What are the steps for using integer tiles to evaluate the expression 45 divided by 15? Start with 15 tiles and separate them into 3 same-sized groups. Start with 45 tiles and separate them into 15 same-sized groups. Assemble 45 groups of 3 tiles each. Assemble 45 groups of 15 tiles each.

Answer:
16cm

Step-by-step explanation:
Volume of a cylinder/ cone = π × r² × h ( Pie × radius square × height)

The cylinder                              The cone
Radius = 4cm                              Radius = 3cm
Height = 9cm                              Height = X(unknown yet)                        
Volume = π × 4² × 9                    Volume = π × 3² × x
Answer a = 452.389cm³           Answer b= 28.274x          

To find the height of the cone;
= Answer a divided by answer b to find X (the height)
= 452.389 ÷ 28.274χ
χ= 16.00cm

Answer:

x = 6\(\sqrt{3}\)

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

( leg of large triangle)² = (part of hypotenuse below it) × (whole hypotenuse) , so

x² = 9 × (9 + 3) = 9 × 12 = 108 ( take square root of both sides )

x = \(\sqrt{108}\) = \(\sqrt{36(3)}\) = \(\sqrt{36}\) × \(\sqrt{3}\) = 6\(\sqrt{3}\)

                                      Rate       Base       Percentage

20% of 40 is 8                 20%         40                 8

15% of 200 is 30             15%         200              30

70% of 50 is 35               70%          50               35

40 is 10% of 400             10%         400              40

50 is 25% of 250             25%          250             50

In this question we need to identify the rate, base and the percentage.

We know that a base is the amount you are taking a percent of. The rate is the ratio of amount to the base. It is written as a percent.

And the percentage is the result obtained when a number (base) is multiplied by a percent (rate).

P = B x R

1) 20% of 40 is 8

rate: 20%

base: 40

percentage: 8

2) 15% of 200 is 30

rate: 15%

base: 200

percentage: 8

3) 70% of 50 is 35

rate: 70%

base: 50

percentage: 35

4) 40 is 10% of 400

rate: 10%

base: 400

percentage: 40

5) 50 is 25% of 250

rate: 25%

base: 250

percentage: 50

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If 51% of people owns dogs and you randomly pick two people,  then probability that they both own a dog is 0.2601

Given,

The percentage of people own dogs= 51%

We know,

Probability = Number of favorable outcomes / Total outcomes.

If you choose random guy and probability that guy own a dog = 0.51

Here the probability of having a dog is independent events

Then,

Probability that they both own a dog = Probability of first person own a dog × Probability of second person own a dog

= 0.51×0.51

=0.2601

Hence, If 51% of people owns dogs and you randomly pick two people,  then probability that they both own a dog is 0.2601

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(1.1) The critical depth can be estimated using the specific energy equation. First, calculate the specific energy (E) at a depth of 1 ft, E1, using E= y + (Q^2 / 2gy^2), where y is the depth, Q is the flow rate (40 cfs), and g is the gravitational constant.

Plugging in the values gives E1 = 1.812 ft. Next, calculate the specific energy at a depth of 2 ft, E2, using the same equation. Plugging in the values gives E2 = 1.821 ft. Since the bed slope is 7 x 10^-3, the critical depth can be estimated using the equation yc = (E2 - E1) / (2.8 x 10^-3), which gives yc = 1.54 ft.
(1.2) The uniform depth can be estimated using the Manning's equation, which relates flow rate, channel dimensions, and roughness to the depth of flow. The equation is Q = (1.49/n) * (A*R^(2/3)) * S^(1/2), where n is the roughness coefficient (0.013 for unfinished concrete), A is the cross-sectional area of flow, R is the hydraulic radius (A/P, where P is the wetted perimeter), and S is the slope of the channel bed. Solving for depth gives y = (Q/nA)^(3/5) * R^(2/5) * S^(1/5). Plugging in the values gives y = 1.34 ft. Therefore, the estimated uniform depth is 1.34 ft.

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It is correct to say that measurements are affected by both bias and chance error, as these factors contribute to the overall uncertainty and variability in the measurement process.

Measurements are typically affected by both bias and chance error. Bias refers to a systematic error or tendency for measurements to consistently deviate from the true value in the same direction. It can be caused by various factors such as calibration issues, instrument inaccuracies, or human error. Bias affects the accuracy of measurements by introducing a consistent deviation from the true value.

On the other hand, chance error, also known as random error, is the variability or inconsistency in measurements that occurs due to unpredictable factors. These factors can include environmental conditions, variations in measurement techniques, or inherent limitations of the measuring instruments. Chance error leads to fluctuations in measurement values around the true value and affects the precision of measurements.

Therefore, it is correct to say that measurements are affected by both bias and chance error, as these factors contribute to the overall uncertainty and variability in the measurement process.

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The conic section as a collection of points(loci) on a plane can be defined in this way .

A conic section is a curve obtained by intersecting a cone with a plane. In Algebra , There are  four main types of conic sections:

circles, parabolas, ellipses and hyperbolas. Each of these conic sections has different characteristics and formulas that help us solve various types of problems.

A locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

According to the question

There are 4 main types of Conic section :

circles, parabolas, ellipses and hyperbolas. Each of these conic sections has different characteristics and formulas

Loci for circle : The locus of a circle is defined as a set of points on a plane at the same distance from the center point.

Loci for parabola : A parabola is a locus of points that are equidistance form a focus and a directrix .

Loci for hyperbola: A hyperbola is the locus of points such that the absolute value of the difference between the distances from to and to is a constant.

Loci for ellipse: An ellipse is the locus of all those points in a plane such that the sum of their distances from two fixed points in the plane, is constant. The fixed points are known as the foci (singular focus), which are surrounded by the curve.

Hence, The conic section as a collection of points(loci) on a plane can be defined in this way .

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Answer:

(a) Explained below.

(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Step-by-step explanation:

The information provided is:

n (Men who finished the marathon) = 25,221

n (Women who finished the marathon) = 12,883

Compute the proportion of men and women who finished the marathon as follows:

\(\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988\)

The combined proportion is:

\(\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989\)

(a)

The hypothesis is:

H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.

Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.

Compute the test statistic as follows:

\(Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}\)

   \(=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78\)

Compute the p-value as follows:

\(p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075\)

The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.

Thus, concluding that the rate of those who finish is the same for men and women.

(b)

Compute the 99% confidence interval for the difference between proportions as follows:

The critical value of z for 99% confidence level is 2.58.

\(CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}\)

     \(=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\\)

Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Answer:

Step-by-step explanation:Solve each triangle. Round side lengths to the

nearest tenth and angle measures to the nearest

degree.

1.

SOLUTION:  

Use the Law of Cosines to find the missing side

length.

Use the Law of Sines to find a missing angle

measure.

Find the measure of  .

ANSWER:  

A ≈ 36°, C ≈ 52°, b ≈ 5.1

2.

SOLUTION:  

Use the Law of Cosines to find the measure of the

largest angle,  .

Use the Law of Sines to find3. a = 5, b = 8, c = 12

SOLUTION:  

Use the Law of Cosines to find the measure of the

largest angle,  .

Use the Law of Sines to find the measure of angle,

.

Find the measure of  .

ANSWER:  

A ≈ 18°, B ≈ 29°, C ≈ 133°

4. B = 110°, a = 6, c = 3

SOLUTION:  

Use the Law of Cosines to find the missing side

length.

Use the Law of Sines to find a missing angle

measure.

Find the measure

ANSWER:  

A ≈ 48°, C ≈ 22°, b ≈ 7.6

To get the velocity vector, we will differentiate x(t) and y(t) as follows: \(dx/dt = (6/t - 3)^1/3\)------------------------(1) \(dy/dt = te^(-t)\) ------------------------(2)Integrating equation (2), we get

\(y(t) = -te^(-t) - e^(-t) + Cy(3) = -3e^(-3) - e^(-3) + C4 = -4e^(-3) + C\)

The equation of y becomes\(y(t) = -te^(-t) - e^(-t) - 4\)

Differentiating equation (1) and solving for t when

dx/dt = 0

\(dx/dt = (6/t - 3)^1/3[(-1/3)(6/t^2)] = 0= > 6/t - 3 = 0\)

=> t = 2

Substitute t = 2 in the equation (1), we get dx/dt = 0Therefore, the particle is farthest to the right at time t = 2.Now, to find the x-coordinate, substitute t = 2 in equation (3) and get

\(y(2) = -2e^(-2) - e^(-2) - 4\)

\(= -3e^(-2) - 4\)

The particle is at the position \((x, y) = (x(2), y(2)) = (7, -3e^(-2) - 4)\)

The particle is farthest to the right at t = 2 and the x-coordinate is 7, which is the answer.

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By applying interior angles of triangles concept, it can be calculated that:

Triangle is a 2D shape that is bounded by three sides and has three vertices.

The three interior angles of triangles will always have a sum of 180°.

ΔABC:

            ∠A + ∠B + ∠C = 180°

4x + (7x - 2) + (5x - 10) = 180°

                       16x - 12 = 180°

                              16x = 192°

                                  x = 12°

Thus, ∠A = 4x = 4*12 = 48°

∠B = 7x - 2 = 7*12 - 2 = 82°

∠C = 5x - 10 = 5*12 - 10 = 50°

ΔDEF:

     ∠D + ∠E + ∠F = 180°

3x + 18x + (5x - 2) = 180°

                26x - 2 = 180°

                      26x = 182°

                           x = 7°

Thus, ∠D = 3x = 3*7 = 21°

∠E = 18x = 18*7 = 126°

∠F = 5x - 2 = 5*7 - 2 = 33°

ΔGHI:

 ∠G + ∠H + ∠I = 180°

16x + 16x + 13x = 180°

                 45x = 180°

                      x = 4°

Thus, ∠G = 16x = 16*4 = 64°

∠H = 16x = 16*4 = 64°

∠I = 13x = 13*4 = 52°

ΔJKL:

                  ∠J + ∠K + ∠L = 180°

(x + 8) + (6x - 5) + (2x - 3) = 180°

                                    9x = 180°

                                      x = 20°

Thus, ∠J = x + 8 = 20 + 8 = 28°

∠K = 6x + 5 = 6*20 - 5 = 115°

∠L = 2x - 3 = 2*20 - 3 = 37°

ΔMNO:

∠M + ∠N + ∠O = 180°, if ∠M = x, then:

     x + 5x + 4x = 180°

                  10x = 180°

                      x = 18°

Thus, ∠M = x = 18°

∠N = 5x = 5*18 = 90°

∠O = 4x = 4*18 = 72°

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A survey timeline does not indicate the date for activation of the measurement instrument and this date is typically determined by the project team.

False. A survey timeline does not indicate the date for activation of the measurement instrument. A survey timeline typically provides a timeline for the duration of a survey, which includes the start date, the end date, and any other important milestones such as when data collection begins, when the data is analyzed, and when the results are reported. The date for activation of the measurement instrument is typically determined by the project team and will depend on the type of instrument used and the purpose of the survey. For example, if the survey is designed to measure customer satisfaction, the instrument might be activated on a certain date in order to ensure that the survey is conducted in a timely manner.

A survey timeline does not indicate the date for activation of the measurement instrument and this date is typically determined by the project team.

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The minimum number of jumps required to reach the flag's height is 3.

Let n be the height of the flag. We can use a recursive approach to determine the minimum number of jumps it takes to reach the flag's height.

For n = 0, it takes 0 jumps to reach the flag's height.

For n = 1, it takes 1 jump to reach the flag's height.

For n > 1, we can calculate the minimum number of jumps using the following equation:

minJumps(n) = 1 + min(minJumps(n-1), minJumps(n-j))

Where minJumps(x) is the minimum number of jumps required to reach the flag's height from ground level x.

For example, if the flag's height is 5 and Bob can jump a height of 2, the minimum number of jumps required to reach the flag's height is 3.

minJumps(5) = 1 + min(minJumps(4), minJumps(3))

= 1 + min(1 + min(minJumps(3), minJumps(2)), 1 + minJumps(2))

= 1 + min(1 + 1, 1 + 1)

= 3

Therefore, the minimum number of jumps required to reach the flag's height is 3.

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In mathematics, the pattern of association refers to the type of correlation that is found between two variables which includes positive, negative, or no correlation.

The connection between two or more variables is referred to as a pattern of association. There are various variations of this relationship, including a positive correlation, a negative correlation, and no correlation. When both variables rise or fall at the same time, there is a positive correlation. In other words, as one variable rises, the other one rises as well, and vice versa.

When two variables move in the opposing directions, there is a negative correlation. The other variable reduces as one grows, and vice versa. When there is no correlation between the variables, a no correlation exists. This indicates that there is no pattern in the data and that the variables do not change simultaneously.

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Answer:

n=-20

Step-by-step explanation:

Answer:

£4.25 each or £8.50 between them

Step-by-step explanation:

£20 each to start with

-£3 for the entrace fee = £17 each

-£7.50 for laser tag = £9.50 each

-£2.25 for mini-bowling = £7.25 each

4 video games will cost 0.75 x 4 = £3

-£3 for video games = £4.25 left each

By the end, each one will have £4.25, or £8.50 between them, wasn't sure what the question was specifying.

Answer:

Explanation:

Here, we want to get the equation of the line

The general equation of a straight line can be expressed as:

where m is the slope and b is the y-intercept (the point at which x = 0)

Now, let us write the given equation in the general form

We have this as:

From here, we can see that the value of the slope which is the coefficient of x is 1

When two lines are parallel, the value of their slopes are equal

This mean that the value of the slope of the line L4 is 1 too

Finally, by using the point slope format, we can get the equation of the line L4

We have the point-slope form as:

Answer:

10 cm³

Step-by-step explanation:

The total surface area of a cube = 6 cm²

The formula for the surface area of the cube is :

A = 6a², a is the side of the cube

6 = 6a²

a = 1 cm

Now, the length of the formed cuboid = 2 cm

Breadth = 1 cm

Height = 1 cm

Required volume of the formed cubiod is :

V = 2(lb+bh+hl)

Put all the values,

V = 2(2(1)+1(1)+2(1))

V = 10 cm³

So, the required volume of the formed cuboid is equal to 10 cm³

Step-by-step explanation:

I don't see the main question but this is the binomial expansion of the expression (4x-2y)^5

Answer:

below

Step-by-step explanation:

The answer of the first expert is correct, this is from Pascal triangle 5th level.

shown in the attached picture, when we extend the brackets the whole function will become...

f(x) = 1*(4x)⁵(-2y)⁰ + 5*(4x)⁴(-2y)¹ + 10*(4x)³(-2y)² + 10* (4x)²(-2y)³ + 5*(4x)¹(-2y)⁴ +   1*(4x)⁰(-2y)⁵

     = (4x - 2y)⁵

Answer:

$43.92

Step-by-step explanation:

1st year:

30 x 10% = 3

30 + 3 = 33

2nd year:

33 x 10% = 3.3

33 + 3.3 = 36.3

3rd year:

36.3 x 10% = 3.63

36.3 + 3.63 = 39.93

4th year:

39.93 x 10% = 3.99

39.93 + 3.99 = 43.92

Answer:

8 dimes and 17 nickels

Step-by-step explanation:

First, we assume all of his coins are nickels. $0.05 * 25 will be $1.25. 165 - 125 is 40, and the money difference of a dime and a nickel is $0.05, so Ralph has 8 dimes and 17 nickels. We can check it by doing (8x10) + (17x5). 80 plus 85 is 165, therefore we can confirm our answer is true.

IT is found that the value of x is 4 and value of y is 5.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given system of equations are

2x-6y=22

-5x+y=1

The matrix form is

\(\left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}22\\1\end{array}\right]\)

Let as assume

\(A = \left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right]\\ \\X = \left[\begin{array}{ccc}x\\y\end{array}\right] \\B = \left[\begin{array}{ccc}22\\1\end{array}\right]\)

WE know that AX = B

Then we have;

\(\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}4\\5\end{array}\right]\)

Therefore, the value of x is 4 and value of y is 5.

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The given statistical study - "For a sample of college students using the ATM in the campus center, data are collected on the dollar amount withdrawn" is a correlational study.

What is a correlational study?                                                                                                                                                                         Correlational study is a research design that helps to measure and describe the relationship between variables without the researcher influencing or manipulating any variables. Correlation allows researchers to test how variables are related to one another, providing a way to find new relationships, understand phenomena, and make predictions.

Classify each statistical study as experimental or correlational. According to the given problem, data are collected on the dollar amount withdrawn for a sample of college students using the ATM in the campus center. As there is no manipulation of variables involved and no control group is assigned, this is a correlational study.

Therefore, the given statistical study - "For a sample of college students using the ATM in the campus center, data are collected on the dollar amount withdrawn" is a correlational study.

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To translate an entire triangle, find the coordinates of each of the triangle's vertices, add the horizontal translation then plot the three translated points.

Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.

There are some steps of translating the triangle:

Step 1: Find the coordinates of each of the triangle's vertices in step one.

Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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Answer:

wouldn't this be 4,2?

Step-by-step explanation:

i remember doing this in school last year and dilation means you would multiple the coordinates by what ever the dilation factor was, in this case its 2.

The ratio of QR to ST in the triangle is 5/7

Three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles defined as congruent.

To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five condition for two triangles to be congruence,  according to  the trials. The congruence qualities are SSS, SAS, ASA, AAS, and RHS.

PQR and PST are congruent

So PQ/PS=QR/ST

We know that

PQ=10

PS=14

QR/ST=10/14

QR/ST=5/7

hence, the ratio of QR to ST in the triangle is 5/7.

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The perimeter is the sum of the side length of the square

The perimeter of the square is 72x + 192

The side length is given as:

L = 18x + 48

The perimeter is calculated as:

P = 4L

So, we have:

P = 4 * (18x + 48)

Expand

P = 72x + 192

Hence, the perimeter of the square is 72x + 192

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Answer:

x=3.48 or -1.98

Step-by-step explanation:

2x^2-3x-8=0

x^2-1.5x-4=0

(x-0.75)^2=0

x^2-1.5x-0.5625=0

(x-0.75)^2-7.4375=0

(x-0.75)=√(7.4375)

x=0.75±√(7.4375)

x=3.48 or -1.98

Answer:

119,940 books are not about math.

What I did:

60x2000=120,000

120,000-60=119,940

Answer:

119940

Step-by-step explanation:

.05 % are about math

b= books

b * .05% = 60

Change to decimal form

b * .0005 = 60

Divide each side by .0005

b = 60/.0005

b =120000 books in the store

we want the ones not about math

120000-60

119940