Fill in the blank:

_?__(x+3)=7x+21

Answer:

-6

Step-by-step explanation:

The number line is created by skip counting of 2.

So, -2 ,  then -4 and then -6.

So,  blue dotted point is (-6)

Answer:

4 2/3

Step-by-step explanation:

14 ÷ 3 = 4 2/3

3 × 4 = 12

14- 12= 2

The colony will need to triple in number after about 7.58 days.

Since the number of bacteria doubles every 5 days, we can write the relationship between the number of bacteria and time as an exponential function:

N(t) = N0 x 2^(t/5)

where N0 is the initial number of bacteria and t is the time in days.

To find out how long it will take for the colony to triple in number, we need to solve the equation:

N(t) = 3N0

Substituting the expression for N(t) from above, we get:

N0 x 2^(t/5) = 3N0

Dividing both sides by N0, we get:

2^(t/5) = 3

Taking the logarithm of both sides (with base 2) gives:

t/5 = log2(3)

Multiplying both sides by 5, we get:

t = 5 x log2(3)

Using a calculator or a computer program to evaluate the logarithm, we get:

t ≈ 7.58

Therefore, the colony will need to triple in number after about 7.58 days.

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the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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To create a scale drawing of the park, we can use the given scale of 1.5 in : 100 ft.

First, we need to determine the dimensions of the scale drawing using the given lengths of the legs of the right triangle.

Let's calculate the dimensions of the park in inches:

Length of one leg in inches = (Length of one leg in feet) * (Scale factor)

Length of one leg in inches = 150 ft * (1.5 in / 100 ft) = 2.25 in

Similarly, for the other leg:

Length of the other leg in inches = 200 ft * (1.5 in / 100 ft) = 3 in

Now, using these dimensions, we can create a scale drawing of the park:

1. Draw a right triangle shape on a piece of paper or a drawing software.

2. Label one leg with a length of 2.25 inches and the other leg with a length of 3 inches.

3. Ensure that the right angle between the legs is correctly represented.

4. Optionally, add labels or markings to indicate the measurements.

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Answer:

∠a = 35°  ∠b = 65°

Step-by-step explanation:

a = 35 ° ( alternate interior angles )

( the line x is parallel to line yz hence we can consider XY as a transversal)

∠b + 35° + 80° = 180 ° ( angle sum property of triangle)

∠b+ 115° = 180°

∠b= 180 - 115

∠b = 65°

If He had 33 coins and then he add up 44, the total number of coins that he has now is 77.

Answer:

In this case, the mean is $1400, and the standard deviation is $200.

So, one standard deviation of the mean is 1400+200= $1600 and 1400-200 = $1200.

Therefore, according to the empirical rule, approximately 68% of the farms will have land and building values per acre between $1200 and $1600.

To estimate the number of farms that fall within this range, we can multiply the total number of farms (74) by 0.68.

(74)*(0.68) = 50.32 or about 50 farms

So, according to the empirical rule, approximately 50 farms will have land and building values per acre between $1000 and $1800.

In the equation\(`x = sin^-1(1/u)`,\) the letter x represents the angle while the letter u represents the value of the trigonometric function.

The inverse sine function is defined as the arc or angle whose sine is equivalent to the value of the input argument.

It's also known as the arcsine function. In trigonometry, it is commonly represented as \(sin^-1\) or arcsin.

In trigonometry, the sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse of a right-angled triangle.

It is often abbreviated as sin.

The sine of an angle x is denoted by

sin(x) = Opposite side / Hypotenuse.

For any angle x, the sine function returns a value between -1 and 1.

In summary, x represents the angle in the equation \(x = sin^-1(1/u)\)while u represents the value of the trigonometric function, which is equal to 1/sin(x).

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The general form of the regression equation is y = a + bx

A regression equation is a statistical model used to identify the relationship between a dependent variable (Y) and one or more independent variables (X) in a dataset. The regression equation is used to make predictions by identifying how a change in one variable affects the other variables. The general form of the regression equation is y = a + bx, where 'y' is the dependent variable, 'x' is the independent variable, 'a' is the intercept value, and 'b' is the slope value.

Therefore, the general form of the regression equation is y= a+bx

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Out of the given options, the set of variables that is most likely to have a cause-and-effect relationship is A. The age of a teacher and the income of the teacher. A cause-and-effect relationship implies that one variable is the cause of changes in the other variable.

In this case, it is possible to argue that the age of a teacher can cause changes in their income. For example, as teachers gain more experience and seniority, they may be eligible for higher salaries. Additionally, teachers who have been in the profession for longer may have more qualifications or skills that make them more desirable to schools and therefore more likely to earn higher incomes. On the other hand, the other options do not necessarily have a clear cause- and- effect relationship. For example, while a person's weight may influence their height to some extent, it is not a direct cause-and-effect relationship. Similarly, while the make of a car may influence its mileage, it is not a direct cause-and-effect relationship. In conclusion, while it is important to consider all variables when analyzing data, it is essential to identify which variables have a direct cause-and-effect relationship. In this case, the set of variables with a cause-and-effect relationship is A. The age of a teacher and the income of the teacher. Based on the given options, the set of two variables most likely to have a cause-and-effect relationship is C. The weight of a box and the postage rate we have to pay to ship the box to California.This relationship is likely cause-and-effect because shipping companies typically charge postage rates based on the weight of the package being sent. As the weight of a box increases, the cost to ship it usually increases as well, demonstrating a direct cause-and-effect relationship between these two variables

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Looking at the graph of g(x) (the red graph), we can see that it has the same format of f(x), but it is 9 units above it (f(x) passes through (0, -6) and g(x) passes through (0, 3)).

Therefore the graph of g(x) can be created using a translation of 9 units up from the graph of f(x).

That means we can write the following expression:

So the correct option is B.

Answer:

51.33

Step-by-step explanation:

to get that, we must subtract area of segment DQE (its look like a slice of pizza) by the triangle DQE

so first, we find the area of segment DQE

Area of DQE = (58/360) * Area of whole circle

A.DQE = 58/360 * πr²

A.DQE = (58 * 3.14 * 25²)/360 = 316.34

save it then we do the second step to find the area of triangle DQE. Triangle DQE is isosceles triangle with ∠DQE = 58,

area of triangle = ½ * base * height * sin ∅

∆DEQ = ½ * DQ * EQ * sin 58°

∆DEQ = ½ * 25 * 25 * 0.848

So Area of ∆DEQ = 265.02

then finally we can find the area of segment the problem said

A.DQE - ∆DEQ = 316.34 - 265.02= 51.32 (near 51.33)

Answer:

a= 11

Step-by-step explanation:

9a+ 6°+75° =180° (straight angle, they are called supplementary angles. so sum is equal to 180°

9a +81 = 180

9a= 99

a= 11

Write an example from daily life that uses rational numbers .

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Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

To find the Taylor polynomials centered at x = 0 for the function f(x) = 16tan(x), we can use the Taylor series expansion for the tangent function and truncate it to the desired degree.

The Taylor series expansion for tangent function is:

tan(x) = x + (1/3)x^3 + (2/15)x^5 + (17/315)x^7 + ...

Using this expansion, we can find the Taylor polynomials of degree 2 and 3 centered at x = 0:

Degree 2 Taylor polynomial:

P2(x) = f(0) + f'(0)(x - 0) + (1/2!)f''(0)(x - 0)^2

= 16tan(0) + 16sec^2(0)(x - 0) + (1/2!)16sec^2(0)(x - 0)^2

= 0 + 16x + 8x^2

Degree 3 Taylor polynomial:

P3(x) = P2(x) + (1/3!)f'''(0)(x - 0)^3

= 0 + 16x + 8x^2 + (1/3!)(48sec^2(0)tan(0))(x - 0)^3

= 16x + 8x^2

Therefore, the Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

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m = 17/4

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The solution to the simultaneous equation is x = -1/2 and y = √71 / 2

What is a Linear Expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

For example, t² is a variable raised to the second power, but t is a variable raised to the first power.

x² + y² = 18 ----- 1

x + 2 = - 3x ---- 2

From equation 2

x + 2 = - 3x

x + 3x = -2

4x = -2

x = -2/4

x = -1/2

Substitute x in equation 1

(-1/2)² + y² = 18

1/4 + y² = 18

y² = 18 - 1/4

y² = (72 - 1)/4

y² = 71/4

y = √71 / 2

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A probability distribution is one that lists all of the outcomes of an experiment or a variable together with their respective probabilities. The total probability must equal 0.0424 because it includes all of the possible outcomes.

probability distribution for 5 fewer girls is

(0.001+0.006+0.022+0.061+0.122) divided by 5

is equal to 0.0424

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Answer:

Yes, the trapezoid is an isosceles trapezoid.

As the diagonals of the trapezoid KLMN are not equal in length it is not an isosceles trapezoid.

The area of a trapezoid is the average length of the parallel sides times the height.

We know isosceles trapezoids have equal legs length and diagonals are also of the same length.

Given a trapezoid KLMN with verticies  K(1, 3), L(3, 1), M(3, 0), and N(1, −2).

∴ KM and LN are two diagonals of the trapezoid and if KM = LN then it is an isosceles trapezoid.

To determine if KM and LN are equal or not we'll simply use the distance formula which is,

D = \(\sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}\).

∴ KM = \(\sqrt{ (3 -1)^2 + (0 - 1)^2}\).

KM = \(\sqrt{ (2)^2 + (-1)^2}\).

KM = \(\sqrt{5}\).

And LN = \(\sqrt{ (1 -3)^2 + (-2 - 1)^2}\).

LN = \(\sqrt{ (-2)^2 + (-3)^2}\).

LN = \(\sqrt{ 4 + 9}\).

LN = \(\sqrt{13}\).

∴ KM ≠ LN hence diagonals are not equal.

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The given statement "the function g(x)=x3 is a linear transformation from r into r." is false. . A linear transformation must satisfy additivity and homogeneity properties, but the function g(x)=x^3 does not satisfy homogeneity, making it nonlinear.

A linear transformation from R into R is a function that satisfies two properties

Additivity T(u + v) = T(u) + T(v) for all u, v in R

Homogeneity T(cu) = cT(u) for all u in R and all scalars c.

However, the function g(x) = x^3 is not linear because it violates the second property, homogeneity. Specifically, g(cx) = (cx)^3 = c^3x^3, which is not equal to cg(x) = c*x^3, unless c = 1. Therefore, g(x) = x^3 is a nonlinear transformation from R into R.

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--The given question is incomplete, the complete question is given

" the function g(x)=x3 is a linear transformation from r into r. True or false"--

Answer:

Step-by-step explanation:

Based on the given conditions, formulate: 2500 x (1 - 8%)

Evaluate the equation/expression: 2300

get the result:2300

Answer: 2300

Answer:

6/8

Step-by-step explanation:

multiply both of them by 2 and its equal.

you get 6/8

Answer:

\( \red{\bold {7x - 9y - 39 = 0}} \)

Step-by-step explanation:

Line passes through the points

\( (3, \: - 2) =(x_1, \: y_1) \:\&\: (-6,\: - 9)= (x_2, \: y_2)\)

Equation of line in two point form is given as:

\( \frac{y-y_1}{y_1-y_2} = \frac{x-x_1}{x_1-x_2} \\\\

\frac{y-(-2)}{-2-(-9)} = \frac{x-3}{3-(-6)} \\\\

\frac{y+2}{-2+9} = \frac{x-3}{3+6} \\\\

\frac{y+2}{7} = \frac{x-3}{9} \\\\

9(y+2) = 7 (x - 3)\\\\

9y + 18 = 7x - 21\\\\

7x - 9y - 21 - 18 = 0\\\\

\huge \purple {\boxed {7x - 9y - 39 = 0}} \)

The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

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Answer:

25 miles per gallon 10 gallons is the UNIT RATE.

Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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Answer:

C: 12/45

Step-by-step explanation:

You have to divide the numerator and the denominator by the same number, and if once you divide it you get the fraction then it's the right answer. So lets take 12/45 and try it.

12/3 =4

45/3 =15

4/15

If the slope of the line segment was r units before dilation, it will still be r units after dilation.

ΔABC is dilated by a scale factor of 3 with the origin as the center of dilation to form ΔA′B′C′. This means that the new triangle, ΔA′B′C′, has side lengths that are 3 times longer than the original triangle, ΔABC.

The slope of a line segment is the ratio of the vertical change to the horizontal change between two points on the line.

Since the scale factor is 3, the horizontal and vertical distances between points A and A′, B and B′, and C and C′ are all multiplied by 3.

However, the slope remains unchanged because the ratio of vertical change to horizontal change remains constant.

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