What is the value of x?
(x+4)=-6
O x = 35
O x = -25
O x = 25
Ox=35

Answer:

Step-by-step explanation:

The perimeter of a quarter circle can be calculated by adding the length of the arc and the two radii that make up the quarter circle.

The length of the arc of a quarter circle is given by (πr)/2, where r is the radius of the quarter circle and π is approximately 3.142 (as given in the question).

So, for a quarter circle with a radius of 7 cm, the length of the arc would be:

(πr)/2 = (3.142 x 7)/2 = 10.997 cm (rounded to 3 decimal places)

The two radii that make up the quarter circle are each equal to the radius of the quarter circle, so the total length of the two radii would be:

2r = 2 x 7 = 14 cm

Therefore, the perimeter of the quarter circle would be:

10.997 cm + 14 cm = 24.997 cm (rounded to 3 decimal places)

So the perimeter of the quarter circle is approximately 24.997 cm. The digits given by the calculator will depend on the specific calculator used.

Answer:

11-3x

Step-by-step explanation:

1) Multiply 5(1-x). To do this, you multiply 5 by both x and 1. You should get     5-5x.

1) Next, multiply 2(x+3). You should get 2x+6.

3) Finally, add like terms. Add 2x and -5x together and add 6 and 5 together. You should get -3x and 11.

The answer is 11-3x.

Answer:

$24,25

Step-by-step explanation:

72.75 ÷ 3 = 24,25

The probability of getting one defective component per customer is very low, less than 1/14,254. The probability of getting five defective components to a single customer is also low, 1/14,254. And the probability of getting two defective components to two different customers and the rest of the customers getting none is 10/14,254.

(a) The probability that each customer will receive one defective component is the probability that the five defective components will be drawn in a specific order, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order. So the probability is (5!)/(5049484746) = 1/14,254.

(b) The probability that one customer will have drawn five defective components is the probability that all five defective components will be drawn in a row, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a row. So the probability is (1!)/(5049484746) = 1/14,254,

(c) The probability that two customers will receive two defective components each, two none, and the other one, is the probability that the five defective components will be drawn in a specific order and then divided among the five customers in a specific way, divided by the total number of ways the 50 components can be drawn. The number of ways to divide the defective components among the customers is 5!/(2!2!1!) = 10. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order, so the probability is (105!)/(50494847*46) = 10/14,254.

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Answer:

x= 10 y=14 : 10 3 point, 14 5 point

Step-by-step explanation:

Write your equation down vertically,

3x + 5y = 100

 x + y   =  24

Next find multiply bottom equation by one number from the tops opposite,

3x + 5y = 100

(-3)x +(-3)y = (-3)24

3x + 5y = 100

-3x - 3y= -72

Add the two functions to isolate y

2y= 28 y=14

Plug y back into original and solve

3x +5(14) =100 --> 3x + 70 =100 --> 3x = 30 x=10

Answer:

4x-10=3x+12

4x+3x= 12+10

7x= 32

x= 32÷7

x=4.571

By answering the presented question, we may conclude that This probability simplifies to approximately 0.0193, so the answer is (e) 0.0193.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

This problem can be solved by using the binomial distribution. The probability of getting exactly k heads in n tosses of a fair coin is given by the formula:

P(k heads in n tosses) = (n choose k) * (1/2)^n

where (n choose k) is the number of ways to choose k heads from n tosses, and is given by the formula:

(n choose k) = n! / (k! * (n-k)!)

where n! means n factorial, i.e., n! = n * (n-1) * (n-2) * ... * 2 * 1.

To find the probability of getting at least 10 heads in 12 tosses, we need to add up the probabilities of getting 10, 11, or 12 heads:

P(at least 10 heads in 12 tosses) = P(10 heads) + P(11 heads) + P(12 heads)

P(10 heads) = (12 choose 10) * (1/2)^12 = 66/4096

P(11 heads) = (12 choose 11) * (1/2)^12 = 12/4096

P(12 heads) = (12 choose 12) * (1/2)^12 = 1/4096

Therefore,

P(at least 10 heads in 12 tosses) = 66/4096 + 12/4096 + 1/4096 = 79/4096

This simplifies to approximately 0.0193, so the answer is (e) 0.0193.

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Answer:

-4

Step-by-step explanation:

y=3x13

2x=y-9

2x=3x+13-9

2x=3x+13-9

2x=3x+4

-3  -3

-x=4

-x/ -x/

x=-4

(You said "3x13" so i'm going to guess you meant to say "3x+13").

(If you meant "3x-13" I can also help you with that too)!

Differentiating each function, we have for all x, unless otherwise indicated,

\(h(x) = 2^x - 1 \implies h'(x) = \ln(2) \, 2^x > 0\)

\(g(x) = -4 (2^x) \implies g'(x) = -4 \ln(2) \, 2^x < 0\)

\(f(x) = -3x+7 \implies f'(x) = -3 < 0\)

\(j(x) = x^2 + 8x + 1 \implies j'(x) = 2x + 8 > 0 \text{ only when } x > -4\)

and only h(x) has a strictly positive derivative. (A)

The area of the trapezoid JKML which is given above would be =88.2in³.

To calculate the area of the trapezoid given the formula for the area of trapezoid should be used which is given below;

Area of trapezoid = 1/2(a+b) ×h

Where;

a = 10.5 in

b = 6.3 in

height = 10.5 in

Therefore the area of the trapezoid;

= 1/2(10.5+6.3) ×10.5

= 1/2×16.8×10.5

= 8.4×10.5

= 88.2in³

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Answer:

3

Step-by-step explanation:

ur smart tbh

The acceleration of the mass at time t=1 is approximately -19.42 inches/second^2.

To find the velocity and acceleration of the mass attached to a vertical spring at time t=1, we need to differentiate the position function with respect to time.

First, we can find the velocity function v(t) by taking the derivative of the position function s(t) with respect to time t:

v(t) = s'(t) = 5cos(2t) * 2 = 10cos(2t)

Plugging in t=1, we get:

v(1) = 10cos(2) ≈ -3.42 inches/second

Therefore, the velocity of the mass at time t=1 is approximately -3.42 inches/second.

Next, we can find the acceleration function a(t) by taking the derivative of the velocity function v(t) with respect to time t:

a(t) = v'(t) = -20sin(2t)

Plugging in t=1, we get:

a(1) = -20sin(2) ≈ -19.42 inches/second^2

Therefore, the acceleration of the mass at time t=1 is approximately -19.42 inches/second^2.

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Using mathematical induction, we have proved that 6ⁿ + 4 is divisible by 5 for n≥0. This result has important applications in various areas of mathematics and science. The proof demonstrates the power and usefulness of mathematical induction in proving statements for all natural numbers.

To prove that 6ⁿ + 4 is divisible by 5 for n≥0 using induction, we need to show that the statement is true for the base case, and then assume that the statement is true for n=k, and prove that it is also true for n=k+1.

Base case: For n=0, we have 6⁰+ 4 = 5, which is divisible by 5. Therefore, the statement is true for the base case.

Assume that the statement is true for n=k, which means that 6ᵃ+ 4 is divisible by 5.

Proof: Now we need to prove that the statement is also true for n=k+1, which means that we need to show that 6ᵃ⁺¹ + 4 is divisible by 5. (LET k=a)

Using the assumption that 6^k + 4 is divisible by 5, we can write:

6ᵃ⁺¹ + 4 = 6 * 6ᵃ + 4 = 5 * 6ⁿ + 6^k + 4 = 5 * 6ᵃ + (6ᵃ + 4)

Since 6ᵃ + 4 is divisible by 5 (by the assumption), and 5 * 6ᵃis also divisible by 5, we can conclude that 6ᵃ⁺¹+ 4 is divisible by 5.

Therefore, by mathematical induction, we can conclude that 6ⁿ + 4 is divisible by 5 for n≥0.


To prove that 6ⁿ + 4 is divisible by 5 for n≥0 using induction, we need to show that the statement is true for the base case, and then assume that the statement is true for n=k, and prove that it is also true for n=k+1. The base case is n=0, and we can see that 6⁰ + 4 = 5, which is divisible by 5. Assuming that the statement is true for n=k, we can use this to prove that it is also true for n=k+1. By the mathematical induction, we can conclude that 6ⁿ + 4 is divisible by 5 for n≥0.


Using mathematical induction, we have proved that 6ⁿ + 4 is divisible by 5 for n≥0. This result has important applications in various areas of mathematics and science. The proof demonstrates the power and usefulness of mathematical induction in proving statements for all natural numbers.

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Answer:

1 / 30

Step-by-step explanation:

For a six - sided die :

Sample space = (1, 2, 3, 4, 5, 6)

P(rolling a 1) = required outcome / sample space = 1/6

Sample space for spinner = (A, B, C, D, E)

P(spinning A ) = required outcome / sample space = 1/5

P(spinning A) = 1 / 5

P(rolling a 1 and spinning A) = P(rolling a 1) * P(spinning A) = 1/6 * 1/5 = 1 / 30

Answer:

250 \(cm^{3}\)

Step-by-step explanation:

First, start with the formula for the volume of a rectangular prism (aka a box):

V=length*width*height

Then, plug in your values:

V=5*5*10

V=25*10

V=250

Don't forget your units!

250 \(cm^{3}\)

We must represent the number 4.082, the options you are giving us are from an apparent decomposition of the previous number

The correct option is B: Four and eighty-two thousandths, It is indeed 4 whole units and 82 thousandths. The other options are not correct

The relative price is a useful measure for comparing the prices of different products or services, especially in the context of consumer preferences and demand.

Relative price refers to the price of a particular product or service in relation to other goods or services in the market.

It is calculated as the ratio of the price of a given product or service to the price of a reference product or service, commonly referred to as a base good or service.

Let the price of a pair of shoes be $5 and the price of a box of tea be $3.

Then the relative price of a pair of shoes is given by:

Relative price of shoes = Price of shoes / Price of tea

= $5 / $3

= 1.67

Thus, the relative price of a pair of shoes is 1.67.

Similarly,

The relative price of a box of tea can be calculated as follows:

Relative price of tea = Price of tea / Price of shoes

= $3 / $5

= 0.6

Therefore, the relative price of a box of tea is 0.6.

This means that the price of tea is relatively cheaper than that of shoes, as its relative price is less than one.

The relative price of shoes is greater than one, which indicates that shoes are relatively more expensive than tea.

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Answer:

2 2/4

Step-by-step explanation:

Answer:

We can use the given information to find the ant's crawling speed and then use that to calculate how far it can crawl in a given amount of time.

The ant crawls 12 feet in 10 minutes, so its crawling speed is:

12 feet / 10 minutes = 1.2 feet/minute

To find how far the ant can crawl in 20 minutes, we can multiply its crawling speed by the time:

Distance in 20 minutes = crawling speed x time

Distance in 20 minutes = 1.2 feet/minute x 20 minutes

Distance in 20 minutes = 24 feet

Therefore, the ant can crawl 24 feet in 20 minutes.

To find how far the ant can crawl in 30 minutes, we can use the same formula:

Distance in 30 minutes = crawling speed x time

Distance in 30 minutes = 1.2 feet/minute x 30 minutes

Distance in 30 minutes = 36 feet

Therefore, the ant can crawl 36 feet in 30 minutes.

Answer:

20 mins=24 feet

30 mins=36 feet

Step-by-step explanation:

if 12 feet = 10 mins and 10 times 2 = 20 then 12 times 2 =24

same for 30 mins.

10 times 3= 30 then 12 times 3= 36

The mole's new surface area is roughly 100.944 mm².

The new surface area of the mole can be estimated by using the formula for the surface area of a hemisphere: A = 2πr².

First, we can calculate the radius of the original mole using the diameter: r = d/2 = 5.7/2 = 2.85 mm.

Next, we can double the radius to get the radius of the new mole: 2r = 2(2.85) = 5.7 mm.

Finally, we can use the formula for the surface area of a hemisphere to calculate the new surface area: A = 2π(5.7)² = 100.944 mm².

Therefore, the new surface area of the mole is approximately 100.944 square millimeters.

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The description corresponds to an observational study, which involves gathering data and information to draw conclusions without intervening in the process. Correct answer: letter D.

An experiment would involve manipulating the variables to see the effect of the manipulation. In this case, it would involve changing the caffeine consumption and observing the effect on heart arrhythmias.

In order to better understand the relationship between heart arrhythmias and caffeine consumption, researchers need to consider a variety of factors, including the amount of caffeine consumed, the timing of consumption, and any potential underlying medical conditions that could be influencing the results.

Furthermore, researchers need to ensure that the study population is large enough and diverse enough to accurately reflect the general population. Additionally, researchers need to consider potential confounding variables, such as lifestyle factors, medications, and other dietary components that could be influencing the results.

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The volume of the given solid is 64π/3 cubic unit

The given solid is a cylinder with radius 4 and infinite height, cut off by the plane y = 3z. Since we are only considering the first octant, we only need to consider the portion of the cylinder where x, y, and z are all non-negative.

The intersection of the cylinder and the plane y = 3z is a circle with radius 4 on the xy-plane, centered at the origin. For any point (x, y, z) on this circle, we have x² + y² = 16 and y = 3z. Solving for x and z in terms of y, we get:

x² + y² = 16

x² + (3z)² = 16

x² + 9z² = 16

x² + 9(y/3)² = 16

x² + (y/3)² = 16/9

This is the equation of a circle with radius 4/3 centered at the origin. Thus, the cross-sectional area of the cylinder at any height y is π(4/3)² = 16π/9.

To find the volume of the cylinder, we need to integrate this cross-sectional area over the range of y values where the cylinder intersects the plane y = 3z. Since the cylinder intersects the plane at y = 0 and y = 12, we have:

V =

∫[0,12] (16π/9) dy

= (16π/9) * y |[0,12]

= (16π/9) * 12

= 64π/3

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Answer:

There's nothing there

Step-by-step explanation:

Answer:

-2

(0, 1)

Step-by-step explanation:

Giveb the function :

F(x) = 3^x + 1 – 2

To obtain the asymptote, take the limit of f(x) as x as tends to ∞

3^(∞+1) - 2 = 0 - 2

Hence,

y = 0 - 2.

y = - 2

The y intercept, this is the value of y when x = 0

Hence, put x = 0

F(0) = 3^(0 + 1) – 2

f(0) = 3^1 - 2

f(0) = 3 - 2

f(0) = 1

Y - intercept = (0, 1)

The probability that the target is hit at least twice, when ten shots are fired independently with a probability of hitting the target of 1/5, is approximately 0.737.

To find the probability that the target is hit at least twice, we need to calculate the probability of hitting the target exactly twice, exactly three times, and so on, up to exactly ten times, and then sum up these probabilities.

Let's use the binomial probability formula to calculate the probabilities of hitting the target a specific number of times:

\(P(X = k) = C(n, k) * p^k * {1 - p}^{n - k}\)

Where:

P(X = k) is the probability of hitting the target exactly k times,

n is the total number of shots fired (in this case, 10),

k is the specific number of hits (from 2 to 10),

p is the probability of hitting the target in a single shot (1/5), and

C(n, k) represents the binomial coefficient (n choose k).

Let's calculate the probabilities for k = 2, 3, 4, ..., 10 and sum them up:

P(hit at least twice) = P(X ≥ 2) = P(X = 2) + P(X = 3) + ... + P(X = 10)

\(P(X = k) = C(10, k) * (1/5)^k * (4/5)^{10 - k}\)

Using this formula, we can calculate the probabilities for each value of k and sum them up:

P(X ≥ 2) = P(X = 2) + P(X = 3) + ... + P(X = 10)

P(X ≥ 2) ≈ 0.037 + 0.122 + 0.233 + 0.267 + 0.201 + 0.106 + 0.038 + 0.009 + 0.001 + 0.000

P(X ≥ 2) ≈ 0.737

Therefore, the probability that the target is hit at least twice, when ten shots are fired independently with a probability of hitting the target of 1/5, is approximately 0.737.

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