Review the table of values showing the mass of a radioactive isotope over time.

Which statement best describes the explanatory and response variables in the regression model?

In the logarithmic regression model, the explanatory variable is time and the response variable is the remaining mass.
In the logarithmic regression model, the explanatory variable is the remaining mass and the response variable is time.
In the exponential regression model, the explanatory variable is time and the response variable is the remaining mass.
In the exponential regression model, the explanatory variable is the remaining mass and the response variable is time.

We add [tex]-3x^3 + 5x^2 +1[/tex] in the polynomial [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex]. So the option 4 is correct.

In the given question we have to find which polynomial should be added to [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex].

A polynomial is a mathematical equation made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division operations.

Let we add the polynomial P to get the polynomial [tex]3x^2 +4[/tex].

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

Subtract the equation [tex]3x^3 - 2x^2 + 3[/tex] on both side, we get

P = [tex]3x^2 +4[/tex] - ([tex]3x^3 - 2x^2 + 3[/tex])

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

Now simplifying the expression

P = [tex]-3x^3 + 5x^2 +1[/tex]

So we add [tex]-3x^3 + 5x^2 +1[/tex] in the polynomial [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex]. So the option 4 is correct.

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Answer:

yes

Step-by-step explanation:

The positive integers are the numbers 1, 2, 3, ...

The inequalities to represent all of the constraints in Eric's problems using x for the number of adults and y for the number of children are as follows:

An inequality is a statement that compares two expressions using one of the following symbols: <, >, <=, >=, or ≠. The expressions being compared can be numbers, variables, or a combination of both.

The result of an inequality is either true or false. For example, the inequality 2x + 3y < 6 represents a set of ordered pairs (x,y) that satisfy the inequality. It describes all the points on a coordinate plane that fall under the solution set of the inequality.

From the inequalities above,

x + y <= 20 (maximum number of scuba divers) means that since the Lois Ann can only accommodate 20 scuba drivers, whether adults or children, their addition could be less than but not above 20

2x + y <= 30 (maximum number of tanks) means the capacity of Lois Ann is 30 tanks and the number of children is 10, and adult is 20, it implies that either all adults and all children or some adults participated twice (2x) plus children, it is their figure can be less than or equals to 30

20x + 10y <= 220 (maximum weight for scuba divers) implies that their entire weight whether adult or children cannot be more than 220

x, y >= 0 (non-negative number of adults and children) implies that no onee is undetermined of his placement as to whether such is adult or children.

Therefore, the correct answer is as given above

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The standard deviation for this sample data set is 1.93.

What is deviation ?

Deviation refers to the difference between an individual value or observation and the average or mean value of a set of data. It can also refer to the extent to which a variable or set of data deviates from a standard or expected value.

To calculate the standard deviation for a sample data set, we first need to find the mean (average) of the data. In this case, the mean of the data set {5, 7, 6, 9, 6, 4, 4, 6, 5, 2, 5} is 5.45.

Once we have the mean, we can calculate the variance by taking the average of the squared differences between each data point and the mean. The variance is given by:

(1/n) * Σ(x_i - mean)^2

where n is the number of data points and x_i is the i-th data point.

The variance for this data set is 3.70.

Finally, we take the square root of the variance to get the standard deviation.

So, the standard deviation for this sample data set is 1.93.

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The correct statements are given below.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: The map of various places.

1)school to gas station-70.71 yards

2)Museum to vet's office-9.94 yards

3) Vet's office to hospital-29.15 yards

4)Museum to bakery-39.68 yards

5) Bakery to house-49.24 yards

6)School to fire station-84.85 yards

Hence, These are the correct answers.

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a) The rate of change for swimmer A is 35.5.

b) the rate of change for swimmer B is 31.5.

c) Simmer A is swimming at faster rate than swimmer B.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

a) The rate of change for swimmer A

= (177.5- 71) / (5-2)

= 106.5/3

= 35.5

b) the rate of change for swimmer B

= (126- 94.5) / (4-3)

= 31.5

c) Simmer A is swimming at faster rate than swimmer B.

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As per the given data, the median number of jumps that the student made before missing is 33.5.

The term Median in math is defined as the middle value or the average of the two center values of a data set.

Here we have given that the high school gym class was jumping rope. They wanted to know how many jumps each student could make before they missed.

Here the results are listed as follows:

=> 2, 5, 6, 7, 9, 11, 12, 14, 14, 15, 17, 19, 21, 22, 23, 24, 27, 32, 35, 39, 39, 44, 47, 53, 60, 61, 82, 85, 88, 90, 93, 96, 101, 103, 114, 125

Here we need to find the center values that is written as,

=> 32, 35

Now, we have to find the average of the two center values is written as,

=> (32+35)/2 = 33.5

Then the median number of jumps is 33.5.

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List pairs of corresponding parts of congruent triangles by determining congruent sides, angles, and vertices from the triangle congruence statement.

What is congruent triangles ?

Congruent triangles are triangles that have the same size and shape. They can be matched up exactly, side-by-side, with no gaps or overlaps.

To list the six pairs of corresponding parts of congruent triangles using the triangle congruence statement, we can use the following steps ,

Begin by stating that the two triangles are congruent, using the triangle congruence statement such as "Triangles ABC and DEF are congruent by ASA, SAS, or SSS."

From the statement, we can determine the pairs of corresponding sides by noting which sides are congruent. For example, if the statement is "Triangles ABC and DEF are congruent by ASA," we know that angle A in triangle ABC is congruent to angle D in triangle DEF, angle B in triangle ABC is congruent to angle E in triangle DEF and side AC in triangle ABC is congruent to side DE in triangle DEF

Next, we can determine the pairs of corresponding angles by noting which angles are congruent. For example, if the statement is "Triangles ABC and DEF are congruent by SAS," we know that side AB in triangle ABC is congruent to side DE in triangle DEF, side BC in triangle ABC is congruent to side EF in triangle DEF, and angle A in triangle ABC is congruent to angle D in triangle DEF.

List pairs of corresponding parts of congruent triangles by determining congruent sides, angles, and vertices from the triangle congruence statement.

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The first equation can be multiplied by -5 to reverse the sign on the x-coefficient: -10x + 30y = 50.

The second equation can be multiplied by -2 to reverse the sign on the y-coefficient: 4x - 4y = -80. To solve these equations, we can add them together, which will eliminate the y-variable and leave us with the x-variable. The equation that results is 6x = -30, which can be solved by dividing both sides by 6 to get x = -5. We can then substitute x = -5 into either of the original equations to find the value of y. For example, when we substitute x = -5 into the first equation, we get -10(-5) + 30y = 50, which simplifies to 50 + 30y = 50, and then 30y = 0, so y = 0. Therefore, the solution to the system is x = -5 and y = 0.

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Answer:

(1, 2)

Step-by-step explanation:

Looking at the graph, you can find the point of intersection. The point of intersection is over 1 on the x-axis, and next to 2 on the y-axis. So, the coordinate of the point of intersection is (1, 2).

Hope this helped!

Please give me brainliest if possible!

Using the formula of probability without replacement, the probability of selecting a heart first is 13 / 52 and a diamond second is 13 / 51

Probability without replacement refers to the likelihood of a specific event occurring when items are removed from a set or collection as they are selected. It differs from probability with replacement, where the items are replaced after each selection and the set remains unchanged.

To calculate probability without replacement, we use the formula:

P(Event) = Number of favorable outcomes / Number of possible outcomes

Where the number of possible outcomes is the total number of items in the set, and the number of favorable outcomes is the number of items that satisfy the conditions of the event.

In the first event;

P(heart) = 13 / 52

In the second event, the first card is not replaced and so, the number of possible outcomes is reduced by 1

p(diamond) = 13 / 51

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Based on the information provided and the discount, Nick will pay a total of $36 for the sweater.

The discount is defined by equation 0.75 x d (regular price) = final price. This means that to find the final price Nick will pay for any product it is required to multiply the regular price by 0.75.

This also means, Nick will pay 75% of the real price, and therefore the store is offering a 35% discount (100 - 75 = 35). This principle can be applied to find the price of the sweater.

Based on the previous information, let's calculate how much is the sweater:

$40 x 0.75 = $36

Based on this, Nick will pay $36 for the sweater.

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Answer:

60

Step-by-step explanation:

there are three sides to a triangle so 20x3 is 60 which is the perimeter

If Researcher like to know if data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12% , then we can say that , (a) Yes, the conditions of inference are met .

The size of the random sample (n) = 100 ;

the number of persons that work on more than one job is (x) = 18 ;

the difference is 12% that means (p) = 0.12 ,

So , [tex]q=1-p = 1-0.12 = 0.88[/tex] ;

To check for the inference ,

we calculate , [tex]n\times p = 100\times 0.12 = 12 > 5[/tex] and

[tex]n\times q = 100\times 0.88 = 88 > 5[/tex] ,

Both the conditions are true .

Therefore , we can say that the Conditions for the inference are met .

The given question is incomplete , the complete question is

According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. Are the conditions for inference met ?

(a) Yes, the conditions for inference are met.

(b) No, the 10% condition is not met.

(c) No, the Large Counts Condition is not met.

(d) No, the randomness condition is not met.

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Answer: -1 and 3

Step-by-step explanation:

The zeros of a function are where the graph of the function intersects the [tex]x[/tex]-axis.

Answer: -1 and 3

Step-by-step explanation:

        Finding the zeros of the function is the same as solving for the function, or what values of x make y equal 0. In this case, it is the x-intercepts, as shown by the graph. These values are  -1 and 3, see attached.

The rate of change of the hypotenuse is 9.5 inches per second.

The rate of change of the hypotenuse of a right triangle can be calculated using the Pythagorean theorem. The theorem states that for a right triangle with sides of length a, b, and c (where c is the hypotenuse), a2 + b2 = c2.

In this case, we know that the two legs are 3 inches and 4 inches, and that the short leg is increasing by 7 in/sec and the long leg is growing at 9 in/sec.

Using the Pythagorean theorem, we can calculate the rate of change of the hypotenuse. We can set up the equation as follows: c2 = 32 + 42, where c is the hypotenuse. Solving for c, we get: c = √(32 + 42).

To calculate the rate of change of the hypotenuse, we need to take the derivative of the equation. Taking the derivative of the equation, we get: c' = (7/2) * (3/c) + (9/2) * (4/c).

Plugging in our values, we get: c' = (7/2) * (3/5) + (9/2) * (4/5). Simplifying, we get: c' = 9.5 in/sec.

Therefore, the rate of change of the hypotenuse is 9.5 inches per second.

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Answer:

Step-by-step explanation:

12. all angles are the same size.

all ik sry

The advantage does a Mercedes g class 6x6 squared have compared to the 4x4 squared for off road driving is explained below.

The term class in math is used to define a grouping of values by which data is binned for computation of a frequency distribution

Here we have to find the advantage does a Mercedes g class 6x6 squared have compared to the 4x4 squared for off road driving

Where we all know that in a 4x4 Transfer Case there is a 50:50 split between Front and Rear axles on the other had in a 6x6 we have the Transfer Case splits the torque 33:66 between Front & Rear Axles.

Then the next one is known as intricate rear Suspension such as Short Radius Arms and coil Springs or elliptical leaf springs/Inverted Leaf Springs.

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Answer:

Step-by-step explanation:

30-12/3=d

d=drinks he bought

$30-$12=$18

$18/$3=6

he got 6 drinks

The given statement is untrue about Pat. Therefore, it is invalid.

If each of the premises must be true in order for the conclusion to be true, the argument can only be validated if it does so. The term "valid" refers to a statement that is true, whereas the term "invalid" refers to a statement that is untrue.

The given situation is an invalid one. Because it's still feasible for Pat to be a woman, even if the premise is accurate. She could be a single woman. Because of this, the premise cannot be used to prove that she is a woman.

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The probability of being dealt a fourth diamond after 3 of the 4 cards dealt are diamonds is 10/ 49.

Out of the four cards that you have been dealt, 3 of them are diamonds, so there is only one card left.

The deck of cards has 13 diamonds and 39 non-diamonds cards, so the probability of drawing a diamond from the remaining deck after taking 3 cards is

= (13 - 3)/ (52 - 3)

= 10/ 49

Since you want a fourth diamond, the probability of being dealt a fourth diamond is 10/49.

It's important to notice that this problem is a conditional probability problem, where the probability of an event happening is dependent on the outcome of another event. In this case, the event of getting a fourth diamond depends on the fact that you already have 3 diamonds in your hand.

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Answer:

Large numbers require a large number of zeros when writing in scientific notation.

To express such quantities in a simpler and more efficient manner, mathematicians and scientists use scientific notation.

Step-by-step explanation:

Answer: Actually kinda ez not gonna lie. y = 11.547, x = 23.094

Step-by-step explanation: we know that y * square root of 3 = 20. 20/ root 3 is 11.547. Hypotenuse is 2 times y. This gives us x = 23.09

The object hits the ground after 17.5 seconds.

f(x) = ax2 + bx + c, where a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they always have the same fundamental "U" form.

The height of an object modeled by the function:

h(t) = −16t^2 + 4900

The object hits the ground when h(t) = 0

The equation becomes:

0 = −16t^2 + 4900

-16t² = -4900

t² = 4900/16

t² = 306.25

t = √306.25

t = 17.5 secs

Thus, the object hits the ground after 17.5 seconds.

Complete question: An object is 4900 ft above the ground. The object falls, and its height is given by the quadratic function: h(t) = −16t 2 + 4900. The height of the object above the ground is in feet and the time, t, is in seconds. Determine when the object hits the ground.

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Answer:

  neither

Step-by-step explanation:

You want to know if the graphed function is even or odd. It appears to be a cubic with a y-intercept of about 40.

Even functions are symmetrical about the y-axis. A function is even if ...

  f(x) = f(-x)

Even polynomial functions have terms that are all even powers of the variable.

Odd functions are symmetrical about the origin. A function is odd if ...

  f(x) = -f(-x)

Odd polynomial functions have terms that are all odd powers of the variable.

The graphed polynomial function has a non-zero added constant (the y-intercept value), so has both even and odd terms. It is neither even nor odd.

The graph is neither symmetrical about the y-axis, nor symmetrical about the origin.

2 to the power of 4 is 16.

2^4 = (2 x 2 x 2 x 2) = 16

2 to the power of 4 is 16.

The answer to 2 to the power of 4 is 16. This means that 2 is multiplied by itself 4 times. To calculate this, it is easiest to start with the base number, 2. Then, multiply 2 by itself 3 more times. The result is 2 multiplied by 2 multiplied by 2 multiplied by 2, or 2 x 2 x 2 x 2, which equals 16. Therefore, 2 to the power of 4 is equal to 16.

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The area to determine 142.5  material she will need to create the kite.

Given that

A kite with two top triangles with height = 5 inches

a base = 7.5 inches

The bottom two triangles share the base but have a height = 14 inches

area of sum of all triangle's area

area = b×h /2

A1 = 7.5 × 5 /2

   = 18.75

the other top triangle has the same area so A1+A2 = 18.75 × 2 = 37.5

A3 = 7.5 ×14/2

     = 52.5

the other top triangle has the same area so A3+A4 = 52.5 × 2 = 105

The area of kite A1 + A2 +A3 +A4 = 37.5 +105 = 142.5

The area to determine 142.5  material she will need to create the kite.

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The expression becomes x-6 > 9 from the given condition The sum of a number and negative six greater than 9.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given,

To find the sum of a number and negative six , greater than 9 .

let the given number be x .

so,

the expression becomes ,

x - 6 > 9

LHS = x-6

as in the question its given the sum of number and negative of six

So whereas in RHS = 9

As it is given greater than 9 .

Hence, the expression becomes x-6 > 9 from the given condition.

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Answer:

( 3a + b ) ( 2a − b )

Step-by-step explanation:

For a polynomial of the form ax^2 + bx + c, rewrite the middle term as a sum of two terms whose product is a • c = 6 • − 1 = − 6 and whose sum is b = − 1.

1) Reorder terms. = 6a^2 − b^2 − ab

2) Reorder −b^2 and − ab. = 6a^2 − ab − b^2

3) Factor −1 out of −ab. = 6a^2 − ( ab ) − b^2

4) Rewrite −1 as 2 plus −3. = 6a^2 + ( 2 − 3 ) ( ab ) − b^2

5) Apply the distributive property. = 6a^2 + 2 ( ab ) − 3 ( ab ) − b^2

6) Remove unnecessary parentheses. = 6a^2 + 2ab − 3 ( ab ) − b^2

7) Remove unnecessary parentheses. = 6a^2 + 2ab − 3ab − b^2

Factor out the greatest common factor from each group.
1) Group the first two terms and the last two terms.
= ( 6a^2 + 2ab ) − 3ab − b^2

2) Factor out the greatest common factor (GCF) from each group.
= 2a ( 3a + b ) − b ( 3a + b )

3) Factor the polynomial by factoring out the greatest common factor,
3a + b .

= ( 3a + b ) ( 2a − b )