Find the matrix A such that
A

1 0

−1 3
=

−1 −3

1 6

The probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur. For example, the probability of flipping a fair coin and getting heads is 1/2 or 0.5.

Since the waiting time for the ABC Ban ATM machine is uniformly distributed between 1 and 5 minutes, the probability density function is given by:

f(x) = 1/(5-1) = 1/4 for 1 ≤ x ≤ 5

To find the probability of waiting between 2 and 3 minutes, we need to find the area under the probability density function between 2 and 3. This is given by the definite integral of the probability density function over the interval [2, 3]:

P(2 ≤ x ≤ 3) = ∫2^3 f(x) dx

= ∫2^3 (1/4) dx

= (1/4) [x]2^3

= (1/4) (3-2)

= 1/4

Therefore, the probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.

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Answer:

1 American pt equals approximately 568.261 mL

OR

1 British Imperial pt is approximately 473 mL

I recommend choosing the answer that better relates to where you are from.

Step-by-step explanation:

There seem to be TWO kinds of pint sizes. A US pint is 16 ounces and an Imperial pint is 20 ounces.

The values of y and z which makes triangle (△) QRS exactly the same (≅) as triangle (△) WVX is

We must note here that the sign, ≅ means exactly the same. Thus,

Line VW = Line QR

The following were obtained from the question:

Line VW = Line QR

31  = y + 20

Collect like terms

y = 31 - 20

y = 11

Thus, the value of y is 11

We can obtain the value of z as follow:

Line QS = Line WX

y + 3z + 28 = 6y + z - 5

11 + 3z + 28 = 6(11) + z - 5

11 + 3z + 28 = 66 + z - 5

3z + 39 = z + 61

Collect like terms

3z - z = 61 - 39

2z = 22

Divide both sides by 2

z = 22 / 2

z = 11

Thus, the value of z is 11

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Answer:

the answer is supposably 75900000

Answer:

g(x)= log(x-1)

Step-by-step explanation:

g(x) = f(x-1)

Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.

1. We can start by using the Pythagorean identity to find the values of sin Φ:

[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1

Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:

1/(7/3) = sin Φ

sin Φ = 3/7

Next, we can use the fact that cot Φ = cos Φ/sin Φ:

cot Φ = cos Φ/(3/7) = - (2√10)/(3)

Simplifying this expression, we get:

cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7

Finally, we can use the fact that sec Φ = 1/cos Φ:

sec Φ = 1/(- 2√10/7) = -7/(2√10)

2. We can use the fact that sec β = 1/cos β to find the value of cos β:

sec β = 6/5

cos β = 5/6

Next, we can use the Pythagorean identity to find the value of sin β:

[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1

sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6

Finally, we can use the fact that tan β = sin β/cos β:

tan β = (√11/6)/(5/6) = √11/5

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Answer:

Its b,

Step-by-step explanation:

I had this test before i chose b and it was right

Answer:

(1, 6), (2, 12), (3, 18), (4, 24)

The geometric mean of the given numbers 8 and 6 is [tex]\sqrt{14}[/tex].

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the collection of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers collectively and calculate their nth root, where n is the total amount of data values.

In other terms, the geometric mean is the product of n numbers divided by the nth root. As a result of the fact that in mathematical mean, the data values are added before being divided by the total number of values. However, when calculating the geometric mean, we add the provided data values before taking the root of the total number of data values using the radical index.

A number's square root is a value that, when multiplied by itself, yields the initial number. The opposite way to square an integer is to find its square root. Squares and square roots are therefore connected ideas.

The geometric mean of the given number is given by the formula

GM=[tex]\sqrt{\\a+b}[/tex]

      =[tex]\sqrt{8+6}[/tex]

      =[tex]\sqrt{14}[/tex]

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Step-by-step explanation:

The average weight of a male African elephant is 15,000 pounds.

To convert pounds to tons, we divide the weight in pounds by 2,000 (the number of pounds in a ton):

15,000 pounds ÷ 2,000 pounds/ton = 7.5 tons

Therefore, the weight of a male African elephant is approximately 7.5 tons.

So the closest answer to this question is "7 tons".

Answer:

7 tons

Step-by-step explanation:

The average weight of a male African elephant is 15,000 pounds. To convert this weight into tons, we need to divide it by 2,000 (since there are 2,000 pounds in a ton).

So, 15,000 ÷ 2,000 = 7.5 tons.

Therefore, the answer is 7 tons (since there are no fractions of tons in the options given).

The length of the segment PD obtained using the relationship between similar right triangles is; PD = 7.5 units

A right triangle is a triangle that has an interior angle of 90° (a right angle) and the side opposite the right angle (90°) interior angle is known as the hypotenuse side, while the other two sides of the triangle are the legs of the right triangle.

The possible drawing in the question, obtained from a similar online question, created with MS Word is attached.

The equation of the line that passes through the points A and D, y = -2·x + 6, indicates;

The coordinates of the y-intercept of the line of the equation, is; (0, 6)

The y-intercept indicates that OD = 6 units

The x-intercept coordinates of the graph of the equation, can therefore be obtained as follows; 0 = -2·x + 6

2·x = 6

x = 6/2 = 3

x = 3

The x-intercept is; (0, 3)

The x-intercept indicates that OA = 3 units

The length of the side of the square, s, is therefore;

s = √(s²) = √(6² + 3²) = 3·√5

OA = The length of the x-intercept of ; y = -2·x + 6

The ∠DAO ≅ ∠OPA, and m∠DOA = m∠POA = 90°

Therefore;

∠DOA  ≅ ∠POA

ΔOPA is similar to ΔOAD, by Angle-Angle similarity postulate

The ratio of corresponding sides of similar triangles indicates;

OP/OA = OA/OD

Therefore;

OP/OA = OA/OD

OP/3 = 3/6

OP = 3 × 3/6 = 1.5

PD = OP + OD (Segment addition postulate)

PD = 1.5 + 6 = 7.5

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Answer:

The given equation is 3 + 7x + 11 + 10x = y.

Simplifying the equation, we get:

y = 17x + 14

Comparing with the standard linear equation y = mx + b, we can see that:

m = 17

b = 14

Therefore, m = 17 and b = 14.

Therefore, there is a 12.12% chance that the chosen party will be made up exclusively of Republicans.

The likelihood or chance of an occurrence occurring is measured by probability. The occurrence is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. By dividing the number of favorable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. Numerous disciplines, including statistics, mathematics, science, finance, and engineering, heavily rely on probability to make predictions and judgments about the chance of various events happening.

given

A. The combination formula can be used to determine how many options there are to choose three individuals from a group of eleven:

C(11, 3) = 11! / (3! (11-3)!) = 165

There are 165 different methods to choose three from this group of eleven people.

b. The combination formula gives the number of options to choose three Republicans from the group of six Republicans:

C(6, 3) = 6! / (3! (6-3)!) = 20

To choose three Republicans from this set of six Republicans, there are 20 possible options.

c. The ratio of the number of ways to choose three Republicans from the group of six Republicans to the total number of ways to choose three people from the group of eleven determines the likelihood of choosing three Republicans out of the group of eleven.

P(3 Republicans) = C(6, 3) / C(11, 3), which translates to 20 / 165 = 0.1212 or roughly 12.12%.

Therefore, there is a 12.12% chance that the chosen party will be made up exclusively of Republicans.

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Answer:

5.5 or 5 1/2 inches

Step-by-step explanation:

The longest is 12 3/4

The two smallest combined are 3 and 4 1/4 = 7 1/4

12 3/4 - 7 1/4 = 5 1/2

The required set of numbers 5, 9, 11, and 14 satisfies all the given conditions.

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set.

a set of four whole numbers that satisfies the given conditions:

5, 9, 11, 14

To check that this set meets the requirements:

The range of the original set (12 - 4 = 8) increased by 2 to become 10 (14 - 4 = 10).

The mean of the original set ((4 + 9 + 10 + 12) / 4 = 8.75) remains the same in the new set ((5 + 9 + 11 + 14) / 4 = 8.75).

The median of the original set is 9.5 (the average of 9 and 10), and the median of the new set is 10 - 1 = 9.

Therefore, the set of numbers 5, 9, 11, and 14 satisfies all the given conditions.

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Answer:

162, 147 etc.

Step-by-step explanation:

we have to find

[tex]N = k^2 \cdot p[/tex]

we can iterate k = 1 to 10 to check all possible solutions,

[tex]N = 9^2 \cdot 2[/tex]

[tex]N = 7^2 \cdot 3[/tex]

N = 162, 147 etc.

Hopefully this answer helped you!!

32. g(x) = 4x + 4

This transformation shifts the graph

of f(x) 4 units upward.

33. g(x) = 4x-3

This transformation shifts the graph

of f(x) 3 units downward.

34. g(x)=4(x+2)

This transformation shifts the graph

of f(x) 2 units left.

35. g(x) = 4(x-5)

This transformation shifts the graph

of f(x) 5 units right.

36. g(x) = -4x

This transformation reflects the graph

of f(x) about the x-axis.

37. g(x) = -4x

This transformation reflects the graph

of f(x) about the y-axis.

chatGPT

Since we are given the lengths of the two legs of the triangle, 14 and 16 respectively, the area of the triangle is 152.97 square units.

To find the area of a triangle, we can use the formula: area = (1/2) x base x height

In this case, we are given the lengths of the two legs of the triangle, 14 and 16, so we can use the Pythagorean theorem to find the length of the base:

a^2 + b^2 = c^2

14^2 + 16^2 = c^2

196 + 256 = c^2

452 = c^2

c = √452

c ≈ 21.26

To find the height, we need to drop a perpendicular from the apex to the base, forming two right triangles. Using the Pythagorean theorem again, we have:

(1/2) x base x height = area

(1/2) x 21.26 x height = area

Let's use the right triangle with legs 14 and height h as our reference. Then we have:

h^2 + 7^2 = 16^2

h^2 + 49 = 256

h^2 = 207

h = √207

h ≈ 14.39

Therefore, the area of the triangle is:

= (1/2) x 21.26 x 14.39

= 152.9657

= 152.97².

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if Leo has provided the coordinates of the jungle gym and the four-square courts, we can use the distance formula to calculate the distance between them.  the four-square courts are approximately   [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).

The distance formula is:

[tex]d = sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where  [tex](x1, y1)[/tex] and [tex](x2, y2)[/tex] are the coordinates of two points, and d is the distance between them.

For example, let's say the jungle gym is located at (3, 4) on the grid, and the four-square courts are located at (9, 8). Using the distance formula, we have:

[tex]d = sqrt((9 - 3)^2 + (8 - 4)^2)[/tex]

[tex]= sqrt(6^2 + 4^2)[/tex]

[tex]= sqrt(36 + 16)[/tex]

[tex]= sqrt(52)[/tex]

[tex]\approx 7.2[/tex]

Therefore, the distance from the jungle gym to the four-square courts is approximately   [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).

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The 5 ft by 8 ft dimensions of the car and the (width) 2 ft by (height) 3 ft dimensions of the chair, indicates that the vehicle can haul both chairs in one trip.

The dimensions of rectangularly shaped solid are the height, the width and the length of the solid.

The possible dimensions of the vehicle and the chair obtained from a similar online question are;

Length of the vehicle = 8 feet

Width of the vehicle = 5 feet

The height of one chair = 3 feet

The width of one chair = 2 feet

Therefore;

The width of the vehicle of 5 feet indicates that the vehicle can contain the two chairs placed side by side with their widths of 2 feet each, to get;

Width of  the two chairs = 2 feet + 2 feet = 4 feet < 5 feet

The two chairs placed horizontally, such that we get;

The total length of the horizontally placed chairs = 3 feet + 3 feet = 6 feet

The combined height of the two chaires, of 6 feet is less than the length of the car which is 8 feet, therefore;

The car can haul both chairs placed horizontally in a single trip.

The vehicle could therefore be used to haul both chairs in a single trip.

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Therefore, cos(K) = √(17)/9, sin(L) = 8/9, and cos(K) and sin(L) together are (√(17)/9, 8/9) are trigonometric ratios as fractions in simplest terms.

It is possible to calculate trigonometric ratios for various orientations. However, we memories the trigonometric ratios of a few particular angles, such as 0°, 30°, 45°, 60°, and 90°, to make computations easier. The numbers of the ratios at these angles can be found in the trigonometric ratios table.

The Pythagorean formula can be applied to the illustration to determine the length of the third side:

c²= a²+ b²

c²= 8² + √(17)²

c²= 64 + 17

c² = 81

c = 9

We can now calculate the trigonometry ratios of angles K and L:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

Using the same hypotenuse number of 9, we can calculate both cos(K) and sin(L) as follows:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

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Answer:

Each tile would be 8.5 in

Step-by-step explanation:

Area of parallelogram is A=bh, so 4.25*2= 8.5

The f(x) = (3/2)ˣ is the correct function that represents the given exponential graph.

An exponential graph is a type of graph that represents an exponential function. An exponential function is a mathematical function in which a constant base is raised to a variable exponent. The general form of an exponential function is: y = a * bˣ.

A graph is a visual representation of data or information that allows us to quickly and easily understand patterns, trends, and relationships. Graphs are used to present information in a way that is easy to interpret and understand.

In the given question,

The function that represents the exponential graph given that (0, 1) and (4, 81/16 ) are points that lie on the graph is:

f(x) = (3/2)ˣ

To verify that this is the correct function, we can substitute x=0 and x=4 into the function to see if the corresponding y-values match the given points on the graph.

When x=0, f(0) = (3/2)⁰ = 1, which matches the point (0, 1).

When x=4, f(4) = (3/2)⁴ = 81/16, which matches the point (4, 81/16).

Therefore, f(x) = (3/2)ˣ is the correct function that represents the given exponential graph.

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Answer:

Step-by-step explanation:

Assuming that the original measurement is in millimeters, since they are commonly used in precision applications, we know that 1 millimeter is equal to 0.03937 inches. Therefore, we can convert 4559.886 millimeters to inches by multiplying by 0.03937:

4559.886 mm * 0.03937 in/mm = 179.72467632 in (rounded to 8 decimal places)

To round this to the nearest inch, we need to look at the first decimal place after the decimal point. In this case, the digit in the first decimal place is 7, which is greater than or equal to 5. Therefore, we round up to the nearest inch, which gives us:

179.72467632 in rounded to the nearest inch is 180 in.

Therefore, 4559.886 rounded to the nearest inch is 180.

A black bear's average adult weight is 4000 kilograms, or 250 pounds.

Average By adding a collection of numbers, dividing by their count, and then summing the results, the arithmetic mean is determined. For instance, the sum for 2, 3, 3, 5, 7, & 10 is equal to 30 split by 6, which equals 5.

If a male black bear's birth weight to adult weight ratio is 3:1000, the following sentence can be written:

weight at birth to adult weight is 3 to 1 000.

Let's calculate the normal adult weight using the information provided. Given that the typical birth is 12 ounces, we can establish the following ratio:

weight at birth to adult weight is 3 to 1 000.

Weight of an adult is 12: 3: 1000.

Cross-multiplying results in:

3 x adult weight is equal to 12,000

By multiplying both halves by 3, we obtain:

4000 ounces for an adult.

Divide by 16 to convert teaspoons to pounds:

Adult weight is equal to 4000 / 16 pounds, or 250 pounds.

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Answer:

Step-by-step explanation:

(a) Since each student needs a shirt of the same size, and 2 meters of cloth is required to make one shirt, the total length of cloth required to make shirts for 15 students would be:

Total length of cloth = 15 x 2 = 30 meters

Therefore, 30 meters of cloth would be required to make shirts for 15 students.

(b) If 2 meters of cloth are required to make one shirt, then the number of shirts that can be made from 9 meters of cloth would be:

Number of shirts = 9 / 2 = 4.5 shirts

However, since we cannot make half a shirt, the actual number of shirts that can be made from 9 meters of cloth would be 4 shirts.

To convert the length of cloth required for a shirt into decimal form, we can simply divide the length in centimeters by 100. Therefore, 2 meters of cloth would be equivalent to 200 centimeters, which is 2.00 meters in decimal form.

(c) If the length of a piece of cloth is 36.25 meters, and we use 30 meters to make shirts for 15 students, then the remaining length of cloth would be:

Remaining length of cloth = 36.25 - 30 = 6.25 meters

Therefore, 6.25 meters of cloth would be left.

By using chi-squared test, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.

What is chi-squared test?

To perform a chi-squared test for independence between breed and milk yield, we need to set up the hypotheses:

Null hypothesis: There is no association between breed and milk yield.

Alternative hypothesis: There is an association between breed and milk yield.

We will use a significance level of 0.05.

To calculate the expected counts for each cell, we will use the formula: (row total x column total) / grand total.

The observed counts and expected counts are:

The grand total is 100.

The degrees of freedom for the test are (number of rows - 1) x (number of columns - 1) = (2 - 1) x (3 - 1) = 2.

Using a chi-squared distribution table or calculator, we find the critical value for a chi-squared test with 2 degrees of freedom and a 0.05 significance level to be 5.99.

To calculate the test statistic, we use the formula:

chi-squared = [tex]sum((observed\ count - expected\ count)^2 / expected\ count)[/tex]

The calculated value of chi-squared is:

[tex]chi-squared = ((32-25.76)^2 / 25.76) + ((20-19.04)^2 / 19.04) + ((16-13.20)^2 / 13.20) + ((10-16.24)^2 / 16.24) + ((18-18.96)^2 / 18.96) + ((4-4.80)^2 / 4.80) = 10.92[/tex]

The degrees of freedom for the test are 2, and the critical value is 5.99.

Since the calculated value of chi-squared (10.92) is greater than the critical value (5.99), we reject the null hypothesis.

Therefore, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.

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Thus,  the area of cross section perpendicular to the base area will be in form of rectangle : Area =  130.32 cm².

The area of a sliced piece of a 3D object, such a pipe, is known as the cross sectional area. The cross sectional area of a pipe when cut perpendicular to it's own longest axis is determined for the circle-shaped top portion of the sliced component.

Given data:

Base area of cylinder = 12.96 π cm²

height of cylinder = 18.1 cm.

Let the radius of the  cylinder be 'r'.

Base area of cylinder = π*r².

π*r² =  12.96 π

r² =  12.96

r = 3.6 cm

now, the area of cross section perpendicular to the base area will be in form of rectangle with.;

Base = 2*r = 2*3.6 = 7.2 cm

height =  18.1 cm.

Area = base * height

Area = 7.2 * 18.1

Area =  130.32 cm²

Thus,  the area of cross section perpendicular to the base area will be in form of rectangle : Area =  130.32 cm².

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Answer:

Step-by-step explanation:

Answer:

= 3x - 5/(6x)

Step-by-step explanation:

El triple de x es: 3x

La expresión es:

3x - 5/(6x)

The scale factor of PQRS to JKLM is 4/5.

The scale factor of JKLM to PQRS is 5/4.

The value of w, x, and y are 20, 12.5, and 20 respectively.

The perimeter ratio is 4:5.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor of PQRS to JKLM = 15/12

Scale factor of PQRS to JKLM = 5/4 or 1.25.

Scale factor of JKLM to PQRS = 12/15

Scale factor of JKLM to PQRS = 4/5 or 0.8.

For the value of w;

15/12 = 25/w

15w = 12 × 25

w = 20

For the value of x;

15/12 = x/10.

12x = 150

x = 12.5

For the value of y:

15/12 = y/16

12y = 15 × 16

y = 20

Perimeter ratio = 12 : 15 = 4:5

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