let a where b and c are square. show that a is invertible if and only if both b and c are invertible.

Answer: [tex]5.301[/tex] x [tex]10^{7}[/tex]

Answer: x10^7

Step-by-step explanation: 5.301 = x10^7

Answer:

75%

Step-by-step explanation:

We know

A year has 12 months

Oliver worked 9 months out of the year

What percent of the year did he work?

We take

9 divided by 12, time 100 = 75%

So, he works 75% of the year.

Step-by-step explanation:

Amounts he payed first = $480

Monthly amount he pays = $73

No of months he payed it for = 12

Additional amount he payed = 73 × 12 = 876

Total amount = 480 + 876 = $1356

Answer:72 feet

$560.88

Answer:

Is there meant to be a picture? I can still try to help if you explain in the comment under this, but I think the picture didn't submit fully!! :)

I'll edit the answer when you edit the question to add the full image

Step-by-step explanation:

A basis {p(x),q(x)} for the vector space {f(x) € P3[x] | f'(1) = f(1)} where P3[x] is the vector space of polynomials in with degree less than 3. p(x) = ,q(x) =  is {p(x) = x² - 1, q(x) = x² + x - 2}

The vector space {f(x) € P3[x] | f'(1) = f(1)} consists of polynomials of degree less than 3 with the property that their derivative at x = 1 is equal to the polynomial itself evaluated at x = 1. To find a basis for this space, we can start by finding a set of two polynomials that satisfy this property, and that are linearly independent.

One possible choice for p(x) is x² - 1, and one possible choice for q(x) is x² + x - 2. These polynomials satisfy the required property (i.e., their derivatives at x=1 are equal to the polynomials themselves evaluated at x=1), and they are linearly independent because their leading terms (x² in both cases) are distinct.

Thus, {p(x) = x² - 1, q(x) = x² + x - 2} is a basis for the vector space {f(x) € P3[x] | f'(1) = f(1)}.

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Notably, this response comes the nearest to choice A (83.3 wins). The right response is thus A.

A mathematical statement that shows the equivalence of two mathematical equations is what a solution in algebra means. For instance, the two numbers 3x + 5 and 14 make up the expression 3x + 5 = 14, which is separated by the sign "equal."

We can change x to 17 in the regression model y = 4.9x + 15.2 and calculate for y to get the number of victories for a squad with 17,000 spectators: y = 4.9(17) + 15.2 = 83.5

Consequently, 83.5 victories are expected for a squad with a 17,000-fan attendance.

To predict the number of wins for a team with an attendance of 17,000, we can substitute x = 17 into the regression equation y = 4.9x + 15.2 and solve for y:

y = 4.9(17) + 15.2 = 83.5

Therefore, the predicted number of wins for a team with an attendance of 17,000 is 83.5 wins.

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Step-by-step explanation:

a probability is always the ratio of

desired cases / totally possible cases

the "group" is the totally possible cases = 119.

we pick 1 student.

female AND off-campus.

there are only 20 students that satisfy that criteria.

the probabilty for this event is then

20/119 = 0.168067227... ≈ 0.168

male AND on-campus.

there are 34 students that satisfy that criteria.

the probability for this event is then

34/119 = 0.285714286... ≈ 0.286

off-campus OR male.

there are 20+11 = 31 students off-campus.

and there are 34+11 = 45 male students.

the overlapping number of 11 students we need to count only once.

so, there are 20+11+34 = 65 students off-campus or male (incl. the on-campus males, as this is an or-criteria).

the probabilty for this event is then

65/119 = 0.546218487... ≈ 0.546

on-campus OR female.

there are 54+34 = 88 students on-campus.

and there are 54+20 = 74 female students.

the overlapping number of 54 students we need to count only once.

so, there are 54+34+20 = 108 students on-campus or female.

the probabilty for this event is then

108/119 = 0.907563025... ≈ 0.908

Let f(x)=-3x+2, g(x)=5 h(x) = -2x+9, and j(x) = 5-x. Find each value or expression.

1. (f +j)(3) = -5

3. (h + g)(-5) = 10

5. (f + g)(2) = 1

7. (g f)(-5) = 22

9. f((5)) = -11

1. (f + j)(3) = f(3) + j(3) = (-3(3)+2) + (5-3) = -7 + 2 = -5

3. To find the value of (h + g)(-5), we need to first add the functions h(x) and g(x), then evaluate the result at x = -5.

h(x) = -2x + 9

g(x) = 5

h(x) + g(x) = -2x + 9 + 5 = -2x + 14

So, (h + g)(-5) = -2(-5) + 14 = 10.

The answer is 10.

5. To find the value of (f + g)(2), we need to first add the functions f(x) and g(x), then evaluate the result at x = 2.

f(x) = -3x + 2

g(x) = 5

f(x) + g(x) = -3x + 2 + 5 = -3x + 7

So, (f + g)(2) = -3(2) + 7 = 1.

The answer is 1

7. (To find the value of (g + f)(-5), we need to first add the functions g(x) and f(x), then evaluate the result at x = -5.

f(x) = -3x + 2

g(x) = 5

f(x) + g(x) = -3x + 2 + 5 = -3x + 7

So, (g + f)(-5) = -3(-5) + 7 = 22.

The answer is 22

9. f(5) = -3(5) + 2 = -13 + 2 = -11

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A. The velocities are given as follows:

B. The graph is given by the image presented at the end of the answer.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

From the table, Devron's rate is given as follows:

k = 180/4

k = 45 miles per hour.

Hence the equation is of:

y = 45x.

For Avery's equation of y = 60x, the rate is of 60 miles per hour.

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For the given normal distribution, The 97th percentile of the cholesterol measurements is 218.8 mg/dL.

The normal distribution, also known as the Gaussian distribution or bell curve, is a continuous probability distribution that is symmetrical around its mean value. It is a widely used distribution in many fields, including finance, engineering, and the natural sciences, due to its important properties, such as the central limit theorem.

To find the 97th percentile of a normal distribution with mean 200 and standard deviation 10, we need to find the value x such that P(X < x) = 0.97, where X is a random variable representing the cholesterol measurement.

This value can be found using a standard normal distribution table (or Z-table), which gives the cumulative probabilities for a standard normal distribution with mean 0 and standard deviation 1.

We first standardize our random variable X by subtracting the mean and dividing by the standard deviation:

Z = (X - 200) / 10

So,

P(X < x) = P((X - 200) / 10 < (x - 200) / 10)

                   = P(Z < (x - 200) / 10) = 0.97.

Using the Z-table, we can find the Z-score corresponding to a cumulative probability of 0.97: Z = 1.88.

Finally, we can convert back to the original units for X by multiplying the Z-score by the standard deviation and adding the mean:

x = 10 * 1.88 + 200 = 218.8

So, the 97th percentile of the cholesterol measurements is 218.8 mg/dL.

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The statement that involves descriptive statistics is -

Option A) The Alcohol, Tobacco, and Firearms Department reported that Houston had 1,791 registered gun dealers in 1997.

What are two categories of field statistics?

There are two categories of field statistics. Descriptive and inferential statistics. Both of them help analysts to make sense of row after row data.

Descriptive statistics presents quantifiable descriptions in a simple way. Inferential statistics is used to draw conclusions that go beyond the raw data only. It is used in making judgments, inferences to deeper general conditions.

The Alcohol, Tobacco, and Firearms Department reported that Houston had 1,791 registered gun dealers in 1997.

Descriptive statistics are useful in describing the basic features of the data being analyzed. They simply provide what the raw data shows. They simplify huge amounts of data sensibly and make it presentable in a manageable form.

With regard to the question, raw data is available stating that the registered gun dealers were 1791 in 1997. It, therefore, involves descriptive statistics.

Therefore, the correct answer is option A.

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Which of the following statements involve descriptive statistics as opposed to inferential statistics?

A) The Alcohol, Tobacco, and Firearms Department reported that Houston had 1,791 registered gun dealers in 1997.

B) Based on a survey of 400 magazine readers, the magazine reports that 45% of its readers prefer double-column articles.

C) The FAA samples 500 traffic controllers in order to estimate the percent retiring due to job-stress-related illness.

D) Based on a sample of 300 professional tennis players, a tennis magazine reported that 25% of the parents of all professional tennis players did not play tennis.

Answer: PLS CROWN ME / brainly :)

13^4 in base 4:

Method 1: Convert 13^4 to base 10 using powers of 4.

13 in base 4 = 1 * 4^1 + 3 * 4^0 = 1 * 4 + 3 * 1 = 7

So, 13^4 in base 4 = (1 * 4^4 + 3 * 4^3) = (1 * 256 + 3 * 64) = 256 + 192 = 448.

Method 2: Convert 13 to base 10 and then find (13 in base 10)^4

13 in base 4 = 1 * 4^1 + 3 * 4^0 = 1 * 4 + 3 * 1 = 7

So, (13 in base 10)^4 = 7^4 = 2401

So, 13^4 in base 10 = 2401.

303^4 in base 4:

Method 1: Convert 303^4 to base 10 using powers of 4.

303 in base 4 = 3 * 4^2 + 0 * 4^1 + 3 * 4^0 = 3 * 16 + 0 * 4 + 3 * 1 = 51

So, 303^4 in base 4 = (3 * 4^6 + 0 * 4^5 + 3 * 4^4) = (3 * 4096 + 0 * 1024 + 3 * 256) = 12288 + 768 = 13056.

Method 2: Convert 303 to base 10 and then find (303 in base 10)^4

303 in base 4 = 3 * 4^2 + 0 * 4^1 + 3 * 4^0 = 3 * 16 + 0 * 4 + 3 * 1 = 51

So, (303 in base 10)^4 = 51^4 = 132651.

So, 303^4 in base 10 = 132651.

132^4 in base 4:

Method 1: Convert 132^4 to base 10 using powers of 4.

132 in base 4 = 1 * 4^2 + 3 * 4^1 + 2 * 4^0 = 1 * 16 + 3 * 4 + 2 * 1 = 22

So, 132^4 in base 4 = (1 * 4^8 + 3 * 4^7 + 2 * 4^6) = (1 * 65536 + 3 * 16384 + 2 * 4096) = 65536 + 49152 + 8192 = 19880.

Method 2: Convert 132 to base 10 and then find (132 in base 10)^4

132 in base 4 = 1 * 4^2 + 3 * 4^1 + 2 * 4^0 = 1 * 16 + 3 * 4 + 2 * 1 = 22

So, (132 in base 10)^4 = 22^4 = 10648.

So, 132^4 in base 10 = 10648.

Step-by-step explanation:

Answer:10101

Step-by-step explanation:

The meaning of the derivative f'(8) is the rate of change of the quantity of coffee sold with respect to the price per pound when the price is $8 per pound.

It represents how the quantity of coffee sold changes with respect to changes in the price per pound, when the price per pound is $8.

In mathematics, the derivative of a function is a measure of how the value of the function changes with respect to changes in one of its variables. In other words, the derivative gives the rate of change of a function with respect to its independent variable.

The derivative can be thought of as the slope of the tangent line to the function at a particular point. It can be calculated using limits, differential calculus, or other methods. The derivative is represented by the symbol "d/dx" for a function of a single variable x, where d/dx represents the rate of change of the function with respect to x.

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The Volume of the given pyramid is 66.7[tex]cm^{3}[/tex].

Volume is defined as the amount of space occupied by any three-dimensional objects. The unit of volume for any solid objects is measured using cubic units.

In this pyramid, length = 5cm, width = 5cm and height = 8cm.

Volume of pyramid is given by , V= [tex]\frac{1}{3}*l*w*h.[/tex]

                                                     V=[tex]\frac{1}{3} *5*5*8[/tex]

                                                        = [tex]\frac{200}{3}[/tex]

                                                     V=66.7[tex]cm^{3}[/tex]

Hence, the volume of the given pyramid is 66.7[tex]cm^{3}[/tex].

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Assuming that an unfair coin is tossed with outcomes of HH, HT, TH, and TT, and the probability is 0.40, 0.92, 0.29, and 0.55, then the given probabilities do not form a valid probability model for the sample space of two coin tosses.

The given probabilities do not form a valid probability model for the sample space of two coin tosses since a valid probability model must satisfy the following conditions:

To calculate the sum of the probabilities, we simply add up all of the given probabilities:

0.40 + 0.92 + 0.29 + 0.55 = 2.16

In this case, the sum of the probabilities is 2.16, which is greater than 1. Hence, the given probabilities do not form a valid probability model for the sample space of two coin tosses.

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The amount of time it takes for E to increase by 10%. it takes 4.81 seconds.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Given that,

Let the amount of time it takes for E to increase by 10% be x.

Thus, after (t + x) seconds, E is increased by 10%.

E(t + x) = E(t) + 10% of E(t)

= E(t) + 10/100 E(t)

= E(t) + 0.1 E(t)

E(t + x) / E(t) = 1.1

As,

[tex]E(t) = 6(1.02)^t\\\\E(t + x) = 6(1.02)^{t + x}\\\\\frac{E(t + x)}{E(t)} = \frac{6(1.02)^{t + x}}{6(1.02)^{t}}\\\\\frac{E(t + x)}{E(t)} = (1.02)^{t + x - t}\\\\(1.02)^x = 1.1[/tex]

Taking log on both sides:

x = log (1.1) / log (1.02)

x = 4.81 seconds.

Hence, the amount of time it takes for E to increase by 10%.

it takes 4.81 seconds.

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The fractional value for [tex]$0.23\overline{72}$[/tex] is 261 / 1100.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The decimal value is given as -

[tex]$0.23\overline{72}$[/tex]

To convert [tex]$0.23\overline{72}$[/tex] repeating into a fraction, begin writing this simple equation -

[tex]n=$0.23\overline{72}$[/tex] ..... (1)

Notice that there are 2 digits in the repeating block (72), so multiply both sides by 1 followed by 2 zeros, i.e., by 100.

[tex]100n=$0.2372\overline{72}$[/tex] .... (2)

Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.

[tex]100n-n=$0.2372\overline{72}$ - $0.23\overline{72}$[/tex]

[tex]99n = 23.49[/tex]

n = 23.49 / 99

n = 2349 / 9900

n = 261 / 1100

Therefore, the fraction is 261 / 1100.

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Answer:

the possible values of x such that the distance between (11, 6) and (x, -9) is 17 are 19 and 3.

Step-by-step explanation:

We can use the distance formula to find the possible values of x:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

17 = √[(x - 11)^2 + (-9 - 6)^2]

289 = (x - 11)^2 + 225

64 = (x - 11)^2

±8 = x - 11

Solving for x in both equations, we get:

x - 11 = 8 or x - 11 = -8

x = 19 or x = 3

Therefore, the possible values of x such that the distance between (11, 6) and (x, -9) is 17 are 19 and 3.

The value of the equation is A = ( x² + y² ) / ( x² - y² )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = x / ( x + y ) + y / ( x - y )

On simplifying the equation , we get

Multiply by the LCM , we get

x / ( x + y ) + y / ( x - y ) = [ x ( x - y ) + y ( x + y ) ] / ( x + y ) ( x - y )

where the denominator ( x + y ) ( x - y ) = ( x² - y² )

Substituting the values in the equation , we get

x / ( x + y ) + y / ( x - y ) = [ x² - xy + xy + y² ] / ( x² - y² )

On further simplification , we get

A = ( x² + y² ) / ( x² - y² )

Hence , the equation is A = ( x² + y² ) / ( x² - y² )

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Answer:

Width of the rectangle is 19 Units

Step-by-step explanation:

24 = x(x-5)

24 = [tex]x^{2}[/tex] - 5x

[tex]x^{2}[/tex] - 5x - 24 = 0

x(x-24) + 1(x-24) = 0

(x-24)(x+1)=0
x= -1 , 24

x = 24 units

x - 5 = 19 units

Step-by-step explanation:

If you look at the picture above you'll see that after connecting the length, width and area you get a quadratic equation which I solved using formula method, but any method can be used to solve the quadratic equation. Also at the end you arrive at two answers which of course you select the positive one.

The patient takes 15mL of of Maalox® in one day.

From the question, we have the following parameters that can be used in our computation:

Take 5mL po 1hr a.c., 1hr p.c., and h.s.

The order says:

Since there are three meals in a day (breakfast, lunch, and dinner),

Then the patient takes 5mL of Maalox® three times a day.

So, the patient takes 5mL * 3 = 15mL in one day.

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The absolute value of this difference is 18 miles, so the walk diagonally across the rectangle park is approximately 18 miles shorter than walking along the two sides of it.

A rectangle is just a square with four perpendicularly in the Euclidean plane. An equiangular quadrant or a quadrant that appears to have identical angles are other names for it. A straight angle is another choice for the parallelogram. A square has four edges that are the same length. Quadrilaterals with four equal edges and four 90° edges are called rectangles. As a consequence, it is occasionally referred to as a "equirectangular square".

Here,

The length of the diagonal of the rectangle can be found using the Pythagorean theorem:

d = √(8^2 + 6^2) ≈ 10

So the length of the diagonal is approximately 10 miles.

To find the distance of walking along the two sides of the rectangle, we can use the formula for the perimeter of a rectangle:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

In this case, we have:

P = 2(8) + 2(6) = 28

So the distance of walking along the two sides of the rectangle is 28 miles.

The difference between walking along the two sides and walking diagonally can be found by subtracting the distance of walking along the two sides from the length of the diagonal:

10 - 28 ≈ -18

The absolute value of this difference is 18 miles, so the walk diagonally across the park is approximately 18 miles shorter than walking along the two sides of it.

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Answer:

Step-by-step explanation:

To find out the part of the report that the coach has left to write, we first need to find out how much of the report he has already written. On Saturday, he wrote 1/8 of the report, and on Sunday, he wrote 1/2 of the report.

So, the total part of the report that the coach has written is:

1/8 + 1/2 = 5/8

Now, we subtract this fraction from 1 to find the part of the report that the coach still has to write.

1 - 5/8 = 3/8

So, the coach has 3/8 of the report left to write.

Step-by-step explanation:

Since we have 9 people and 13 burgers, the problem set up is dividing 13 burgers between 9 people

[tex] \frac{13 \: burgers}{9 \: people} [/tex]

= 1.44 burgers per person

The reasons for the steps are given below.

The value of x is -4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

-2(4x + 3) = 26

[ The distributive property of multiplication over addition ]

-2(4x) + -2(3) = 26

-8x - 6 = 26

[ Adding 6 on both sides ]

-8x - 6 + 6 = 26 + 6

-8x = 32

[ Divide -8 into both sides ]

-8x/-8 = 32/-8

x = -4

Thus,

The reasons for the steps are given above.

x = -4

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Answer:

350

Step-by-step explanation:

calculator

Step-by-step explanation:

try the suggested solution; the lines and their inequalities are shown with the same colours. Points A[0;-1] and B[0;-3] are interception points, according to them to define equations of the lines.