2) x sqrt((a-b)^2 + 0^2)

54 = sqrt((5-a)^2 x (a-b)^2 + 0^2)

2916 = (5-a)^2 x (a-b)^2

Since a and b are both positive, we know that 5 > a > b. Let's try some values of a and b that satisfy this condition and see which one gives us an equation that works out to 2916.

If a = 4 and b = 2, we get:

2916 = (5-4)^2 x (4-2)^2 = 4

This doesn't work. Let's try a = 3 and b = 2:

2916 = (5-3)^2 x (3-2)^2 = 4

Still doesn't work. Let's try a = 6 and b = 2:

2916 = (5-6)^2 x (6-2)^2 = 16

This works! So the two points on the x-axis are (2,0) and (6,0).

Now we can find the length and width:

length = sqrt((5-6)^2 + 9^2) = sqrt(82)

width = sqrt((6-2)^2 + 0^2) = 4

Finally, we can find the perimeter:

perimeter = 2 x length + 2 x width

perimeter = 2 x sqrt(82) + 2 x 4

perimeter = 2(sqrt(82) + 4)

Therefore, the perimeter of the rectangle is 2(sqrt(82) + 4) units.

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Answer:

Step 1: Locate and underline the whole numbers place (2) then look at the digit to the right (6):

2.6

Step 2: In this case, the digit to the right (6) is 5 or above. So, we add 1 to the whole numbers place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 3 as the answer.

In short: 2.6 rounded to the nearest whole number is 3.

Bob needs to run at a speed of at least 10.39 feet per second to catch the elevator.

To catch the elevator, Bob needs to reach the door before it fully closes, which means he needs to cover the distance of 4.3 - 0.6 = 3.7 feet in the time it takes the door to close. We can use the formula:

distance = rate x time

to find the time it takes for the door to close, and then use this time to find the speed that Bob needs to run. Let's set up the equation:

3.7 = 1.2t

where t is the time it takes for the door to close.

Solving for t, we get:

t = 3.7/1.2 = 3.08 seconds

Now we can use the formula again to find the speed that Bob needs to run:

speed = distance / time

speed = 32/3.08

speed = 10.39 feet per second (rounded to the nearest hundredth)

Therefore, Bob needs to run at a speed of at least 10.39 feet per second to catch the elevator.

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Answer:

C(t) = 25+34.37t

Step-by-step explanation:

It is given that,

The monthly fee to be a member is $25 and the total cost of membership, including the joining fee, would be $300 for 8 months.

We need to write an equation for C in terms of t representing the total cost of the gym membership over t months.

At t=0, Jonathan pays $25 as joining fee.

Equation will be :

C(t) = Co+kt

Initially, Co = 25

C(t) = 25

At t = 8,

C(8) = 25 + k(8) = 300

8k = 275

k = 34.37

⇒ C(t) = 25+34.37t

Hence, this is the required equation.

Answer: 4

Step-by-step explanation:

27,900/2 =  13,950

27,900 * .115 =3208.5

13,950/3208.5 = 4.3

4

Answer:

(-11.667, -9.333)

Step-by-step explanation:

were you looking for the intersection? that's what i just found. have a great day and thx for your inquiry.

a) The point estimate is 3 thousand dollars.

b) The 9% confidence interval for the difference between the two population means is -1.829 to 7.829 thousand dollars.

The point estimate is given by the mean of the sample data for each type of project. For the first type of project, the mean is (3.3 + 2.7 + 3.5)/3 = 3.17 thousand dollars.

For the second type of project, the mean is (4.3 + 4.6 + 4.2)/3 = 4.37 thousand dollars.

The difference between the means is 4.37 - 3.17 = 1.2 thousand dollars.

To calculate the confidence interval, we need to find the standard error of the difference and the critical value for a t-distribution with n1 + n2 - 2 degrees of freedom. The formula for the standard error is:

SE(d) = sqrt[ (s1^2 / n1) + (s2^2 / n2) ] = sqrt[ ((0.4)^2 / 3) + ((0.2)^2 / 3) ] = 0.282

The critical value for a 9% two-tailed t-test with 4 degrees of freedom is 2.306 (from a t-table or using Excel's TINV function).The margin of error for the 9% confidence interval is:

ME = t(0.09/2, 4) * SE(d) = 2.306 * 0.282 = 0.649

The 9% confidence interval for the difference between the population means is:

d ± ME = 1.2 ± 0.649 = (0.551, 1.849)

Therefore, the 9% confidence interval for the difference between the two population means is -1.829 to 7.829 thousand dollars (rounded to three decimal places).

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Answer:

The additional length is 3 ft

The new length of the rectangle after the increase is 15 ft and the width 13 ft

Step-by-step explanation:

The area A of a rectangle is given as

A = L * B

where L is the length of the rectangle and B is the width

As such for a rectangle 10 ft by 12 ft, the area

= 10 * 12

= 120 sq ft

If this is increased by 75 sq ft, the new area becomes

= 120 + 75

= 195 sq ft

If the length and the width are to be increased by the same amount, let this amount be x then the new length will be 12 + x and width 10 + x such that

(12 + x)(10 + x ) = 195

expand

x² + 22x + 120 =  195

x² + 22x +120 - 195 = 0

x² + 22x - 75 = 0

x² +25x -3x - 75 = 0

x(x +25) -3(x + 25) = 0

(x + 25) (x- 3) = 0

x = -25 or 3

since the additional length cannot be negative, it is 3ft.

As such the new length

= 3 + 12 = 15 ft

the new width

= 10 + 3

= 13 ft

Answer:

A. 2x square root 11x

Step-by-step explanation:

The equivalent expression for the given expression is 2x√11x.

The given expression is 2x√44x-2√11x³.

We need to find the equivalent expression.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Now, factor and rewrite the radicand in exponential form.

That is, 2x√44x-2√11x³=2x√2².11x-2√x. 11x²

Rewrite the expression using \(\sqrt[n]{ab}= \sqrt[n]{a}.\sqrt[n]{b}\)

Simplify the radical expression.

That is, 4x√11x-2x√11x=2x√11x

Hence, the equivalent expression is 2x√11x.

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The coordinates of the first charge, Q1, are (2, -1, 3), and its magnitude is -5 μC = -5 x 10^-6 C V = k * (Q1 / r1 + Q2 / r2) = (8.99 x 10^9 Nm²/C²) * (-5 x 10^-6 C / sqrt(6) + 4 x 10^-6 C / sqrt(52))

To determine the potential at a point due to multiple point charges, we can use the formula:

V = k * (Q1 / r1 + Q2 / r2 + ...)

Where:

V is the potential at the point,

k is Coulomb's constant (8.99 x 10^9 Nm²/C²),

Q1, Q2, ... are the magnitudes of the charges,

r1, r2, ... are the distances between the point charges and the point where potential is being calculated.

Let's calculate the potential at point (4, 0, 4) due to the given charges.

The coordinates of the first charge, Q1, are (2, -1, 3), and its magnitude is -5 μC = -5 x 10^-6 C.

The distance between Q1 and the point (4, 0, 4) is given by:

r1 = sqrt((4 - 2)^2 + (0 - (-1))^2 + (4 - 3)^2)

= sqrt(2^2 + 1^2 + 1^2)

= sqrt(6)

The coordinates of the second charge, Q2, are (0, 4, -2), and its magnitude is 4 μC = 4 x 10^-6 C.

The distance between Q2 and the point (4, 0, 4) is given by:

r2 =\(sqrt((4 - 0)^2 + (0 - 4)^2 + (4 - (-2))^2)\\\\ sqrt(4^2 + (-4)^2 + 6^2) \\= sqrt(52)\)

Now, let's calculate the potential using the formula:

V = k * (Q1 / r1 + Q2 / r2)

= (8.99 x 10^9 Nm²/C²) * (-5 x 10^-6 C / sqrt(6) + 4 x 10^-6 C / sqrt(52))

Calculating this expression will give you the potential at point (4, 0, 4) due to the given charges.

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Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

Answer:

B and A

Step-by-step explanation:

Took on Edg

Answer:

x = 2700 y=2900

Step-by-step explanation:

x+y = 5600

5/100 x + 9/100 y = 396

x+y=5600

5x+9y=39600

5x+5y = 28000

5x+9y=39600

-4y = -11600

y= 2900

x = 5600-2900 = 2700

Answer:

2km

Step-by-step explanation:

Jamie is jogging from the park to the school

He has jogged 1.62 km so far

He has 0.38 km left

Hence he distance of the park from the school Is

1.62+0.38

= 2km

D

Step-by-step explanDAdadadad

Answer:

Pretty sure the Answer is:

=XOR(B4=12;C4<9) and =AND(B4=12;C>9) return TRUE, if the value in cell B4 is 12 and the value in C4 is 29.

Step-by-step explanation:

An =XOR function returns TRUE if any of the clauses in it are true, while an =AND function returns true only if both are true. Therefore, since in =XOR(B4=12;C4<9) B4 does equal 12, since this is an =XOR function. =AND(B4=12;C>9) is correct because B4 = 12 and C4 is greater than 9.

Hope this made some sense...

Mark brainliest if it helped!

The area of the triangle is 19.5 square units.

To find the area of the triangle, we can use the formula:

Area = (1/2) * base * height

where the base and height are the distance between two of the vertices of the triangle. We can choose any two vertices to use as the base and height, as long as we use the same units for both. Let's choose (-3,2) and (6,-2) as our base.

The distance between (-3,2) and (6,-2) can be found using the distance formula:

d = \(\sqrt((6 - (-3))^2 + (-2 - 2)^2)\)
d = \(\sqrt(81 + 16)\)
d = \(\sqrt(97)\)

Now we need to find the height of the triangle. The height is the perpendicular distance from the third vertex (3,5) to the line containing the base (-3,2) and (6,-2). We can use the formula:

height = \(|Ax + By + C| / \sqrt(A^2 + B^2)\)

where A, B, and C are the coefficients of the line in the standard form Ax + By + C = 0, and x and y are the coordinates of the third vertex. We can find the coefficients of the line by using the two points (-3,2) and (6,-2):

A = 2 - (-2) = 4
B = (-3) - 6 = -9
C = 6*(-2) - (-3)*2 = -18

Now we can plug in the values to find the height:

height = \(|4*3 - 9*5 - 18| / \sqrt(4^2 + (-9)^2)\)
height = \(39 / \sqrt(97)\)

Finally, we can plug in the base and height to find the area:

Area = \((1/2) * \sqrt(97) * (39 / \sqrt(97))\)
Area = 19.5

Therefore, the area of the triangle is 19.5 square units.

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In a system of two equations, the graph of one line has a positive slope and the graph of the other line has a negative slope. This statement is indicative of a system of linear equations which will have no solution.

A system of linear equations is a collection of two or more linear equations with the same variables. A system of linear equations is a collection of two or more linear equations with the same variables. A solution of a system of linear equations is a set of values that make all of the equations true.

Let's look at the general form of two linear equations that are given:

y = mx + by = nx + c

where m and n are the slopes of each line. If m and n have different signs, one is positive and one is negative, then they will never meet and therefore will have no solution. We can thus conclude that the system of two equations has no solution.

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The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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Answer:

\(2*y^{2}\)

Step-by-step explanation:

The product of 2 is multiplication and the second power of y is just y squared

Answer:

Step-by-step explanation:

Parameterize the ellipse as (acos∙,bsin∙). Take points P:=(acosp,bsinp) and Q:=(acosq,bsinq) on the ellipse, with midpoint M:=(P+Q)/2.

If |PQ|=2k, then

a2(cosp−cosq)2+b2(sinp−sinq)2=4k2

The coordinates of M are

xy==a2(cosp+cosq)b2(sinp+sinq)

Answer:

Step-by-step explanation:

Answer:

2500

Step-by-step explanation:

the sum of the squares of the odd integers between 0 and 100 is 2500

Step-by-step explanation:

i hope it's helpful......

Answer:

19

Step-by-step explanation:

on edge 2020

d. 19

that is the correct answer

The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

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Answer:

$973.77

Step-by-step explanation:

$927.40 = 100%

New price = 100% + 5%

New price = 105% of 927.40

105% of 927.40 = 1.05(927.40)

1.05(927.40) = 973.77

-Chetan K

Answer:

Difference = Surface Area_small - Surface Area_large ≈ 63.72 cm^2 - 85.39 cm^2 ≈ -21.67 cm^2

Step-by-step explanation:

Radius of the larger hollow ball (r_outer) = 3 cm

For the smaller hollow balls, since they are identical, we assume that the outer and inner radii are the same:

Radius of the smaller hollow balls (r_inner) = r_outer/2 = 3 cm / 2 = 1.5 cm

Now, let's calculate the surface area for both cases:

Surface area of the larger hollow ball:

Surface Area_large = 4π(r_outer^2 - r_inner^2)

Surface Area_large = 4π(3^2 - 1.5^2)

Surface Area_large = 4π(9 - 2.25)

Surface Area_large = 4π(6.75)

Surface Area_large ≈ 85.39 cm^2

Surface area of the smaller hollow balls (each):

Surface Area_small = 4π(r_outer^2 - r_inner^2)

Surface Area_small = 4π(1.5^2 - 0.75^2)

Surface Area_small = 4π(2.25 - 0.5625)

Surface Area_small = 4π(1.6875)

Surface Area_small ≈ 21.24 cm^2

Now, let's compare the surface areas:

The total surface area of the three smaller hollow balls = 3 * Surface Area_small ≈ 3 * 21.24 cm^2 ≈ 63.72 cm^2

Therefore, it takes more paint to paint the three smaller hollow balls compared to the larger hollow ball. The difference in surface area is given by:

Difference = Surface Area_small - Surface Area_large ≈ 63.72 cm^2 - 85.39 cm^2 ≈ -21.67 cm^2

The difference is negative because the surface area of the larger hollow ball is greater than the combined surface area of the three smaller hollow balls.