An ant crawls 14 cm down into an ant hole. It then crawls 6 cm up to the queens nest. What is the ants location in a math sentence

Step-by-step explanation:

To find the next term or number, we'll need to keep subtracting 5. So the formula is: n-5

Answer:

(4,0)

Step-by-step explanation:

You basically are plotting a point on the positive number 4 on the x line. Since they're only asking for an X and not a Y, you'd leave it as (4,0). Hope this helps!

Answer:

The probability that the sample proportion exceeds 0.16 is 0.2061.

Step-by-step explanation:

We are given that according to a 2009 Reader's Digest article, people throw away approximately 13% of what they buy at the grocery store.

You plan to randomly survey 101 grocery shoppers to investigate their behavior.

Let \(\hat p\) = sample proportion

The z-score probability distribution for the sample proportion is given by;

                               Z  =  \(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\)  ~ N(0,1)

where, \(\hat p\) = sample population = 0.16

           n = sample of grocery shoppers = 101

Now, the probability that the sample proportion exceeds 0.16 is given by = P(\(\hat p\) > 0.16)

  P(\(\hat p\) > 0.16) = P( \(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) > \(\frac{0.16-0.13}{\sqrt{\frac{0.16(1-0.16)}{101} } }\) ) = P(Z > 0.82) = 1 - P(Z \(\leq\) 0.82)

                                                               = 1 - 0.7939 = 0.2061

The above probability is calculated by looking at the value of x = 0.82 in the z table which has an area of 0.7939.

Let the random variables x and y have joint pdf as follows: f(x,y) = 1/5(11x^2 + 4y^2) so Cov(x,y) (round off to third decimal place) is 0.241.

The covariance formula in statistics is used to evaluate the relationship between two variables. In essence, it serves as a gauge for the variation between two variables. Covariance is calculated by multiplying the units of the two variables, and it is expressed in units. Any positive or negative value might be the variance.

E[(X−EX)(Y−EY)]

=E[XY−X(EY)−(EX)Y+(EX)(EY)]

=E[XY]−(EX)(EY)−(EX)(EY)+(EX)(EY)

=E[XY]−(EX)(EY).

E(Y) = ∫ 1/x dx = ∫ 11/5 = ln 11/5 = 0.788

E(XY) = E[X 1/X]= 1

It is feasible to get the correlation coefficient formula from the covariance using the aforementioned formula, and vice versa. Units of covariance are calculated by multiplying the units of the two provided variables.

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Answer:

7

mark me as brainliest please

Step-by-step explanation:

The graph of the translated function is g ( x ) = ( x + 5 )² + 2

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x²

On simplifying , we get

The function is translated 5 units to the horizontal left direction:

And , when the function is translated 2 units in the vertical upward direction:

So , the translated function is

g ( x ) = ( x + 5 )² + 2

Now , the vertex of the function g ( x ) = ( x + 5 )² + 2 is (-5, 2)

Hence , the graph of the function is plotted and g ( x ) = ( x + 5 )² + 2

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Answer:

\(y =\frac{x}{4}\)

Step-by-step explanation:

We are given several functions, and we want to figure out which one is linear.

A linear function has both of its variables (x and y) with a power of 1. Variables with other powers do not mean that the function is linear.

Let's go through the list.

Starting with \(y=\frac{3}{x} -7\), we can see that x is in the denominator. If this is the case, it means that the power of x is -1.

Even though y has a power of 1, this is NOT linear, because x has a power of -1.

Now, with y=√x-2, this is also not linear. This is because √x = \(x^\frac{1}{2}\), even though y has a power of 1.

For x² - 1 = y, we can clearly see that x has a power of 2, while y has a power of 1. This means that the function is not linear.

This leaves us with \(y = \frac{x}{4}\). x is in a fraction, however it is not in the denominator. This means that the power of x in this function is 1. We can also see that the power of y in this function is 1.

This means that \(y=\frac{x}{4}\) is linear.

Answer:

The answer is 1 or A.

Step-by-step explanation:

53 is a prime number meaning the only multiple it has is 1 and itself.

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Answer:

The speed of Todd's snowmobile was 22 miles an hour

Step-by-step explanation:

:))

The speed of Todd's automobile is 31 miles per hour.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that It took Todd 11 hours to travel over pack ice from one town in the Arctic to another town 330 miles away. During the return journey, it took him 15 hours.

For the first journey,

v₁ + v₂ = 330 / 11    ......................( 1 )

For the return journey,

v₂ - v₁ = 330 / 15 .........................( 2 )

From equation ( 1 ) and equation ( 2 ),

2v₂ = ( 330 / 11 ) + ( 330 / 15 )

2v₂ = ( 330 ) ( 31 / 165 )

v₂ = 165 ( 31 / 165 )

v₂ = 31 miles per hour

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Using the inverse of the function from the table, the value of f⁻¹(4) is 107/3

The inverse of a function is a new function that "undoes" the original function. It reverses the mapping of inputs and outputs, allowing you to find the original input value when you know the output value.

In this problem, we have to use the table to find the original function which is f(x) and use it to find the inverse of the function;

Taking two points from the table;

m = y₂ - y₁ / x₂ - x₁

m = 0 - (-3) / -9 - (-11)

m = 3 / 20

Using the slope and one point on the table;

y = mx + x

-3 = 3/20(-11) + c

-3 = -1.65 + c

c = -3 + 1.65

c = -1.35

Putting the slope and y - intercept together;

y = 3/20x - 1.35

y = 3/20x - 27/20

f(x) = 3/20x - 27/20

Taking the inverse of the function;

f⁻¹(x) = (20x + 27)/3

To find the value of f⁻¹(4), we just need to substituting the value of x in the function;

f⁻¹(4) = (20(4) + 27)/3

f⁻¹(4) = 107/3

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The probability of all three of the selected homes having a security system is 0.3277, the probability of none of the three selected homes having a security system is 0.0414, and the probability of at least one of the selected homes having a security system is 0.9709. The events are dependent.

The probability of all three of the selected homes having a security system is 0.3277, which can be calculated using the formula P(A and B and C) = P(A) x P(B) x P(C). In this case, P(A) is the probability of the first home having a security system, which is 8/11 (since 8 out of 11 homes have a security system). P(B) is the probability of the second home having a security system, which is 7/10 (since 7 out of 10 remaining homes have a security system). P(C) is the probability of the third home having a security system, which is 6/9 (since 6 out of 9 remaining homes have a security system). Therefore, P(A and B and C) = (8/11) x (7/10) x (6/9) = 0.3277.

The probability of none of the three selected homes having a security system is 0.0414, which can be calculated using the formula P(A and B and C) = P(A') x P(B') x P(C'). In this case, P(A') is the probability of the first home not having a security system, which is 3/11 (since 3 out of 11 homes do not have a security system). P(B') is the probability of the second home not having a security system, which is 3/10 (since 3 out of 10 remaining homes do not have a security system). P(C') is the probability of the third home not having a security system, which is 3/9 (since 3 out of 9 remaining homes do not have a security system). Therefore, P(A and B and C) = \((3/11) x (3/10) x (3/9) = 0.0414\).

The probability of at least one of the selected homes having a security system is 0.9709, which can be calculated using the formula P(A or B or C) = 1 - P(A' and B' and C'). In this case, P(A' and B' and C') is the probability of none of the three selected homes having a security system, which is 0.0414 (as calculated above). Therefore, P(A or B or C) = 1 - 0.0414 = 0.9709.

The events are dependent because each selection is affected by the previous selections. For example, the probability of the second home having a security system is affected by whether or not the first home had a security system. If the first home had a security system, then there are 7 out of 10 remaining homes with a security system; if the first home did not have a security system, then there are 8 out of 10 remaining homes with a security system.

The probability of all three of the selected homes having a security system is 0.3277, the probability of none of the three selected homes having a security system is 0.0414, and the probability of at least one of the selected homes having a security system is 0.9709. The events are dependent.

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Answer:

Oldest to newest:

10^-35, 10 ^-10, 0

Step-by-step explanation:

Scientific notation

To figure out the power of 10 think "how many places do I move the decimal point?"

When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.

When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.

Answer:

y = x + 7

Step-by-step explanation:

Your original equation was:

y - 3 = (x+4)

First distribute

= (x+4)

Since there is no a value, then there is an invisible one and your result is:

y - 3 = x + 4

Then add 3 to both sides to get:

y = x +4 +3

y = x + 7

Since the slope-intercept form of a line is y = mx + b

where m is the slope and b is the intercept, then your equation is now in slope-intercept form.

Hope this helps! =D

Answer:

Length of a Road

Step-by-step explanation: No man that has ever lived (Well unless they're a nephilim or smth) is over a mile tall. Swimming pools and buildings aren't usually big enough to be measured in miles unless they're either a skyscraper or a Wisconsin water park attraction.

Answer:

You can spend all of the money by getting 1 sandwich and 2 things of chips

Step-by-step explanation:

1 sandwich =4$

1 bag of chips =3$

4 + 3 =7

7+ 3= 10

Steps to solve:

f(x) = 1/2(4 - x) when x = 2

~Substitute

f(2) = 1/2(4 - 2)

~Subtract whats in parenthesis

f(2) = 1/2(2)

~Multiply

f(2) = 1

Best of Luck!

Answer:

1

Step-by-step explanation:

substitute \(x\) with 2

\(\frac{1}{2}(4-2)\)

subtract 2 from 4

\(\frac{1}{2} (2)\)

multiply \(\frac{1}{2}\) by 2 or cancel the common factor

1

Answer:

Step-by-step explanation:

1.) 6

2.) A

3.)5

Answer:

8 because 56/7 = 8

Step-by-step explanation:

Answer:

8.04% to 15.96%

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

Suppose that you take a random sample of 259 people leaving a grocery store over the course of a day and find that 12% of these people were overcharged.

This means that \(n = 259, \pi = 0.12\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a p-value of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 - 1.96\sqrt{\frac{0.12*0.88}{259}} = 0.0804\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 + 1.96\sqrt{\frac{0.12*0.88}{259}} = 0.1596\)

So 8.04% to 15.96%

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

Answer:

Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)

Step-by-step explanation:

As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.

11^2 + 5^2 = AC^2

121 + 25 = AC^2

146 = AC^2

sqrt(146) = AC^2

Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)

Answer:

i believe the first one should be 20 5 since its supposed to be in expanded form but i dont know the second one sorry hope you do good

Step-by-step explanation:

Answer:

Step-by-step explanation:

Function representing the bacterial growth has been given as,

\(b_1(t)=1200(1.8)^t\)

a). Here 1200 represents the initial number of bacteria taken for the study (1).

b). 1.8 represents the growth factor by which the population of the bacteria is multiplying.

c). Second study is modeled by the function given as,

  \(b_2(t)=1000(1.8)^t\)

  Here, initial population of bacteria = 1000

  Difference in 1200 and 1000 in two studies means → Second study was conducted on 1000 bacteria while in study (1) number of bacteria were 1200.

The experimental probability that the next student will register for German is 9/79.

What is probability?

To find the experimental probability that the next student will register for German, we need to divide the number of students who have registered for German by the total number of students who have registered so far:

P(German) = number of students who have registered for German / total number of students who have registered

P(German) = 108 / (108 + 360 + 21 + 459) [Adding all the students who registered for each language]

P(German) = 108 / 948

P(German) = 9/79

Therefore, the experimental probability that the next student will register for German is 9/79.

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3/16 into decimal form is 0.1875

Answer:

The 3/16into decimal form is 0.1875

So the different number has a 4 with a value of 40.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first identify the place value of the digit 4 in the given number.

The digit 4 is in the hundreds place in the number 431.67, so its value is 4 x 100 = 400.

According to the problem statement, the 4 in the different number represents a value which is one-tenth of the value of the 4 in 431.67. Therefore, the value of the 4 in the different number is:

400/10 = 40

To determine the value of the different number, we need to look at the other digits in the number. Since we don't have any information about the other digits, we cannot determine the value of the different number. The answer is that the value of the different number cannot be determined with the information given.

Therefore, So the different number has a 4 with a value of 40.

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Answer:

option D

Step-by-step explanation:

Angle ADF and Angle FDE

ADF+ FDE

Answer:

D

Step-by-step explanation:

The mathematics SAT score representing the top 1% of all scores is approximately 780.

a. The random variable in this case is the mathematics SAT score.

b. To find the probability that a person has a mathematics SAT score over 700, we need to calculate the z-score first.

The z-score is calculated as \(\frac{(X - \mu )}{\sigma}\),

where X is the value we're interested in, μ is the mean, and σ is the standard deviation.

In this case, X = 700, μ = 514, σ = 117.

Using the formula, the z-score is \(\frac{(700 - 514)}{117 } = 1.59\).

To find the probability associated with this z-score, we can consult a standard normal distribution table or use a calculator.

The probability is approximately 0.0564 or 5.64%.

c. To find the probability that a person has a mathematics SAT score of less than 400, we again calculate the z-score using the same formula.

X = 400, μ = 514, and σ = 117.

The z-score is \(\frac{(400 - 514) }{117 } = -0.9744\).

Looking up the probability associated with this z-score, we find approximately 0.1635 or 16.35%.

d. To find the probability that a person has a mathematics SAT score between 500 and 650, we need to calculate the z-scores for both values.

Using the formula, the z-score for 500 is \(\frac{(500 - 514)}{117 } = -0.1197\),

and the z-score for 650 is \(\frac{(650 - 514)}{117 } = 1.1624\).

We can then find the area under the normal curve between these two z-scores using a standard normal distribution table or calculator.

Let's assume the probability is approximately 0.3967 or 39.67%.

e. To find the mathematics SAT score that represents the top 1% of all scores, we need to find the z-score corresponding to the top 1% of the standard normal distribution.

This z-score is approximately 2.33.

We can then use the z-score formula to calculate the corresponding SAT score.

Rearranging the formula,

\(X = (z \times \sigma ) + \mu\),

where X is the SAT score, z is the z-score, μ is the mean, and σ is the standard deviation.

Substituting the values,

\(X = (2.33 \times 117) + 514 = 779.61\).

Rounded to the nearest whole number, the mathematics SAT score representing the top 1% of all scores is approximately 780.

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If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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