n an informal survey of students, 20 have dogs, 15 have cats, and five have both. one has only pet squirrel. how many people have only a pet cat

Answer:

\(a=-5, b=5\)

Step-by-step explanation:

\(\frac{10-\sqrt{32}}{\sqrt{2}} \\ \\ =\frac{10-5\sqrt{2}}{\sqrt{2}} \\ \\ =\frac{10}{\sqrt{2}}-5 \\ \\ =5\sqrt{2}-5 \\ \\ \therefore a=-5, b=5\)

Probability  that the two numbers are multiples of 3 after replacing first

It is a branch of mathematics that deals with the occurrence of a random event.

The odd integers from11 to 22 are

11,13,15,17,19,21

So there are 6 events

Out of these 6 numbers, 2 numbers (15,21) are multiples of 3.

One number out of these 2 numbers can be chosen in 2 ways.

Therefore, favourable number of elementary events = 2.

Required probability =2/6=1/3

Hence 1/3 is the probability  that the two numbers are multiples of 3 after replacing first

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Answer:

Yes! Good job!

If you can pick multiple its also C. and B.

Hey there! I'm happy to help!

SLOPE

To find the slope, you divide the difference of the y values by the difference in the x values.

10-(-2)=10+2=12

-6-(-3)=-6+3=-3

12/-3=-4

So, our slope is -4.

Y- INTERCEPT

To find the y-intercept, we plug our slope and one of our points into the slope intercept equation (y=mx+b) and solve for b, which is the y-intercept. We will use the point (-6,10).

10=-4(-6)+b

Flip the equation so b is on the left.

-4(-6)+b=10

24+b=10

Subtract 24 from both sides.

b=-14

Our y-intercept is -14.

EQUATION

The slope intercept equation is y=mx+b, where m is the slope and b is the y-intercept. Therefore, we have the following answers.

Slope: -4

y-Intercept: -14

Equation of the Line: y=-4x-14

Have a wonderful day! :D

The matrix is a not invertible when it's column do not span because it is not linearly independent.

According to the statement

we have find that the matrix can be a invertible or not when its column is spaned.

So, For this purpose, we know that the

Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.

And according to the statement it is not possible for thr matrix to be invertible.

Because for matrix it is not a possible because it is not independent,

In other words, No, if the columns don't span R5 -> NOT linearly independent -> not invertible.

So, The matrix is a not invertible when it's column do not span because it is not linearly independent.

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Answer:

Please find attached the drawing of quadrilateral KLMN created with MS Whiteboard using the Ink to Shape command

(a) Two pairs of opposite sides are \(\overline {KN}\), \(\overline {LM}\) and \(\overline {KL}\), \(\overline {NM}\)

(b) Two pairs of opposite angles are ∠LKN, ∠LMN, and ∠KLM and ∠KNM

(c) Two pairs of adjacent sides are \(\overline {KN}\), \(\overline {NM}\) and \(\overline {KL}\), \(\overline {LM}\)

(d) Two pairs of adjacent angles are ∠LKN, ∠KLM and ∠LMN, ∠KNM

Step-by-step explanation:

Answer:

1). Rational

2). Irrational

3). Rational

4). Rational

5). Irrational

Step-by-step explanation:

To solve this question we should follow the rule,

"Addition of rational and an irrational number is an irrational number."

1). \(\sqrt{16}=4\) (rational number)

   \(-\frac{21}{5}\) (negative rational number)

   \(\sqrt{16}-\frac{21}{5}=4-\frac{21}{5}\)

                  \(=-\frac{1}{5}\) [rational number]

2). π → (Irrational number)

   24 → (rational number)

   π + 24 → (Irrational number)

   Since addition of a rational and an irrational number is an irrational number.

3). \(\sqrt{4}\) = 2 (rational number)

     5 (rational number)

    2 + 5 = 7 (rational number)

4). \(\sqrt{36}=6\) (rational number)

   \(\sqrt[3]{27}=3\) (rational number)

    \(\sqrt{36}+\sqrt[3]{27}=9\) (rational number)

5). \(\frac{3}{4}\) (rational number)

   \(\sqrt{27}\) → (Irrational number)    

   \(\frac{3}{4}+\sqrt{27}\) → (Irrational number)

See graph below

Plotting the graph:

The first one is in units of 2

The second one is in units of 1

The normal curve with a mean of 0 and standard deviation of 1 is called (D)  the z-value.

Therefore, the normal curve with a mean of 0 and standard deviation of 1 is called (D)  the z-value.

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Yes, a logarithmic function is the inverse of an exponential function.

An exponential function is of the form f(x) = aˣ where 'a' is the base and 'x' is the exponent. The exponential function represents exponential growth or decay.

A logarithmic function is an exponential function's inverse. A logarithmic function is of the form g(x) = logₐ(x), where 'a' is the base and 'x' is the argument. The logarithmic function represents the power to which the base 'a' must be raised to obtain the value 'x'.

When an exponential function and its inverse logarithmic function are composed together, they "cancel out" each other, returning the original input. Similarly, when a logarithmic function and its inverse exponential function are composed together, they also "cancel out" each other, returning the original input.

Therefore, an exponential function and its inverse logarithmic function are mathematically related as inverse functions.

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To answer these questions, we will use the given regression equation:

To find the actual satisfaction when the clothing cost is $50, we simply substitute 50 for Cost in the regression equation:

Satisfaction = 0.0444(50) + 4.6694

Satisfaction = 6.7213

Therefore, the actual satisfaction when the clothing cost is $50 is 6.7213 (Option D).

When clothing cost is $50, what is the predicted satisfaction?

To find the predicted satisfaction when the clothing cost is $50, we use the same regression equation:

Satisfaction = 0.0444(50) + 4.6694

Satisfaction = 6.7213

Therefore, the predicted satisfaction when the clothing cost is $50 is 6.7213 (Option D).

If the clothing cost is $50, is the residual positive, negative, or neither?

To find the residual when the clothing cost is $50, we subtract the predicted satisfaction from the actual satisfaction:

Residual = Actual satisfaction - Predicted satisfaction

Residual = 6.7213 - 6.7213

Residual = 0

Since the residual is 0, we can say that it is neither positive nor negative (Option C).

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Answer:

Triangle 3: 3, 4 ,5

Step-by-step explanation:

Well, you can easily tell by 3, 4, 5 being a Pythagorean triple.

But you have to use the Pythagorean Theorem to solve this.

So you get the side lengths of the two shortest sides, and you add the squared versions of them together.

So: 3^2+4^2 and if that equals the biggest side:5^2 then it's a right triangle.

The total fixed costs for the event amount to £2,800, which includes the security costs and the cost of the main band. Fixed costs are expenses that do not change with the number of attendees or sales.

To calculate the total fixed costs for the event, we need to identify the costs that do not change with the number of attendees. Based on the given information, the fixed costs include the security costs and the cost of the main band. Let's break it down:

Security costs: The security costs of £300 are fixed and do not depend on the number of attendees. This means the cost remains the same regardless of how many tickets are sold.

Cost of the main band: The cost of the main band is £2,500. Similar to the security costs, this cost is fixed and does not vary based on the number of attendees.

Therefore, the total fixed costs for the event would be the sum of the security costs and the cost of the main band:

Total Fixed Costs = Security Costs + Cost of Main Band

Total Fixed Costs = £300 + £2,500

Total Fixed Costs = £2,800

However, it's important to note that the cost of the supporting band, ticket prices, and the cost of the water bottles are not fixed costs. The cost of the supporting band and the cost of the water bottles are variable costs as they depend on the number of attendees. The ticket prices represent revenue, not costs.

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Based on the number of members and the ratio in which they chose the types of film, the number who chose Action in the second week more than the first week is 6 people.

Assuming that the number of members is 99 members, the number who chose Action on the second week were:

= (7 / (5 + 7 + 6)) x 99

= 39 people

The number who chose Action in the first week:

= (5 / (2 + 5 + 8)) x 99

= 33

The difference is:

= 39 - 33

= 6 people

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Answer and Step-by-step explanation:

To find the sequence, we must plug in values for n and solve, starting with 0.

f(0) = ⁻13 - 2(0) = ⁻13

f(1) = ⁻13 - 2(1) = ⁻13 - 2 = ⁻15

f(1) = ⁻13 - 2(2) = ⁻13 - 4 = ⁻17

f(1) = ⁻13 - 2(3) = ⁻13 - 6 = ⁻19

When seeing this, we can see that the answer to the questions is A.

#teamtrees #PAW (Plant And Water)

The two inequalities that define the shaded region in the diagram are:

y ≥ 4 and y < x

For the solid vertical line, the slope (m) is 0. The inequality sign we would use would be "≥"  because the shaded region is to the left and the boundary line is solid.

The y-intercept is at 4, therefore, substitute m = 0 and b = 4 into y ≥ mx + b:

y ≥ 0(x) + 4

y ≥ 4

For the dashed line:

m = change in y / change in x = 1/1 = 1

b = 0

the inequality sign to use is: "<"

Substitute m = 1 and b = 0 into y < mx + b:

y < 1(x) + 0

y < x

Thus, the two inequalities are:

y ≥ 4 and y < x

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The ratio of false positives to true positives is 8 over 54.

According to the Question

Results of a strep throat test performed on a sample of 400 ill people are displayed in the table's data. People who have the flu and those who don't are separated into two categories. The patients are then separated into groups based on whether they tested positive or negative for strep throat within each of these categories.

We must first define what a true positive and a false positive are in order to calculate the ratio of false positives to true positives. A patient who tests positive for strep throat but does not actually have the illness is said to have a false positive. The 8% of patients in this instance who tested positive for strep throat but did not have the flu would fall under that category. A patient who tests positive for strep throat and truly has the illness is said to have a true positive. That would be the 54% of patients who tested positive for both the flu and strep throat in this instance.

We divide the percentage of false positives (8%) by the percentage of true positives (54%), which gives us the ratio of false positives to true positives.

As a result, the ratio becomes 8% / 54%, or 8/54.

It's critical to remember that this ratio is dependent on the sample and test performed and may not be the same for different populations or testing methodologies.

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The number of positive and negative real roots of the function

x³ - x² - x - 5 are 1 and 2 respectively.

What is Descartes' Rule?

Descartes' rule of sign is used to determine the number of real zeros of a polynomial function. It tells us that the number of positive real zeros in a polynomial function f(x) is the same or less than by an even numbers as the number of changes in the sign of the coefficients.

Number of positive real roots of f(x) ≤ Number of sign changes f(x)

Number of negative roots of f(x) ≤ Number of sign changes of f(-x)

According to the given questions:

The given polynomial function f(x) = x³ - x² - x - 5

We can observe the number of sign changes in the coefficients

The sign changes only once

hence there is one positive real root

Now, f(-x) = -x³ + x² - x + 5

Clearly sign changes 2 times evenly

Therefore the function has 2 negative real roots

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Answer:

60 ft

Step-by-step explanation:

a² + b² = c²

20² + 15² = c²

c = √625

c = 25

total distance = 20 ft + 15 ft + 25 ft = 60 ft

Answer:

The ans is 0.8

Step-by-step explanation:

80% = 0.8 in decimal form.

Percent means 'per 100'. So, 80% means 80 per 100 or simply 80/100.

If you divide 80 by 100, you'll get 0.8 (a decimal number). Read more below on this webpage.

As you can see, to convert from percent to decimal just divide the percent value (80) by 100, and remove the "%" sign.

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Answer:

The change in elevation of the seagull is -16 ft

Step-by-step explanation:

Displacement

The displacement, unlike distance, considers the direction of the lengths occurring in the systems.

To solve the problem, we need to set a zero-level reference. Let's assume the sea level as zero height, any position above this reference as positive, and any position below this reference as negative.

The seagull is flying at a height of 10 ft above the ocean. Thus, its position is positive +10 feet.

The seagull then dives into the water to catch a fish at a depth of 6 feet. This position is negative: -6 ft.

The change in elevation is found by subtracting the final elevation and the initial elevation:

change = -6 ft - 10 ft = -16 ft

The change in elevation of the seagull is -16 ft

Answer:

$6.25

Step-by-step explanation:

divide the weight by price

Answer:

x=5/16

Step-by-step explanation:

3-8x=8x/5

(3-8x)5=8x

15-40x=8x

15=8x+40x

15=48x

x=15/48

x=5/16 ans.

Answer: No, the triangle sum theorem is not true for a sphere surface.

Explanation:

Consider 3 cities A,B,C at the following locations

The placement of C is important because this then allows angle ABC to be 90 degrees. Angles BAC and BCA are also 90 degrees each because B is directly north of both A and C (all northerly roads lead to the north pole at point B). This bizarre triangle has all three angles of 90 degrees. The angles here sum to 90+90+90 = 270 degrees.

No, the triangle sum theorem is not true on the surface sphere.

The triangle sum theorem states that, the sum of the three interior angles of any triangle is always 180°.

Given that, is the triangle sum theorem true on the surface sphere or not, so in relation to Euclid's geometry,

A statement that is equivalent to the parallel postulate is that there exists a triangle whose angles add up to 180°. Since spherical geometry violates the parallel postulate, there exists no such triangle on the surface of a sphere. The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere's surface that is enclosed by the triangle. For any positive value of f, this exceeds 180°.

Hence, there exists no such triangle on the surface of a sphere.

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The expression for the number of bacteria after t hours is N(t) = 50e\(^(0.4427t)\) , rounded to four decimal places.

Let N(t) be the number of bacteria after t hours.

Since the culture grows at a rate proportional to its size, we can write:

dN/dt = kN

where k is the proportionality constant.

This is a separable differential equation, which we can solve by separating the variables and integrating:

dN/N = k dt

ln(N) = kt + C

where C is the constant of integration.

To find the value of C, we use the initial condition that the culture initially contains 50 cells:

ln(50) = k(0) + C

C = ln(50)

Substituting C into the previous equation, we get:

ln(N) = kt + ln(50)

Taking the exponential of both sides, we obtain:

N = e\(^(kt + ln(50)) = 50e^(kt)\)

Now we need to find the value of k. We know that after 1.5 hours, the population has increased to 825:

N(1.5) = 825

Substituting this into the previous equation, we get:

825 = 50\(e^(1.5k)\)

Taking the natural logarithm of both sides, we obtain:

ln(825/50) = 1.5k

k = ln(825/50) / 1.5

k ≈ 0.4427

Finally, substituting this value of k into the expression we obtained for N(t), we get:

N(t) = 50e\(^(0.4427t)\)

Therefore, the expression for the number of bacteria after t hours is N(t) = \(50e^(0.4427t)\), rounded to four decimal places.

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we can continue solving the equation correctly and find the accurate value for x. identify where Chelsea made a mistake, let's analyze the equation and her solution step by step:

Given equation: 4x - 5 = 23(x - 3)

Chelsea's solution:
Step 1: Distribute the 23 to the terms inside the parentheses:
4x - 5 = 23x - 69

Step 2: Simplify the equation by subtracting 23x from both sides:
4x - 23x - 5 = -69

Step 3: Combine like terms:
-19x - 5 = -69

Step 4: Add 5 to both sides to isolate the variable:
-19x = -64

Step 5: Divide both sides by -19 to solve for x:
x = -64 / -19
x ≈ 3.3684

Chelsea's mistake occurred in step 4. Instead of adding 5 to both sides, she subtracted it. The correct equation should be:

-19x + 5 = -69

By making this correction, we can continue solving the equation correctly and find the accurate value for x.

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Answer:

The negative sign in the function will make it a downward-opening parabola, and its vertex will be its highest point.

Answer:

It reflects the graph across x-axis

Step-by-step explanation:

It's a vertical reflection.

Answer:

D. y= - 1/2x +9

Explanation:

In the graph, a line of best fit is drawn as shown below:

Using the points (8,5) and (6,6)

The y-intercept of the line = 9.

Therefore, the equation of the line of best fit for the set of data points is:

Answer:

The side length is 100, and the perimeter is 400

Step-by-step explanation:

Square-4 sides so side*4

100ft^2-Just 100*100, so the sides are 100 (This probably doesn't make sense)

To find c, cdf and P(. 1 ≤ X <. 5), the calculation is given.

Suppose that X has the density function f (x) = cx² for 0 ≤ x ≤ 1 and f (x) = 0 otherwise.
a. Find c.
To find c, we need to use the fact that the integral of the density function over the entire range of x should equal 1. That is,
∫0¹ f(x) dx = 1
Substituting the given density function, we get
∫0¹cx² dx = 1
Integrating and simplifying, we get
c(1/3) = 1
Solving for c, we get
c = 3
So, the value of c is 3.
b. Find the cdf.
The cdf is the integral of the density function from the lower limit of x to a given value of x. That is,
F(x) = ∫₀ˣ f(t) dt
Substituting the given density function and simplifying, we get
F(x) = ∫₀ˣ 3t²dt
Integrating and simplifying, we get
F(x) = x³
So the cdf is F(x) = x³
c. What is P(.1 ≤ X < .5)?
To find this probability, we need to find the difference between the cdf at the upper limit and the cdf at the lower limit. That is,
P(.1 ≤ X < .5) = F(.5) - F(.1)
Substituting the cdf that we found earlier, we get
P(.1 ≤ X < .5) = (0.5)³ - (0.1)³
Simplifying, we get
P(.1 ≤ X < .5) = .125 - .001
P(.1 ≤ X < .5) = 0.124
So the probability that X is between .1 and .5 is .124.

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