Which of the following types of functions have inverse functions?
A.May-to-one
B.One-to-many
C.One-to-one
D.Many-to-many​

The inverse matrix R⁻¹ does not exist

The inverse of a matrix written as A⁻¹ is such that when the inverse matrix multiplies A, the result is the identity matrix.

Given the matrix [tex]R = \left[\begin{array}{ccc}0&0\\1&3\end{array}\right][/tex], to determine if this matrix has an inverse it must satisfy the following condition.

For a matrix A to have an inverse, its determinant must not be equal to zero. That is det(A) ≠ 0

So, to determine if the above matrix has an inverse, its determinant must not equal zero.

So, the determinant of the matrix det(R) = 0 × 3 - 0 × 1

= 0 - 0

= 0

Since the determinant equals zero, thus we see that its inverse R⁻¹ does not exist

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Answer:

4(2)^(2/3)   or   4∛(4)

Step-by-step explanation:

Rules of Exponents..

16^(2/3)

= (2^4)^(2/3)

= 2^(8/3)

= 2^(2 + 2/3)

= 2^2 · 2^(2/3)

= 4(2)^(2/3)   or   4∛(4)

Using law of cosines, the group that is farther from the locker room is; Group B

The law of cosines gives that;

c² = a² + b² - 2ab cos C

Now, for group A, we can use law of cosine to find their current distance from the locker room as;

a² = 4.6² + 2.1² - 2(4.6*2.1)*cos 40°

a² = 21.16 + 4.41 - 14.8

a = √10.77

a = 3.28 miles

Similarly, for Group B, we have;

b² = 4.6² + 2.1² - 2(4.6*2.1)*cos 50°

b² = 21.16 + 4.41 - 12.42

b = √13.15

b = 3.63 miles

This means that group B is farther from the locker room

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Answer:

Step-by-step explanation:

The length of the side AB represented by x in the triangle ABC is equal to 16 using the trigonometric ratio of sine.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

The triangles ABC and ADB are right-angled triangles, we shall be considering the trigonometric ratio of the sine of angle A which is common to both triangles.

For triangle ABC;

sinA = adjacent/hypotenuse

sinA = x/32

for triangle ADB;

sinA = 8/x

thus we can say that;

x/32 = 8/x {cross multiplication}

x² = 3 × 32

x² = 256

x =√256 {take square root for both sides}

x = 16.

Therefore, 16 is the length of the side AB labelled x, using the trigonometric ratio of sine of the common angle A to the triangles ABC and ADB.

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A dealer bought some 9-volt batteries for $2,400. She sold them for $5,600, making a profit of $1.60 on each battery. 2,500 batteries were involved in the deal.

The dealer bought some 9-volt batteries for $2,400 and she sold them for $5,600. To find out how many batteries were involved, we need to calculate how much she made from each battery. We can do this by subtracting the cost of the batteries from the selling price and then dividing it by the number of batteries. Profit per battery = $5,600 - $2,400 = $3,200. Number of batteries = $3,200/$1.60 = 2,500. Therefore, the dealer bought 2,500 batteries.

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After subtracting the fractions, we know that Jordan runs 1/24 miles more on Monday than Tuesday.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. Both are integers in a simple fraction.

A fraction appears in the numerator or denominator of a complex fraction.

The numerator of a proper fraction is less than the denominator.

So, we know that:

Jordan runs on Monday: 7/8 miles

Jordan runs on Tuesday: 5/6 miles

Jordan runs more on Monday:

7/8 - 5/6

3*7 - 4*5/24

21 - 20/24

1/21 miles

Therefore, after subtracting the fractions, we know that Jordan runs 1/24 miles more on Monday than Tuesday.

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Correct question:
Jordan ran 7/8 miles on Monday and 5/6 miles on Tuesday.

How much farther did Jordan run on Monday than on Tuesday?

Enter your answer as a fraction in simplest form.

Answer: lines j and k are perpendicular

Step-by-step explanation:

Let's find the equations of lines j and k

                       [tex]\displaystyle\\\boxed{\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

Line j: (8,2)  (-2,-2)

x₁= 8     x₂=-2    y₁=2     y₂=-2

[tex]\displaystyle\\\frac{x-8}{-2-8}=\frac{y-2}{-2-2} \\\\\frac{x-8}{-10}=\frac{y-2}{-4} \\\\[/tex]

 Multiply both parts of the equation by -4:

[tex]\displaystyle\\\frac{2}{5} (x-8)=y-2\\\\\frac{2}{5} x-\frac{16}{5} =y-2\\\\\frac{2}{5} x-3.2+2=y-2+2\\\\\frac{2}{5}x-1.2=y\\\\ Thus,\ y=\frac{2}{5}x-1.2[/tex]

Line k: (-4,3)   (-6,8)

x₁=-4    x₂=-6    y₁=3    y₂=8

[tex]\displaystyle\\\frac{x-(-4)}{-6-(-4)} =\frac{y-3}{8-3} \\\\\frac{x+4}{-6+4}=\frac{y-3}{5} \\\\\frac{x+4}{-2} =\frac{y-3}{5}[/tex]

Multiply both parts of the equation by 5:

[tex]\displaystyle\\-\frac{5}{2}(x+4)=y-3\\\\ -\frac{5}{2}x-10=y-3\\\\ -\frac{5}{2}x-10+3=y-3+3\\ -\frac{5}{2}x-7=y\\Thus,\ y=-\frac{5}{2} x-7[/tex]

Hence, lines j and k are perpendicular

The system of equations is:

2b + 4.25s = 53.75

b - s = 5  

The number of bagels bought is 12 and the number of sandwiches bought is 7.

2b + 4.25s = 53.75 equation 1

b - s = 5  equation 2

Where:

The elimination method would be used to determine the required values.

Multiply equation 2 by 2

2b - 2s = 10 equation 3

Subtract equation 3 from equation 1 :

6.25s = 43.75

Divide both sides of the equation by 2.25

s = 43.75 / 6.25

s = 7

Substitute for s in equation 1:

2b + 4.25(7) = 53.75

2b + 29.75 = 53.75

2b = 53.75 - 29.75

2b = 24

b = 24 / 2

b = 12

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Answer:

y < -1x + 2

y [tex]\geq \\[/tex] 2x + 4

Step-by-step explanation:

The steps taken to find the two inequalities are on the GraphInequalities worksheet.  The derived equations are graphed on DESMOS and attached, for comparison.

The basic steps are to find the slopes of the two lines and to identify the y-intercepts from the graph.  The inequalities can be assigned based on the darkened areas and presence of either a solid or dashed line.  All are outlined in the worksheet.

Answer:

988 m^2

Step-by-step explanation:

A=wl

A=38*26 = 988 m^2

Answer:

The store needs [tex]988m^2[/tex] of flooring.

Step-by-step explanation:

To find how many square meters of flooring the store needs, we need to find the area of the floor.

⭐ What does the area of a shape mean?

We are given that the length is 38 meters and the width is 26 meters.

Substitute these values into the area formula.

area = length*width

area = 38*26

∴ area = 988[tex]m^2[/tex]

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The volume of the smaller cone is 19.6cm³

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

The above parameter mean that

Smaller cone

Side length = 2 cm

Volume = [?] cm³

Large cone

Side length = 3 cm

Volume = 66 cm³

The ratio of the cones can be represented as

Ratio = Side length³ : Volume

So, we have

2³ : Volume of smaller cone = 3³ : 66

Evaluate the exponents

8 : Volume of smaller cone = 27 : 66

Express as fraction

Volume of smaller cone/8 = 66/27

So, we have

Volume of smaller cone = 8 * 66/27

Evaluate

Volume of smaller cone = 19.6

Hence, the volume is 19.6cm³

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The fence Ben paints is 150 square feet.

Given:

ratio of the amount of work allen does to the amount of work ben does is 3:5

allen : ben = 3:5

total work done in ratio = 3 + 5 = 8

Count the fence Ben paints

Since , fence requires a total of 240 square feet to be painted

Thus, ben = ratio of ben/ total ratio × total of works

ben = 5/8 × 240

ben = 1,200/8

ben = 150

Hence , The fence Ben paints is 150 square feet .

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The conclusion that can be made from the given observations is that the dew factor temperature is 90% of the air temperature.

Humidity is the quantity of water vapor withinside the air. If there is lots of water vapor withinside the air, the humidity might be high.

The temperature have to upward push so as for air to come to be saturated with water vapor.

The air holds little water vapor and is rather dry.

The quantity of water vapor withinside the air is 90% of what the air can hold.

The dew factor temperature is 90% of the air temperature.

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The probability that 3 out of 7 randomly chosen processors have computing speeds of 3.55 or higher is 0.2937.

In the given question,

Suppose computing speed of processors are normally distributed with mean 3.5GHz with standard deviation 0.26GHz

We have to find the probability that 3 out of 7 randomly chosen processors have computing speeds of 3.55 or higher.

Probability that 3 out of 7 randomly chosen processors clocks a speeds of 3.55 or higher is given

p = 0.4247

Now the probability follows a Binomial Distribution with the parameters, n=7 ad p=0.4247

P(X=x) = [tex]^nC_{k}(p)^k(1-p)^{n-k}[/tex]

Now putting the values

P(X=x) = [tex]^7C_{3}(0.4247)^3(1-0.4247)^{7-3}[/tex]

After solving;

P(X=x) = 0.2937

Hence, the probability that 3 out of 7 randomly chosen processors have computing speeds of 3.55 or higher is 0.2937.

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The write question is:

Suppose computing speed of processors are normally distributed with mean 3.5GHz with standard deviation 0.26GHz. The probability that a randomly selected processor clocks a speed of 3.55 or higher is 0.4247.

What is the probability that 3 out of 7 randomly chosen processors have computing speeds of 3.55 or higher?

28sinθ is the maximum area of the triangle

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

The two sides of triangle are of length 7 and 8.

Triangle has an included angle has a measure of θ degrees.

We need to find the maximum area

A=1/2×7×8×sinθ

A equal to one by two time of seven times of eight times sin theta.

A=7×4×sinθ

A=28sinθ

Hence, 28sinθ is the maximum area of the triangle

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the truth table of expression (A+B).A is T ,T ,F,F . A truth table has one column for each input variable (such as P and Q) and a final column that lists all potential outcomes.

Truth tables are mathematical tables that are used in logic, specifically in relation to Boolean algebra, Boolean functions, and propositional calculus. They contain the functional values of logical expressions on each of their functional arguments, or more specifically, for each combination of values that their logical variables can take.

given

( A+B) . A

A          B      (A + B)      (A+B).A

T           T         T                  T

T           F         T                 T

F           T         T                 F

F           F         F                 F

So , the truth table of expression (A+B).A is T ,T ,F,F .

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Answer:

1.   d = 40; 2 irrational

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real solutions.\\when $b^2-4ac=0 \implies$ one real solution.\\when $b^2-4ac < 0 \implies$ no real solutions.\\\end{minipage}}[/tex]

Given quadratic equation:

[tex]3x^2+4x-2=0[/tex]

Therefore:

Substitute the values of a, b and c into the discriminant formula:

[tex]\begin{aligned}\implies b^2-4ac&=(4)^2-4(3)(-2)\\&=16-12(-2)\\&=16+24\\&=40\end{aligned}[/tex]

Therefore, as d = 40 and 40 > 0:

[tex]\implies b^2 - 4ac > 0 \implies \text{two real solutions}.[/tex]

To determine if the solutions are irrational or rational, simply square root the discriminant.

[tex]\implies \sqrt{d}=\sqrt{40}=2 \sqrt{10}[/tex]

As the discriminant is not a perfect square, then its square root is irrational and so the solutions of the quadratic equation are irrational.

Answer:

the answer is number three

Step-by-step explanation:

820×10 = 8200

The percent decrease in the number of people who went to the pool over these four weeks is 30%.

From the information given, in the the first week of July, a record 1060 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 130 more people went to the pool than in the second week. In the fourth week, 348 fewer people went to the pool than in the third week

The total number of people at the end of the week will be:

= 1060 - 100 + 130 - 348

= 742

The percentage decrease will be:

Decrease / Original value × 100

= (1060 - 742) / 1060 × 100

= 30%

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To find [tex]\frac{2}{3}[/tex] of a whole number, you can divide the number by 3 and then multiply the result by 2.

For example, if you want to find [tex]\frac{2}{3}[/tex] of the number 15, you can perform the following calculation:

[tex]\frac{2}{3}[/tex] × 15 = 10

This means that [tex]\frac{2}{3}[/tex] of the number 15 is equal to 10.

You can also find [tex]\frac{2}{3}[/tex] of a whole number by dividing the number by 3 and then multiplying the result by 2.

For example:

[tex]\frac{15}{3}[/tex] = 5

2 × 5 = 10

So, [tex]\frac{2}{3}[/tex] of the number 15 is also equal to 10.

Alternatively, you can find [tex]\frac{2}{3}[/tex] of a number by expressing it as a decimal. [tex]\frac{2}{3}[/tex] can be expressed as 0.6666666667, so you can multiply the whole number by 0.6666666667 to find [tex]\frac{2}{3}[/tex] of it. For example:

0.6666666667 × 15 = 10

So [tex]\frac{2}{3}[/tex] of the number 15 is equal to 10.

A whole number is a positive integer that is greater than 0, such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc. Whole numbers do not include fractions, decimals, or negatives.

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If the 34% of the college students major in STEM than the probability that exactly 15 of them major in STEM is 0.1162   .

In the question ,

it is given that ,

percent of students that major in STEM is = 34% ;

that means , p = 0.34 ; so , q = 0.6

number of students randomly selected (n) = 40 ,

By the Binomial Probability Distribution ,

we get ;

p(x = 15) = ⁴⁰C₅*(0.34)¹⁵*(0.66)²⁵

Simplifying the above value further ,

we get ;

p(x = 15) = 0.1162 .

Therefore , the required probability is 0.1162 .

The given question is incomplete , the complete question is

The 34% of all college students major in stem (science, technology, engineering, and math). if 40 college students are randomly selected, find the probability that exactly 15 of them major in stem  .

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Angle DCE = 91°

Hope it helps

The mean number of number of people in passengers cars on the highway is given as follows:

E. 6.28.

The expected value of a discrete distribution is calculated as the sum of each value multiplied by it's respective probability.

The distribution in this problem is given as follows:

Then the expected value before the transformation is given as follows:

E(X) = 0.56 x 1 + 0.28 x 2 + 0.08 x 3 + 0.06 x 4 + 0.02 x 5 = 1.7.

The transformation is given as follows:

Y = 0.75x + 5.

Thus the expected value after the transformation is of:

E(X) = 0.75(1.7) + 5 = 6.28.

Meaning that option E is correct.

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The system of equations which is used to find out the cost of each item (i.e cotton candy and funnel cake) bought by two families McCartney and Lennon Family is

3c + 2f = $24

2c + 4f = $32

We have given that

McCartney family bought

total number of bags of cotton = 3

total number of funnel cakes = 2

total cost of 3 bags and 2 funnel cakes is $24.

Lennon Family bought

total number of bags = 2

total number of funnel cake = 4

total cost of 2 bags and 4 funnel= $32

we have to find out the system of equations which used to find the cost of each item.

let the cost of each funnel cake be f and cotten candy be c .

then, using the above data we get

3c + 2f = $24 ---(1)

2c + 4f = $32 --(2)

Hence, equation (1) and (2) make a system of linear equations which is used to determine the cost of each item.

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Complete question:

HEME At the circus, the McCartney family bought 3 bags of cotton candy and 2 funnel cakes for $24. The Lennon Family bought 2 bags of cotton candy and 4 funnel cakes for $32. Which system of equations could be used to find the cost of each item? Let f represent funnel cake and c represent cotton candy

The graph that shows the function with the determined behavior is the last graph, circled on the image given at the end of the answer.

The graph of a function is classified as either increasing, decreasing or constant, as follows:

Hence the fourth graph on the image given at the end of the answer is the one with the desired behavior on each interval.

The graphs are given by the image shown at the end of the answer.

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The value of the function h(x) = -3(x - 1) + 4 when x is -5 is 19.

It is important to note that a function is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, the function is given a :

h(x) = -3(x - 1) + 4

When x = -5. This will be:

h(-5) = -3(-5 - 1) + 4

= -3(-6) + 1

= 18 + 1

= 19

The value is 19.

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14 orders of guacamole need  24.5  avocadoes

What are equivalent ratios?

The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.

4 orders of guacamole need  7 avocadoes

14 orders of guacamole need  x avocadoes

Equivalent ratios:

4/7 = 14/x

Solve for x.

=> 4x = 7*14 = 98

=> x = 98/4 = 24.5

So, 14 orders of guacamole need  24.5  avocadoes

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The slope m of a line passing through two points (x1 , y1) and (x2 , y2) is:

m = (y2 − y1) / (x2 − x1)

If the graph of a line rises from left to right, the slope is positive.

What is slope ?

Slope is a ratio and can have a value that is positive, negative, equal to zero, or undefined. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run".

What is positive slope ?

A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y also decreases. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises. We will learn in other sections that “price” and “quantity supplied” have a positive relationship; that is, firms will supply more when the price is higher.

The slope m of a line passing through two points (x1 , y1) and (x2 , y2) is:

m = (y2 − y1) / (x2 − x1)

If the graph of a line rises from left to right, the slope is positive.

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Answer:

252 in.²

Step-by-step explanation:

12 in. by 21 in. rectangle

The 6 in. by 3 in. rectangle missing on the left bottom corner is made up by the same-sized rectangle on the right side.

A = LW

A = 21 in. × 12 in.

A = 252 in.²