1. Select all equations for which -3 is a solution.
A. x² = 9
B. x² = -9
C. x³ = 27
D. x³ = -27
E. -x² = 9
F. (-x)² = 9

Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

For more questions on isolate

https://brainly.com/question/11389214

#SPJ8

Answer:

125

thats the answer nothing more is needed to say. plus 25/.2= 25x10/5= 125

Answer:

125

Step-by-step explanation:

25/0.2 = 25 ÷ 2/10 = 25 × 10/2 = 25 × 5 = 125

Hello!

distance = speed * time

distance

= 40km/h * 1.5h

= 60km

She travel 60km.

Answer:

60 km

Step-by-step explanation:

In order to find the distance that Anna has travelled, we can derive the formula from the speed formula which is:

[tex]\displaystyle{v=\dfrac{s}{t}}[/tex]

where v is speed, s is distance and t is time. So by solving for distance (s), we have:

[tex]\displaystyle{s=vt}[/tex]

Apply the distance travelled formula, we know that speed (v) = 40 km/h and time (t) = 1.5 hours. Thus,

[tex]\displaystyle{s=40 \ \text{km/h} \cdot 1.5 \text{h}}\\\\\displaystyle{s=60\ \text{km}}[/tex]

Therefore, Anna travels 60 kilometers.

The word sentence should be written as an inequality as follows;

In Mathematics and Geometry, an inequality is a relation that compares two (2) or more numerical data, number, and variables in an algebraic equation based on any of the inequality symbols;

Generally speaking, "at most" simply means less than or equal to (≤), "at least" simply means greater than or equal to (≥), "exceed" simply refers to greater than (>).

Read more on inequality here: https://brainly.com/question/30665021

#SPJ1

The line of best fit for the given data is represented by equation C, which is y= 0.95x + 12.

To find the line of best fit, the data points are plotted on a graph, and the line is drawn so that the distance between each data point and the line is minimized.

This is done using various statistical methods, such as the least squares method, to determine the equation of the line that best represents the data.
The equation of the line of best fit can then be used to make predictions or estimations about future values of the dependent variable based on the independent variable.

In this case, the line of best fit represents the relationship between x and y, and can be used to predict the value of y for a given value of x.
In conclusion, the line of best fit for the data is represented by equation C, y= 0.95x + 12.

This line provides the closest approximation to the data points and can be used to make predictions about future values of the dependent variable based on the independent variable.

for such more questions on line

https://brainly.com/question/24644930

#SPJ8

The values of the compound probabilities are

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

The cubes

Where we have

Blue = 2

Green = 3

Red = 4

Yellow = 6

Givn the the cubes are not replaced after they are chosen, we have

P(Blue then Red) = 2/15 * 4/14

P(Blue then Red) = 4/105 = 3.81%

Next, we have

P(Red then Green) = 4/15 * 3/14

P(Red then Green) = 2/35 = 5.71%

P(Green then Green) = 3/15 * 2/14

P(Green then Green) = 1/35 = 2.85%

P(Yellow then Yellow) = 6/15 * 5/14

P(Yellow then Yellow) = 1/7 = 14.29%

P(Red then Red then Red) = 4/15 * 3/14 * 2/13

P(Red then Red then Red) = 4/455 = 0.88%

Read more about probability at

https://brainly.com/question/31649379

#SPJ1

The sum of the infinite geometric series representing the population of the local species of flies is given by the sigma notation ∑ (from n = 1 to ∞) 940 * (1/5)^(n-1). The series converges, and the sum, which represents the upper limit of the population, is 1175.

To write the sum in sigma notation, let's break down the given information step by step:

The first term of the infinite geometric series is a1 = 940.

The common ratio (r) is one fifth (1/5), which means each term is obtained by multiplying the previous term by 1/5.

In sigma notation, the sum of an infinite geometric series can be expressed as follows:

∑ (from n = 1 to ∞) a1 * r^(n-1)

In this case, the first term a1 is 940, and the common ratio r is 1/5. Therefore, the sigma notation for the sum of this series is:

∑ (from n = 1 to ∞) 940 * (1/5)^(n-1)

To calculate the upper limit of this population, we need to find the sum of the series. However, to determine if the sum is possible, we can check if the series converges or diverges.

For a geometric series to converge, the absolute value of the common ratio (|r|) must be less than 1. In this case, |1/5| = 1/5, which is less than 1. Therefore, the series converges.

The sum of an infinite convergent geometric series can be calculated using the formula:

S = a1 / (1 - r)

In our case, a1 = 940 and r = 1/5. Substituting these values into the formula, we can calculate the sum:

S = 940 / (1 - 1/5)

S = 940 / (4/5)

S = 940 * (5/4)

S = 1175

So, the upper limit of the population is 1175.

For more such question on geometric. visit :

https://brainly.com/question/24375372

#SPJ8

The equation of the perpendicular line is y = 1/5x + 2

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

Line; y = -5x + 1

The slope of the above line is

m = -5

The slopes of perpendicular lines are opposite reciporcals

So, the new slope is 1/5

New = 1/5

The line passes through (10, 4)

So, we have

y = mx + c

Where

m = 1/5

This gives

1/5 * 10 + c = 4

Evaluate

c = 4 - 1/5 * 10

c = 2

So, we have

y = 1/5x + 2

Hence, the equation of the perpendicular line is y = 1/5x + 2

Read more about equation at

brainly.com/question/18831322

#SPJ1

Answer:

The answer is,

f(-2) = -2

Step-by-step explanation:

Since -2 < 0, and f(x) = x for x < 0,

so we get,

f(-2) = -2

Answer:

Step-by-step explanation:

a) 4/10 = 40%

b) 3/10 = 30%

c) 1/10 = 10%

d) 2/10 = 20%

e) 8/12 = 67%

f) 10/12 = 83%

g) 9/12 = 75%

h) 12/12 = 100%

i) 4/12 = 33%

j) 5/12 = 42%

k) 2/12 = 16%

l) 3/12 = 25%

The sample space of a spinner refers to the set of all possible outcomes that can occur when the spinner is spun. In order to determine the sample space, we need to consider the different sections or options on the spinner.

For example, if the spinner has 4 equal sections, each labeled with a different color (red, blue, green, and yellow), then the sample space would consist of these 4 possible outcomes: {red, blue, green, yellow}.
Alternatively, if the spinner has 6 sections with numbers 1 to 6, then the sample space would be {1, 2, 3, 4, 5, 6}.
In general, the sample space of a spinner depends on the number and nature of its sections. It can include colors, numbers, or any other distinct options available on the spinner.

In summary, the sample space of a spinner is the set of all possible outcomes, which can vary depending on the specific design and labeling of the spinner.

For more similar questions on sample space

brainly.com/question/2117233

#SPJ8

Answer:

11/2 times 1/3 is 11/6

Step-by-step explanation:

11/2 times 1/3,

We have to multiply the numerators and denominators,

[tex](11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6[/tex]

hence we get 11/6

Answer:

See below

Step-by-step explanation:

Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.

Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.

(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.

To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).

Given:

f(x) = (4+x)(6+x)

g(x) = 1+x

Substituting -5 into the functions:

f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1

g(-5) = 1+(-5) = -4

Now, we can calculate (f/g)(-5):

(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4

Therefore, (f/g)(-5) equals 1/4.

Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.

To find the values that make the denominator zero, we solve the equation:

1 + x = 0

Subtracting 1 from both sides, we get:

x = -1

So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.

for such more question on domain

https://brainly.com/question/16444481

#SPJ8

Answer:

C = 18.2 in.

Step-by-step explanation:

Step 1:  Find the diameter of the circle:

The normal formula for the circumference of a formula is given by:

C = πd, where

We're given the radius, r, and since the diameter is simply twice the radius, we can find the diameter by multiplying 2.9 by 2:

d = 2r

d = 2(2.9)

d = 5.8

Thus, the diameter is 5.8 in.

Step 2:  Find the circumference, C (rounded to the nearest tenth), by plugging in 5.8 for d and 3.14 for π in the circumference formula:

C = 3.14(5.8)

C = 18.212

C = 18.2

Thus, the circumference of the circle is about 18.2 in.

Answer:

C

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 4x² + 5x - 3 + 4x³ - 3x² + 5 ← collect like terms

= 4x³ + (4x² - 3x²) + 5x + (- 3 + 5)

= 4x³ + x² + 5x + 2

The probability is 5/9 or approximately 0.5555.

The probability that one of the books selected is a mathematics book and the other two are either physics or history books can be calculated as follows:

1. Calculate the total number of possible combinations of selecting 3 books out of the given options. Since there are 3 mathematics books, 3 physics books, and 1 history book, the total number of combinations is:

  Total Combinations = C(3,1) * C(3,2) = 3 * 3 = 9, where C(n,r) represents the number of combinations of selecting r items from a set of n items.

2. Calculate the number of favorable combinations where one book is mathematics and the other two are either physics or history books. There are 3 ways to select one mathematics book and 3 ways to select two books from the remaining 6 (3 physics + 1 history) books. Therefore, the number of favorable combinations is:

  Favorable Combinations = C(3,1) * C(6,2) = 3 * 15 = 45.

3. Calculate the probability by dividing the number of favorable combinations by the total number of combinations:

  Probability = Favorable Combinations / Total Combinations = 45 / 9 = 5/1 = 5.

Therefore, the probability that one of the books selected is a mathematics book and the other two are either physics or history books is 5/9 or approximately 0.5555.

For more such questions on probability, click on:

https://brainly.com/question/251701

#SPJ8

Check the picture below.

Their house will be worth approximately $240,154.57 in 8 years.

Non of the options is correct.

To determine how much their house will be worth in 8 years, we can substitute the value of t = 8 into the exponential equation:

y = 150,000(1.004)^(12t)

y = 150,000(1.004)^(12*8)

y = 150,000(1.004)^96

Using a calculator or computer software to evaluate the exponential expression, we find:

y ≈ 150,000 * 1.601030475

y ≈ 240,154.57

None of the provided answer choices match the calculated value. However, we can examine the available options and make an estimation:

A) $240,000: This option is very close to the calculated value of $240,154.57 and is a reasonable estimate.

B) $220,000: This option is significantly lower than the calculated value and is not a close estimate.

C) $1,258,884: This option is significantly higher than the calculated value and is not a close estimate.

D) $14,457,600: This option is extremely higher than the calculated value and is not a realistic estimate.

Based on the provided answer choices, option A) $240,000 is the closest estimate to the calculated value of $240,154.57. However, please note that the actual value may vary depending on the specific calculations and rounding methods used.

Non of the options is correct.

For more such questions on exponential expression

https://brainly.com/question/2456547

#SPJ8

Given the mathematical expression, it must be solved with the result [tex](\text{a} + \text{b})[/tex]

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

We are given the expression:

[tex]\dfrac{(\text{x} + 100)}{(\text{x} - 100)} = \dfrac{(\text{a} + \text{b} + 100)}{(\text{a} + \text{b} - 100)}[/tex]

The Denominators go to the other side of the equality by multiplying, so that we now have:

[tex](\text{x} + 100)(\text{a} + \text{b} - 100) = (\text{a} + \text{b} + 100)(\text{x} - 100)[/tex]

The products of the binomials are developed by the trinomials.

[tex]\text{ax} + \text{bx} - 100\text{x} + 100\text{a} + 100\text{b} - 10000 = \text{ax} + \text{bx} + 100\text{x} - 100\text{a} - 100\text{b} - 10000[/tex]

Like terms are removed.

[tex]100\text{a} + 100\text{b} - 100\text{x} = 100\text{x} - 100\text{a} - 100\text{b}[/tex]

[tex]100\text{a} + 100\text{b} - 100\text{x} - 100\text{x} + 100\text{a} + 100\text{b}[/tex]

[tex]200\text{a} + 200\text{b} - 200\text{x} =[/tex]

Grouping.

[tex]200(\text{a} + \text{b})[/tex]

Result.

[tex](\text{a} + \text{b})[/tex]

Hence, the solution to the mathematical expression is [tex](\text{a} + \text{b})[/tex]

To know more about mathematical expressions, visit:

https://brainly.com/question/30350742

Answer:

Step-by-step explanation:

You want the values of x and z in the figure where one pair of parallel lines crosses another.

Where a transversal crosses parallel lines, corresponding angles are congruent. This gives rise to several other relationships, each with its own name. The net result is that all acute angles are congruent, and all obtuse angles are congruent. The acute and obtuse angles are supplementary. (If the crossing is at right angles, then all angles are congruent.)

Here, the angle marked x° is supplementary to the one marked 77°:

  x = 180 -77 = 103

The angle marked (3z -19)° is congruent to the one marked 77°:

  3z -19 = 77

  3z = 96 . . . . . . add 19

  z = 32 . . . . . . . divide by 3

The value of x is 103; the value of z is 32.

__

Additional comment

The various pairs of angles at a transversal can be described as "consecutive", "alternate", "interior", "exterior", "same-side". Of course, where lines cross, the angles can also be "vertical" or "opposite" or "adjacent" or a "linear pair."

Depending on the relationship, the angles will be congruent or supplementary. For example, "alternate exterior angles" are congruent; "consecutive interior angles" are supplementary.

<95141404393>

g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8

The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.

Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).

for more search question  function

https://brainly.com/question/25638609

#SPJ8

The probabilities are:

1. P(yellow) = 2/5

2. P(red) = 3/10

3. P(blue) = 3/10

4. P(blue or yellow) = 7/10

5. P(red or blue) = 3/5

To find the probability that a person in each color seat would receive the free tickets, we need to calculate the probabilities of each event.

1. P(yellow): There are 8 yellow seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a yellow seat at random is P(yellow) = 8/20 = 2/5.

2. P(red): There are 6 red seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a red seat at random is P(red) = 6/20 = 3/10.

3. P(blue): There are 6 blue seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a blue seat at random is P(blue) = 6/20 = 3/10.

4. P(blue or yellow): To calculate the probability of selecting a blue or yellow seat, we add the individual probabilities of selecting a blue seat and a yellow seat: P(blue or yellow) = P(blue) + P(yellow) = 3/10 + 2/5 = 7/10.

5. P(red or blue): To calculate the probability of selecting a red or blue seat, we add the individual probabilities of selecting a red seat and a blue seat: P(red or blue) = P(red) + P(blue) = 3/10 + 3/10 = 6/10 = 3/5.

For more such question on probabilities. visit :

https://brainly.com/question/251701

#SPJ8

Step-by-step explanation:

70 to 85 % of his maximum

Maximum is estimated to be 220 - age  = 220 - 42 = 178

70% of this is 125

85 % is 89  151  

I believe I would go with the third choice  116-160 bpm

The equation that best represents the relationship between x and y is:

y = -1/2x + 11

To determine the equation that best represents the relationship between the quantities x and y, we can examine the pattern in the table.

Looking at the x-values and their corresponding y-values, we can observe that as x increases by 2 units, y decreases by 1 unit.

Using this pattern, we can find the equation that represents the relationship.

When x = 2, y = 10

When x = 4, y = 9

When x = 6, y = 8

When x = 8, y = 7

Based on the pattern, we can see that y decreases by 1 unit for every 2 units increase in x.

Therefore, the equation that best represents the relationship is:

y = -1/2x + b

To find the value of b (the y-intercept), we can substitute the values of x and y from any point in the table. Let's use the first point (x = 2, y = 10):

10 = -1/2(2) + b

10 = -1 + b

b = 11

So the equation that best represents the relationship between x and y is:

y = -1/2x + 11

Therefore, the correct answer is: y = -1/2x + 11.

For such more questions on equation

https://brainly.com/question/24907633

#SPJ8

The value of AC is 10.Hence, the correct option is (1) 11.

From the diagram, C is the midpoint of AB.

Now,

AC = CB (As C is the midpoint of AB)

Assuming the length of AB is 32 and the length of AC is +10, we can find the length of CB by subtracting the length of AC from the length of AB.

CB = AB - AC

CB = 32 - 10

CB = 22

Therefore the length of CB is 22.

Let's look at the following possible answers:

(1) 11 - This is not the length. CB

(2) 12 - This is not the length of the CB.

(3) 3 - This is not the CB length.

(4) 44 - not CB length.

None of the given answer options correspond to CB length (22).

Therefore, none of the specified options are valid values.

Therefore, AC + CB = AB+10 + CB = 32CB = 32 - 10 = 22

Thus, the length of CB is 22.

For more questions on value :

https://brainly.com/question/30145972

#SPJ8

Answer:

2

as it is a positive integer

Answer:

To list the sides of triangle ∆ from shortest to longest, we need the lengths of the sides. However, the given information only provides the measures of the angles (∠). Without the side lengths, we cannot determine the order of the sides from shortest to longest.