Find the sum of the first 12 terms of the geometric series
2 + 4 + 8 +...

Mary paid $3.80 per pound and Mark paid $4.00 per pound.

19 ÷ 5 = 3.80

16 ÷ 4 = 4

Mary's unit rate is less than Mark's unit rate.

To compare the unit rate of Mary and Mark, we need to find how much each of them paid per pound of grapes.

Mary paid $19 for 5 pounds of grapes, so her unit rate can be calculated as:

The unit rate of Mary = Total cost of grapes / Total amount of grapes purchased

= $19 / 5 pounds

= $3.80 per pound

Mark paid $16 for 4 pounds of grapes, so his unit rate can be calculated as:

The unit rate of Mark = Total cost of grapes / Total amount of grapes purchased

= $16 / 4 pounds

= $4.00 per pound

Comparing the unit rate of Mary and Mark, we can see that Mary paid less per pound of grapes than Mark did.

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Answer:18

Step-by-step explanation:15 + 6 u add the 15 and the 6 for it to be 18

Answer
Since this is a right triangle, we can use the inverse cosine function to solve for the angle θ.

cos θ = Opposite side / Adjacent side

cos θ = 14 / 22

cos θ = 0.6363

θ = cos^-1 (0.6363)

θ ≈ 45.9°

The length of AB would be = 10 units and the midpoint of segment AB would be (-5, 2).

What are the distance formula and midpoint of a segment?

The distance formula is a mathematical formula that can be used to determine the distance between two points in a coordinate plane. The distance between two points (x1, y1) and (x2, y2) is given by the formula:

[tex]d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

The midpoint of a segment is a point that is exactly in the middle of a line segment. Given the endpoints of the line segment, (x1, y1) and (x2, y2) the coordinates of the midpoint, (x, y) can be calculated using the following formulas:

x = (x1 + x2) / 2

y = (y1 + y2) / 2

The given points are (-8, 6) and (-2, -2).

Given two points A(x1, y1) = (-8, 6) and B(x2, y2) = (-2, -2), we can use the distance formula to find the length of the line segment AB. The distance formula is:

[tex]d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\\\d= \sqrt{((-2) - (-8))^2 + ((-2) - (6))^2}\\\\d=\sqrt{36 + 64}\\\\d=\sqrt{100}\\\\d=10[/tex]

The length of AB would be 10.

To find the coordinates of the midpoint of AB, we can use the midpoint formula:

x = (x1 + x2) / 2

y = (y1 + y2) / 2

Plugging in the values for A and B, we get:

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

y = (6 + (-2)) / 2 = 2

The coordinates of the midpoint of AB are (-5, 2).

Hence, the length of AB would be = 10 units and the midpoint of segment AB would be (-5, 2).

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The process of logarithmic functions in real-worlds problems is given below.

And an example of an application of logarithmic function is given.

The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

We know,

logarithmic function and exponential function are inverse of each other.

So, whenever we solve the exponential function,

we use the help of logarithmic functions.

To compute the number with bigger exponents,

we use the logarithms.

Because it reduces the size of the numbers.

Let the bacteria is growing exponentially,

b = 2ⁿ.

We know that the bacteria grows every hour.

We want to find time.

Here, we will use the inverse function to the exponential function.

How long will it take them to get 1000 bacteria?

1000 = 2ⁿ

Taking log on both sides,

log(1000) = n log2

n = log(1000)/log(2)

n = 9.96

n ≈ 10 hours.

Therefore, an application of logarithmic function is given above.

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On solving the provided question, we cans ay that By unitary method, the amount to be removed = original - shortened = 3/9 - 2/9 = 1/9

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

By unitary method,

original length of pipe = 3/9 inch

shortened length of pipe = 2/9

so, the amount to be removed = original - shortened = 3/9 - 2/9 = 1/9

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The pound of cement used based on the information will be C. 2 pounds.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.

The pound of cement used will be:

Gravel = 1 2/3 × 3

= 5 pounds

Cement used will be:

= 2/5 × 5.

= 2 pounds.

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[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- \cfrac{3}{4}}(x-\stackrel{x_1}{(-4)}) \implies y +4= -\cfrac{3}{4} (x +4) \\\\\\ y+4=-\cfrac{3}{4}x-3\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-7 \end{array}}[/tex]

Answer:

y = -3/4x - 7

Step-by-step explanation:

Given: slope = m = -3/4

Plug this value into the standard slope-intercept equation of y = mx + b.

y = -3/4x + b

To find b, we want to plug in a value that we know is on this line: in this case, point (-4, -4). Plug in the x and y values into the x and y of the standard equation.

-4 = -3/4(-4) + b

To find b, multiply the slope and the input of x(-4)

-4 = 3 + b

Now, subtract 3 from both sides to isolate b.

-7 = b

Plug this into your standard equation.

y = -3/4x - 7

This is your equation.

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The required measure of the value of x is given as 2√3. Option A is correct.

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

here,
Consider the given triangle,

perpendicular = 6
base = x

Applying trigonometric operation,
tan30 = perpendicular/base
tan30 = 6/ x
x = 6/√3
x = 2√3

Thus, the required measure of the value of x is given as 2√3. Option A is correct.

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Therefore , the solution of the given problem of domain is The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,), after answering the given question.

A function's domain is the set of values that can be sent into it. This collection represents all x values in a function like f. (x). A function's range is the set of possible values that it can accept. This collection includes the values that the return statement when we enter an x value. Assume that x and y are indeed the independent and dependent variables of a function with the formula y = f(x). If a function f provides a way to generate a single value y successfully while using a value of x .

Here,

In this case, f(x)=-3x-2 x < 4

3/4x-1 x≥ 4

Domain

This range, which is the range of -3x-2 (-14,), is a subset of the range of f(x).

Therefore , the solution of the given problem is The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,), after answering the given question.

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To solve this problem, we can set up the following equation:

Torrie + John = Sonia - John

This equation represents the fact that John has the same number of dollars more than Torrie as he has less than Sonia. We can then substitute the given values for Torrie, Sonia, and John to solve for John:

430 + John = 760 - John

Combining like terms, we get:

2 * John = 330

Dividing both sides of the equation by 2, we get:

John = 165

Thus, John has $165.

Answer: line AB and RS are parallel because their lines do not interact anywhere on the model, because it is 3D. this is the only one i am sure of, you may have to ask another person to get the other two.

Answer:

A. Line AB and Line CG are parallel, C. Line CG and Line RS are perpendicular, and E. Line CG lies in plane X

Step-by-step explanation:

A. Line AB and Line CG are parallel is true because the arrows are pointing in the same directions and do intersect or cross each other.

B. Line AB and Line RS are parallel is false because although they do not intersect, they also do not go in the same direction. These are also not perpendicular lines because they do not intersect other, even though they make a right angle.

C. Line CG and Line RS are perpendicular is true because these lines intersect at exactly 90° angle (as shown by the square).

D. Line AB and Line RS must intersect is false because Line AB does not intersect Line CG (which is the line that does intersect Line RS).

E. Line CG lies in plane X is true because point C and point G are in plane X.

F. Line RS lies in plane X is false because point r and point 2 are in plane Y.

Answer:

3

Step-by-step explanation:

[tex] \sin(45) = \frac{a}{7 \sqrt{2} } [/tex]

[tex]a = 7[/tex]

[tex] \tan(30) = \frac{7}{c} [/tex]

[tex]c = 7 \sqrt{ 3} [/tex]

therefore 3 is required in the green box

Answer:

26

Step-by-step explanation:

if she is 8 years older, then is just 34-8 which is 26

Answer: 125y³

To rise a product to a power, rise each factor to that power:

(5y)³ = 5³y³ = 125y³

Answer:

1809/27=67 is your answer........

The amount that her clothes weigh more than her books would be = 57kg

The amount for the shipping cost for her school would be = 5600+25400 = $31000

Postal service is the type of service that helps.in the delivery of goods from one location to another when the goods are properly registered.

The mass of Moya's books = 70 kilograms

The mass of Moya's clothing = 127 kg

The difference between the bothe masses = 127 - 70 = 57kg

The cost per kg for books = $80 per kg

The cost per kg of clothing = $200

Therefore, the amount for the shipping cost for her school would be = (70×80) + (127 ×200)

= 5600+25400 = $31,000.

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The discriminant is calculated using the formula b squared minus 4ac.It reveals how many possible answers there are to a quadratic problem.

The section of the quadratic formula following the square root symbol, b2-4ac, is the discriminant. If there are two solutions, one solution, or no solutions, the discriminant informs us of this. There are two solutions if the discriminant is bigger than zero. The square root's input (i.e., its contents), which is the phrase b2 4ac, is known as the "discriminant" because using its value, you may "discriminate" between (i.e., be able to distinguish between) the different solution types.

here

Keeping in mind that a, b, and c are the coefficients of your quadratic in standard form,

the discriminant is calculated using the formula b squared minus 4ac.

It reveals how many possible answers there are to a quadratic problem.

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The following is the proper response to this problem's inequality. The relationship between negative one fifth and negative two thirds is higher than or equal when y is bigger than or equal to three tenths.

In mathematics, an inequality is a link between two expressions or values that is not equal. Thus, inequality arises as a result of imbalance. An inequality in mathematics describes the connection between two values that are not equal. Many simple inequalities can be eliminated by modifying both sides until just the variables are left. However, a number of things lead to inequality: On both sides, divide or add negative values. Toggle between left and right.

Given

One fifth less is -1/5.

When a negative two thirds is added to a number, the result is -2/3x. Since the value is unknown, we refer to it as x.

The following is the sign for more than or equal inequality:

The inequality is therefore: -1/5 -2/3x.

So that it will be easier for us to isolate x:

2/3x ≥ 1/5

2x ≥ 3/5

x ≥ 3/10.

Since y is more than or equal to three tenths, the right answer for the inequality is: negative one fifth is greater than or equal to negative two thirds y.

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Answer: Congruent by AAS

Step-by-step explanation:

FG and EH are congruent because they are given.

EH is perpendicular to EG because of the definition of perpendicular lines. Lines are perpendicular if they create right angles when they intersect.

FG is perpendicular to EG because of the definition of perpendicular lines. Lines are perpendicular if they create right angles when they intersect.

Angle G is congruent to Angle E because they are both right angles, and right angles are congruent.

Angle EIH and Angle FIG are congruent because of the vertical angles theorem.

Triangle EHI and Triangle GFI are congruent by the Angle-Angle-Side Theorem, or AAS.

Answer:

7/12 (seven over twelve)

Step-by-step explanation:

1/3 -1/4 =4/12- 3/12=1/12

1/2+1/12=6/12+1/12=7/12

so the answer is 7/12

hopefully this helps

We have mapped the correct equivalent expressions.

3/16 ⇒ 0.1875

0.85 ⇒ 17/20.

3/8 ⇒ 0.375.

0.425 ⇒ 17/40.

What is the equivalent expression?

An equivalent expression is a mathematical expression that has the same value as another expression but is written differently. Equivalent expressions can be obtained by using the properties of arithmetic such as the commutative, associative, and distributive laws.

3/16 can be described as 0.1875

0.85 can be described as 17/20.

3/8 can be described as 0.375.

0.425 can be described as 17/40.

Hence, we have mapped the correct equivalent expressions.

3/16 ⇒ 0.1875

0.85 ⇒ 17/20.

3/8 ⇒ 0.375.

0.425 ⇒ 17/40.

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The slope-intercept form of the equations presented on the graph are;

y = 4

y = 3

The slope-intercept form of the equation of a line is; y = m·x + c, where;

m = The slope of the graph

c = The y-intercept of the graph

The equation of the lines in the graphs (blue line, and red line) are found as follows;

The slope of the blue line is found using the points on the graph as follows;

The coordinates of points on the blue line graph are; (0, 4), (2, 4), (4, 4)

The slope is therefore; m = (4 - 4)/(4 - 2) = 0

The y-intercept, obtained from the graph is; c = 4

The value of the slope, m = 0, indicates that the graph is an horizontal line with an equation y = c

c = 4

The equation of the blue line graph in slope-intercept form is therefore;

The coordinates of points on the red line graph are; (0, 3), (2, 3), (4, 3)

The slope of the red line graph is therefore;

m = (3 - 3)/(4 - 2) = 0

The y-intercept of the red line graph is; c = 3

The value of the slope, m = 0, and the y-intercept, c = 3, indicates that the equation of the red line graph is therefore;

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Answer:

- 420° =  -7/3 π ≈ - 2.333 π

Step-by-step explanation:

- 420° =  -7/3 π ≈ - 2.333 π

Coterminal angle in [0, 360°) range:

300°, located in the fourth quadrant.

Positive coterminal angles: 300°, 660°, 1020°, 1380°, 1740°...

Negative coterminal angles: -60°, -420°, -780°, -1140°

I hope this helps!1!!

-420° = -360° - 80° = -80°

-80° = 360° - 80° = 280°

Co terminal angle = 280° and -80°

[tex]m-16[/tex] when m is 30

Substitute for m with given value:

[tex](30)-16[/tex]

[tex]=\fbox{14}[/tex]

Answer:

Step-by-step explanation:

a.we can get the equation is m-16 = 30-16=10+20-10-6=10-6+20-10=4+10=14

answer is 14