Sara went on a holiday for 20 days. It rained on a quarter of the days. On how many days did it rain?

A matrix such that T(x) =Ax is [tex]Ax = \left[\begin{array}{ccc}-3&7\\5&-2\end{array}\right][/tex].

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

The matrix is [tex]x = \left[\begin{array}{ccc}x_1\\x_2\end{array}\right][/tex], [tex]v_1= \left[\begin{array}{ccc}-3\\5\end{array}\right][/tex] and [tex]v_2 = \left[\begin{array}{ccc}7\\-2\end{array}\right][/tex].

The linear transformation is R² → R².

T is defined by the vector equation -

T(x) = x1v1 + x2v2

Substitute the values in the equation -

T(x) = [tex]x_1 \left[\begin{array}{ccc}-3\\5\end{array}\right] + x_2 \left[\begin{array}{ccc}7\\-2\end{array}\right][/tex]

A vector equation like this can be rewritten as a matrix equation Ax where the columns of A are just v1 and v2 -

[tex]Ax = \left[\begin{array}{ccc}v_1&v_2\end{array}\right][/tex]

Substitute the values in the matrix -

[tex]Ax = \left[\begin{array}{ccc}-3&7\\5&-2\end{array}\right][/tex]

Therefore, the matrix obtained is [tex]Ax = \left[\begin{array}{ccc}-3&7\\5&-2\end{array}\right][/tex].

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The rate of inflation for potatoes was 21%, for oranges it was 40%, and for ground beef it was 67%.

In mathematics, rate is a concept used to describe the change in one quantity with respect to another. It is usually represented as a fraction or a ratio and can be thought of as a measure of how fast one quantity is changing with respect to another.

For example, the rate of change of position with respect to time is called velocity. The rate of change of velocity with respect to time is called acceleration. Similarly, the rate of change of any function with respect to its independent variable is called the derivative of the function, and it represents the instantaneous rate of change at a given point.

Rate can also be used to describe the relationship between two quantities that are changing at the same time. For example, in economics, the interest rate is the ratio of the amount of interest earned or paid to the amount of money invested or borrowed. In science, the rate of a chemical reaction is the change in the concentration of a reactant or a product over time.

The rate of inflation for each item can be calculated using the formula:

r = (P2/P1)¹/ⁿ - 1

where P1 is the price per pound in 2009 and P2 is the price per pound in the given year, and n is the number of years between the two prices (in this case, n = 1 year).

For Potatoes:

P1 = $0.620

P2 = $0.749

n = 1

r = (0.749/0.620)¹/¹ - 1 = 0.21 or 21%

For Oranges:

P1 = $0.910

P2 = $1.280

n = 1

r = (1.280/0.910)¹/¹ - 1 = 0.40 or 40%

For Ground beef:

P1 = $2.251

P2 = $3.775

n = 1

r = (3.775/2.251)¹/¹ - 1 = 0.67 or 67%

So, the rate of inflation for potatoes was 21%, for oranges it was 40%, and for ground beef it was 67%.

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On solving the provided question, we can say that there is a probability 20.66% chance that Mr. Larson rode his motorbike on both Monday and Tuesday.

Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.

Assuming that his decisions for the two days are independent, we must multiply the chance that he rides his motorbike on Monday by the probability that he rides it on Tuesday in order to get the likelihood that he does so on both Monday and Tuesday. Considering that his decisions on the two days are separate, Hence, the likelihood is:

(10/22) x (10/22) = 100/484 = 0.2066 or 20.66%

Hence, there is a roughly 20.66% chance that Mr. Larson rode his motorbike on both Monday and Tuesday.

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The equation that represents each change is given as follows:

a) y = 2^x-  6.

b) y = 2^(x + 1).

c) y = -2^x.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

Additionally, when a function is reflected over the x-axis, we have that the function's definition is multiplied by -1.

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114.9 feet did Adam run more than Julie.

Two or more expressions with an Equal sign is called as Equation.

To compare the distances run by Adam and Julie, we need to convert both distances to feet.

Given Adam ran 2/5 mile and Julie ran 3/8 mile.

2/5 of a mile is equal to 2/5 * 5780 = 2312.4 feet

3/8 of a mile is equal to 3/8 × 5780 = 2167.5 feet.

Now let us find the difference between two persons.

So, Adam ran 2312.4 - 2167.5 = 114.9 feet.

Hence, 114.9 feet did Adam run more than Julie.

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The ratio of Kenny's weight to Melvin's weight is 6/7.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Kenny’s weight is 6/7 times Melvin's weight.

Let x be the weight of Melvin.

Then, Kenny's weight = 6/7 x, as per the information given.

Ratio of Kenny’s weight to Melvin's weight = (6/7 x) / x = 6/7

Hence the required ratio of Kenny's weight to Melvin's weight is 6/7.

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The expression when simplified gives the value as f(-3) = 1.

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

The given expression is:

f(x) = x² - 8

To find the value of f(-3), substitute the value of x = -3:

f(x) = x² - 8

f(-3) = (-3)² - 8

f(-3) = 9 - 8

f(-3) = 1

Hence, the expression when simplified gives the value as f(-3) = 1.

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Answer:

[tex]m\angle C\approx42.774^\circ[/tex]

Step-by-step explanation:

Use the Law of Sines

[tex]\displaystyle \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\\ \\ \frac{\sin47^\circ}{28}=\frac{\sin C}{26}\\ \\ 26\sin47^\circ=28\sin C\\ \\C = \sin^{-1}\biggr(\frac{26\sin47^\circ}{28}\biggr)\\\\C\approx42.774^\circ[/tex]

The equation for the tangent plane at the point (1,3,3) on the surface [tex]x2 + 3y2 + 4z2 = 64 is 2x + 6y + 8z - 71 = 0[/tex].

The equation of the tangent plane at the point (1,3,3) on the surface [tex]x2 + 3y2 + 4z2 = 64 is 2x + 6y + 8z - 71 = 0[/tex]. This equation gives the equation of a plane that has the same normal vector as the surface at the given point and passes through the given point. The normal vector of the surface at the given point can be found by taking the partial derivatives of the surface equation with respect to x, y, and z, and then evaluating the partial derivatives at the given point. The partial derivatives are 2x, 6y, and 8z. When evaluated at (1,3,3), the normal vector is (2,18,24). The equation of the tangent plane can then be found by taking this normal vector and the given point, and using the point-normal form of the equation of a plane. We have the normal vector (2,18,24) and the point (1,3,3). When substituted into the point-normal form of the equation of a plane, we get [tex]2x + 6y + 8z - 71 = 0[/tex], which is the equation of the tangent plane.

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The measure of trapezoid's opposite angle is 135°. The solution has been obtained by using properties of trapezoid.

What is a trapezoid?

Four sides make up the quadrilateral of a trapezoid, two of which are parallel while the other two are not. It is also referred to as a trapezium. A closed, four-sided form or figure known as a trapezoid has its own perimeter and can enclose an area.

We are given that one base angle is equal to 45°

We know that in a trapezoid

Base angle + Opposite angle = 180°

Using this, we get

⇒45° + Opposite angle = 180°

⇒Opposite angle = 180° - 45°

⇒Opposite angle = 135°

Hence, the measure of trapezoid's opposite angle is 135°.

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Answer:

Tha answer to your question is 15m

Step-by-step explanation:

pi * r^2 * h / 3

Area of the base = pi*r^2 = 70   so...

350 = 70 * h / 3  

350 = (70/3) * h     multiply both sides by 3/70

350 (3/70) = h = 15 m

Hope this helps you

Answer:

15m

Step-by-step explanation:

Using Fomula- V=AB h/3

h= 3 V/AB= 3· 350/70= 15m

The required equation of the line passing through (4,2) and parallel to y = 1/2x - 3 is y = 1/2x.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The slope of the given line,
y = 1/2x - 3
m = 1/2

The slope of the parallel lines is always equal

Now, the Equation of the parallel line passing through the point (4, 2) is given as
y - y₁ = m (x - x₁)
y -2 = 1/2(x - 4)
y = 1/2x

Thus, the required equation of the line passing through (4,2) and parallel to y = 1/2x - 3 is y = 1/2x.

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Answer:

Step-by-step explanation:

x = 24

Answer:

30/2 = 15cm = r

(Pi)r^2 = area of circle

(Pi)(15)^2 =706.5cm

Area of circle x height = volume

706.5 x 325 = 229613cm^3

No, the product of 7/8 multiplied by 2/9 will not be greater than either of the two factors.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers. In a fraction, the top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Here,
To find the product, we can multiply the two fractions,

(7/8) × (2/9) = (7 × 2) / (8 × 9)
                = 14/72 = 1/6

Since 1/6 is less than both 7/8 and 2/9, the product is not greater than either of the two factors.

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The number of values greater than 10.5 and less than 12.5 is 5. By adding the frequencies between these quantities, we could get the number.

A histogram is a graph representing frequency distribution of data points in a dataset. In one axis the data points are given, and the other axis is the frequency. It can be used in both discrete and continuous dataset. In discrete data, there will be individual data points and for continuous it will be a range.

Here the given dataset is a continuous dataset. The frequency of datapoints between 10.5 and 11.5 is 2 and frequency between 11.5 and 12.5 is 3. So the total will be 2+3 = 5.

So the frequency or values between 10.5 and 12.5 is 5

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The complete question is in the image.

Answer:

Step-by-step explanation:

Since −f(x) is constant with respect to f, the derivative of −f(x) with respect to f is 0.0

According to the Centers for Disease Control

and Prevention, kids should get C) at least 60 minutes of exercise each day.

Exercise is a movement activity that has an important role for health. With exercise, one's body becomes healthier and stronger. Not only maintaining physical health, exercise also affects spiritual health.

The aim of exercise is to improve one's health. In addition to improving physical fitness, exercise can also improve and improve the performance of the human brain so that it can work more optimally. Therefore, exercise is considered to be able to increase one's self-confidence.

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Answer:

2

Step-by-step explanation:

4/2 = 2 therefore 2 women will be in two committies.

Answer:

15.11

Step-by-step explanation:

first you have to change 182% to a decimal (1.82) then multiply it by the number of hours (8.3) then you get your answer 15.106. last round it to the nearest tenth (15.106) and you get 15.11

a) The measure of side PN of the triangle is PN = 18 cm

b) The measure of ∠CDA = 45°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the first triangle be represented as ΔOMP

Let the second triangle be represented as ΔOPN

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Now , the measure of OP = √ ( OM² - MP² )

Substituting the values in the equation , we get

The measure of OP = √ ( 25 )² - ( 7 )²

The measure of OP = √ ( 625 - 49 ) = √ ( 576 )

The measure of OP = 24 cm

And , the triangle OPN is a right triangle ,

So , the measure of PN = √ ( ON )² - ( OP )²

Substituting the values in the equation , we get

The measure of PN = √ ( 30 )² - ( 24 )²

The measure of PN = √ ( 900 - 576 ) = √ ( 324 )

The measure of PN = 18 cm

Therefore , the measure of PN of the triangle is 18 cm

b)

The two parallel lines are l₁ and l₂ where line t is the transversal

The measure of ∠FAE = 55°

The measure of ∠GAF = 80°

Now , the measures of angles in a straight line is 180°

So , the measure of ∠GAB = 180° - ( 55° + 80° )

The measure of ∠GAB = 45°

And , measure of ∠GAB = measure of ∠DAE ( alternate angles are equal )

So , the measure of ∠DAE = 45°

And , the measure of ∠DAE = the measure of ∠CDA ( alternate interior angles of a transversal line are equal )

Therefore , the measure of ∠CDA = 45°

Hence , the side PN of triangle is 18 cm and angle ∠CDA = 45°

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Answer:

21-68+5$567798876545

Answer: The answer should be 0.207%

Step-by-step explanation:

540.54/261040.5

54054/26104050

429/207175

0.00207 X 100/100

0.207/100

0.207%

Step-by-step explanation:

1.  Calculate the mean of the data: (6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 10) /    10 = 8

2.  Subtract the mean from each data point to get the deviation:

3. Square each deviation:

4. Add up the squared deviations: 4 + 1 + 1 + 0 + 0 + 0 + 0 + 1 + 1 + 4 = 12

5.Divide the sum of squared deviations by the number of data points (n-1), which is 9 in this case: 12 / 9 = 1.33

Answer:
So, the variance is 1.33.

The best description for this distribution is bimodal.

What is the Bimodal ?

Bimodal is a term used in statistics to describe a distribution with two modes, or peaks, in the frequency of occurrence of the values.

The distribution of the values: 3, 3, 5, 4, 3, 2, 5, 6, 5, 1 is best described as:

c. Bimodal

Bimodal means that the distribution has two modes, or peaks, in the frequency of occurrence of the values. In this case, the values 3 and 5 both have a high frequency of occurrence, forming two distinct modes in the distribution.

Therefore, the best description for this distribution is bimodal.

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The balloon payment due at the end of 48 months is approximately $19,726.27.

Answer choice (A) is the closest option.

What is the present value of an annuity?

Present value of an annuity is a financial concept that refers to the current value of a series of regular and equal payments or cash flows to be received or paid out in the future.

To find the balloon payment due at the end of 48 months, we can use the formula for the present value of an annuity:

PV = PMT x ((1 - (1 + r)^-n) / r)

where PV is the present value of the annuity (i.e. the balloon payment), PMT is the monthly payment, r is the interest rate per month (i.e. 6% / 12 = 0.005), and n is the number of periods (i.e. 48).

We can first find the total amount paid over 48 months:

Total payments = $199/month x 48 months = $9,552

We can then find the remaining balance on the car after 48 months:

Remaining balance = $24,000 - $9,552 = $14,448

Finally, we can use the present value formula to find the balloon payment:

PV = $199 x ((1 - (1 + 0.005)^-48) / 0.005) + $14,448

PV ≈ $19,726.27

Hence, the balloon payment due at the end of 48 months is approximately $19,726.27.

Answer choice (A) is the closest option.

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Answer: I got u ma

Step-by-step explanation:

The unit rate for the speed of Runner A and B is 12 and 15 ft / sec respectively, where Rubber B is faster.

A unit rate means a rate for one of something.

Given that, Two runners are training for their next competitions. Each runner is able to run a certain distance in proportion to the time. The table displays the distance Runner A can run in relation to the time. Meanwhile, the graph on the right displays the distance Runner B can run in relation to time. We need to find the unit rates for both runners,

Runner A =

Unit rate = distance / time

= 54 / 4.5

= 12 ft / sec

Therefore, unit rate for the speed of Runner A is 12 ft / sec

Runner B =

According to graph, the Runner B can run 75 ft in seconds

Unit rate = distance / time

= 75 / 5

= 15 ft / sec

Therefore, unit rate for the speed of Runner B is 15 ft / sec

Since, the speed of Runner B is greater than Runner A therefore, Rubber B is faster.

Hence, the unit rate for the speed of Runner A and B is 12 and 15 ft / sec respectively, where Rubber B is faster.

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