The ratio of boys to girls in a group is 5:1. If there are 60 more boys than girls, work out how many people there are in total.

Answer:

The number of balloons varies directly with the number of tables. The two variables are directly proportional. The relationship of balloons to tables is the ratio 5:1, where 5 is the constant of variation. Use the equation y = kx, where k is the constant of variation resulting in the equation y = 5x.

Step-by-step explanation:

i just did it

Answer:

Step-by-step explanation:

The number of balloons varies directly with the number of tables. The two variables are directly proportional. The relationship of balloons to tables is the ratio 5:1, where 5 is the constant of variation. Use the

PLACE VALUE. VALUE

6. Hundreds. 200

7. Ones. 1

8. Hundreds. 0

9. Hundreds. 800

10. Tens. 60

c) 2x^2 > 10

The inequality graphed on the number line is:

c) 2x^2 > 10

This inequality represents a quadratic function that opens upwards with its vertex at (0,0) and its axis of symmetry along the y-axis. The inequality indicates that all values of x that make the function greater than 10 on the y-axis are solutions to the inequality.

On the number line, the solution to the inequality would be all values of x such that x is greater than the square root of 5 or less than the negative square root of 5.

This would be represented on the number line by shading the region to the right of the positive square root of 5 and the region to the left of the negative square root of 5.

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This ain't an answer but if you look up mixed number calculator soup it's really helpful

Make sure you write fractions as 2 4/9

Answer:

3 3/11

Step-by-step explanation:

8                         22                 8      x       9           72

_     divided by    _      =          __________    =   __

1                           9                   1      x       22         22

If you simplify 72/22, you will get 3 3/11

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Answer:

a. 2^(x-2) = g^(-1)(x)

b. A, B, D

Step-by-step explanation:

the phrasing attached in the image is flagged as inappropriate, so i will be replacing it with g(x) and its inverse with g^(-1)(x)

1. replace g(x) with y and solve for x

y = log₂(x) + 2

subtract 2 from both sides to isolate the x and its log

y - 2 = log₂(x)

this text is replaced by the second image -- it was marked as inappropriate

thus, 2^(y-2) = x

replace x with g^(-1)(x) and y with x

2^(x-2) = g^(-1)(x)

2. plug this in to points A, B, C, D, E, and F

A: (2,1)

plug 2 in for x

2^(2-2) = 2⁰ = 1 so this works

B: (4, 4)

2^(4-2) = 2²= 4 so this works

C: (9, 3)

2^(9-2) = 2⁷ = 128 ≠ 3 so this doesn't work

(5, 8)

2^(5-2) = 2³ = 8 so this works

E: (3, 5)

2^(3-2) = 2¹ = 2 ≠ 5 so this doesn't work

F: (8, 5)

2^(8-2) = 2⁶ = 64 ≠ 5 so this doesn't work

Answer:

B (a + b)^1/2

Step-by-step explanation:

\(\sqrt[m]{x^n} =a^{n/m}\)

Is the formula for radical to exponent notation.

Answer:

69.08 cm

Step-by-step explanation:

circumference= 2πr = 2 × 3.14 × 11 cm

Answer:

69.12 cm

Step-by-step explanation:

C = 2πr

C = 2(3.14)11

C = 6.28(11)

C = 69.12 cm

13.  The probability of obtaining no defective microprocessors is 53.14%.

14.  If a coin is flipped 10 times, the probability of no heads is 0.0977%

15.  If a coin is flipped 10 times, the probability of at least one head is 99.9023%

13. To find the probability of obtaining no defective microprocessors when randomly selecting six from a lot of 100 microprocessors, we need to calculate the probability of selecting a non-defective microprocessor each time.

The probability of selecting a non-defective microprocessor on the first draw is (90/100) because there are 90 non-defective microprocessors out of the total 100.

Since the microprocessors are selected randomly, the probability remains the same for each subsequent draw. Therefore, the probability of selecting a non-defective microprocessor on each draw is also (90/100).

To find the probability of obtaining no defective microprocessors, we multiply the probabilities of each individual draw together since the events are independent:

Probability of no defective microprocessors = (90/100) * (90/100) * (90/100) * (90/100) * (90/100) * (90/100)

Calculating this expression, we find the probability of obtaining no defective microprocessors is approximately 0.531441, or 53.14% (rounded to two decimal places).

14. If a coin is flipped 10 times, the probability of getting no heads is the same as getting all tails. Since each flip is independent and the probability of getting tails on a fair coin is 0.5, the probability of getting all tails in 10 flips is:

Probability of no heads = (0.5) * (0.5) * (0.5) * (0.5) * (0.5) * (0.5) * (0.5) * (0.5) * (0.5) * (0.5)

Calculating this expression, we find the probability of getting no heads is 0.0009765625, or 0.0977% (rounded to four decimal places).

15. The probability of getting at least one head in 10 coin flips is the complement of the probability of getting no heads.

Probability of at least one head = 1 - Probability of no heads

Using the result from the previous question, the probability of no heads is 0.0009765625. Therefore,

Probability of at least one head = 1 - 0.0009765625 = 0.9990234375, or 99.9023% (rounded to four decimal places).

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Answer:

2 x 8 = 16

2x8+8 = 24

Step-by-step explanation:

Answer:

its going to be 2&3(x+2)(x+3)

Step-by-step explanation:

Answer:

Length = 5cm

Breadth = 4cm

Height = 3cm

Area of 4 wall = 2(l + b) x h

= 2(5 + 4) x 3

= 2 x 9 x 3

= 54 cm²

Cost = 7.50 x 54

= Rs405

To simplify the expression 7r^2/2r^4 • 6√2g^12, we can combine the coefficients and variables separately.

First, let's simplify the coefficients:

7 • 6 = 42

Next, let's simplify the variables:

r^2/r^4 = 1/r^(4-2) = 1/r^2

Finally, we simplify the square root and exponent:

√2g^12 = √(2 • g^12) = √2 • √g^12 = √2 • g^(12/2) = √2 • g^6 = g^6√2

Now we can rewrite the simplified expression:

7r^2/2r^4 • 6√2g^12 = 42 • (1/r^2) • (g^6√2)

Multiplying the coefficients:

42 • 1 = 42

Combining the variables:

1/r^2 • g^6√2 = g^6√2/r^2

Therefore, the simplified expression is 42 • g^6√2/r^2.

The correct answer is D. 42r^12/2.

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Answer:

------------------------

Apply geometric mean theorem to find the value of x:

Find the value of y using Pythagorean:

Answer:

\(x = \sqrt{6}\)

\(y=\sqrt{15}\)

Step-by-step explanation:

To find the value of x, apply the Geometric Mean Theorem (Altitude Rule).

The Geometric Mean Theorem (Altitude Rule) states that the altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude.

From inspection of the given right triangle:

\(\implies \sf \dfrac{altitude}{segment\:1}=\dfrac{segment\:2}{altitude}\)

\(\implies \dfrac{x}{3}=\dfrac{2}{x}\)

\(\implies x^2=6\)

\(\implies x=\sqrt{6}\)

Therefore, the value of x is √6.

To find the value of y, apply the Geometric Mean Theorem (Leg Rule).

The Geometric Mean Theorem (Leg Rule) states that the altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment segment directly opposite the leg.

From inspection of the given right triangle:

\(\implies \sf \dfrac{hypotenuse}{leg\:1}=\dfrac{leg\:1}{segment\;1}\)

\(\implies \dfrac{5}{y}=\dfrac{y}{3}\)

\(\implies y^2=15\)

\(\implies y=\sqrt{15}\)

Therefore, the value of y is √(15).

A system of equations with one linear equation and one quadratic equation has "zero or one or two" solutions.

Consider a system of equations with one linear equation and one quadratic equation as

Case (1): y = x² + 4x + 2 ...(1)

and x + y = 2 ...(2)

By the substitution method:

from (2), y = 2 - x; Substituting in (1)

⇒ 2 - x = x² + 4x + 2

⇒ x² + 4x + 2 + x - 2 = 0

⇒ x² + 5x = 0

⇒ x(x + 5) = 0

∴ x = 0 and x = -5

If x = 0, then y = 2 - 0 = 2

If x = -5, then y = 2 + 5 = 7

So, the system has two solutions at (0, 2) and (-5, 7).

Case (2): y = x² + 4x + 2 ...(1)

and x - y = 2 ...(2)

By the substitution method:

from (2), y = x - 2; Substituting in (1)

⇒ x - 2 = x² + 4x + 2

⇒ x² + 4x + 2 + 2 - x = 0

⇒ x² + 3x + 4 = 0

we know that b² - 4ac will decide the nature of roots.

So, (3)² - 4(1)(4) = 9 - 16 = -7 < 0

Since the determinant is less than 0, the roots are imaginary. Hence the system has no solution. That means the line and the parabola do not meet.

Case (3): y = x² + 4x + 2 ...(1)

and y = x - 1/4 ...(2)

Substituting (2) in (1), we get

⇒ x - 1/4 = x² + 4x + 2

⇒ x² + 4x + 2 - x + 1/4 = 0

⇒ x² + 3x + 9/4 = 0

⇒ 4x² + 12x + 9 = 0

⇒ (2x + 3)² = 0

⇒ 2x + 3 = 0

∴ x = -3/2

If x = -3/2 then y = -3/4 - 1/4 = -7/4

So, the system has one solution at (-3/2, -7/4).

Therefore, the given type of system has "zero or one or two" solutions.

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Answer: x=7

Step-by-step explanation:

Answer:

X=7 is correct via a p e x

It will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.

First, we need to calculate the amount of money that we need to save in order to cover the cost of the trip. This can be done by subtracting the amount we have already saved from the total cost of the trip:

Total cost of trip = 2500

Amount already saved = 2200

Amount to save = 2500 - 2200 = 300

Next, we can use the compound interest formula to calculate how long it will take to earn 300 with an interest rate of 1.55% compounded annually. We can set up the formula as follows:

A = P(1 + i)n

where:

A = accumulated amount = 300 + 2200 = 2500 (the total cost of the trip)

P = principal = 2200

i = interest rate per year = 1.55%

n = number of years we need to save for

We can now solve for n:

2500 = 2200(1 + 0.0155)n

Divide both sides by 2200:

1.13636 = 1.0155n

Take the natural logarithm of both sides:

ln(1.13636) = n ln(1.0155)

Divide both sides by ln(1.0155):

n = ln(1.13636)/ln(1.0155) ≈ 4.4 years

Therefore, it will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.that we rounded our final answer to the nearest tenth as instructed.

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a) The required solution is that  the inverse of 2 modulo 13 is k = 12. To determine an inverse of a modulo m, where a = 2 and m = 13, we'll follow the method outlined in the question.

Step 1: Calculate the value of ϕ(m), where ϕ is Euler's totient function.

Since m = 13 is a prime number, ϕ(13) = 13 - 1 = 12.

Step 2: Find the value of k such that ak ≡ 1 (mod m).

We need to find k such that 2k ≡ 1 (mod 13).

To simplify the calculation, we can check the powers of 2 modulo 13:

2^1 ≡ 2 (mod 13)

2^2 ≡ 4 (mod 13)

2^3 ≡ 8 (mod 13)

2^4 ≡ 3 (mod 13)

2^5 ≡ 6 (mod 13)

2^6 ≡ 12 (mod 13)

2^7 ≡ 11 (mod 13)

2^8 ≡ 9 (mod 13)

2^9 ≡ 5 (mod 13)

2^10 ≡ 10 (mod 13)

2^11 ≡ 7 (mod 13)

2^12 ≡ 1 (mod 13)

We observe that 2^12 ≡ 1 (mod 13). Therefore, k = 12.

Step 3: Verify that 2k ≡ 1 (mod 13).

Checking 2^12 ≡ 1 (mod 13), we can conclude that k = 12 is indeed the inverse of 2 modulo 13.

Hence, the inverse of 2 modulo 13 is k = 12.

b) Besides the inverse 12, two other inverses of 2 modulo 13 can be found by subtracting or adding multiples of 13 to the inverse 12.

Adding 13 to 12: 12 + 13 ≡ 25 ≡ 12 (mod 13)

Subtracting 13 from 12: 12 - 13 ≡ -1 ≡ 12 (mod 13)

Therefore, the two other inverses of 2 modulo 13 are also 12, as all three inverses are congruent to each other modulo 13.

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The probability of obtaining the observed results or more extreme results under the assumption of the null hypothesis.

The P value is a statistical measure that helps to determine the level of significance of a hypothesis test. In hypothesis testing, the null hypothesis is the initial assumption that is tested against an alternative hypothesis.

The decision criterion for a hypothesis test using the P value is to compare the calculated P value with the specified significance level, denoted by alpha (α).
If the calculated P value is less than or equal to the specified significance level, we reject the null hypothesis.

This means that we have sufficient evidence to support the alternative hypothesis, which is the opposite of the null hypothesis.

The significance level is typically set at 0.05 or 0.01, which means that we are willing to accept a 5% or 1% chance of making a type I error (rejecting the null hypothesis when it is actually true).
It simply means that we do not have enough evidence to reject it at the specified significance level.
In conclusion,

The decision criterion for a hypothesis test using the P value is straightforward.

If the P value is less than or equal to the specified significance level, we reject the null hypothesis.

Otherwise, we do not reject the null hypothesis.

This decision is based on the level of evidence that is provided by the calculated P value.

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4a + b - |2c|

First, 2c = 20, so absolute value of 20 is still 20
-> 4a + b - 2c.
Substitute a = 4, b = -3 and c = 10.

= 16 - 3 - 20 = -7

An eating disorder characterized by bingeing and purging is called bulimia nervosa.

The minimum amount of body fat needed for good health is variable and can depend on factors such as age, gender, and individual circumstances. However, essential body fat is typically estimated to be around 3-5% for men and 8-12% for women.

The term used to describe a person who is very overfat is obese. Obesity refers to having excessive body fat, which can have negative effects on health.

People with anorexia nervosa, an eating disorder characterized by restrictive eating and an intense fear of gaining weight, often see themselves as too fat even when they are extremely thin. This distorted body image is a characteristic feature of anorexia nervosa.

A technique for assessing body fat levels that involves being weighed under water is called hydrostatic weighing or underwater weighing. It is considered one of the more accurate methods for determining body composition.

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Answer: (a) The equation 2x^2 + 4x + 3 = k has real roots if and only if its discriminant, which is 4^2 - 4(2)(3), is nonnegative. The discriminant is equal to 0, so the equation has real roots if and only if k = 3.

(b) For the equation f(x) = kx^2 + kx + 1 to have real roots, its discriminant, which is 1 - 4k, must be nonnegative. This gives us k >= 1/4. The range of values of k for which the equation has real roots is k >= 1/4.

(c) When k = -2, the equation f(x) = -2x^2 - 2x + 1 = 0. Solving this equation using the quadratic formula, we get x = (-1 ± √(1 + 8))/4. So, the roots are x = (-1 ± √(9))/4 = (-1 ± 3)/4 = 1/2, -2.

To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Common instruments used to measure angles are:

1. Protractor

2.Compass

3.Digital Angle finder

4.Angle finder

5.Clinometer

6. Inclinometer

You can take the following actions to copy angle ABC:

Create a line segment that will serve as the foundation for the new angle you're going to create.

Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.

Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.

Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.

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the main answer is that the probability that a defective spindle can be salvaged is 1/2. This is based on the assumption that the location of the gouge along the spindle is best described by a uniform distribution.

To find the probability that a defective spindle can be salvaged, we need to determine the length of the longest consecutive segment without a gouge.

Let's assume the length of the spindle is L inches. Since the location of the gouge is described by a uniform distribution, each inch along the spindle has an equal probability of having a gouge.

The probability that the first inch does not have a gouge is 1 (since it is the starting point).

For each subsequent inch, the probability of not having a gouge is (L - 1)/L, because there are L - 1 inches left without a gouge out of the remaining L inches.

Therefore, the probability of having consecutive inches without a gouge is the product of these probabilities for each inch. This can be calculated as (1 * (L - 1)/L * (L - 2)/(L - 1) * ... * 2/3 * 1/2).

Simplifying the expression, we get (L - 1)/L * (L - 2)/(L - 1) * ... * 2/3 * 1/2 = 1/2.

So, the probability that a defective spindle can be salvaged is 1/2.

the main answer is that the probability that a defective spindle can be salvaged is 1/2. This is based on the assumption that the location of the gouge along the spindle is best described by a uniform distribution.

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Answer:

1 solution

Step-by-step explanation:

A system of linear equations has no solution when the graphs are parallel.

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

Answer:

Identifying and moving the base is the key to changing from logarithmic form into exponential form. Identifying the base of the logarithmic equation and moving the base to the other side of the equal sign is how to change a logarithmic equation into and exponential equation.

Example- log 8 base 2=3

then 2^3=8

The opposite of a logarithmic function is an exponential equation, and vice versa

As a general rule, we have the following equation to convert a log function to an exponential.

\(\log_ba = x \to a = b^x\)

Take for instance, we have the following logarithmic function

\(\log_216 = x\)

The equivalent exponential equation is:

\(16 = 2^x\)

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If i paid weekly, I realized my income is $73.155.

Answer:

Solution given;

1 hour =$10

13 hour = 13*10=$130

Taxes

federal :10%

FICA:7.65%

state: 3%

contribute to company: $30

now

My income each week :

No. Since the limit as x approaches 3 from both sides of f(x) equals 6, f(x) will have a hole at x equals 3 and not a vertical asymptote.

A vertical asymptote is a vertical line on a graph that the function approaches but never touches as the input values approach a certain value. In other words, it is a value of the independent variable for which the function approaches infinity or negative infinity as the independent variable approaches that value.

It is often found in rational functions, where the denominator becomes zero at some value, causing the function to become undefined at that point.

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Answer:

Step-by-step explanation:

Let the number be x

14 ÷ x = \(\frac{14}{x}\)

Answer:

14 / x

Step-by-step explanation:

quotient = /

14 = 14

a number = the variable, let's call it x

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