John is thinking of a number. He gives the following 3 clues. ``My number has 125 as a factor. My number is a multiple of 30. My number is between 800 and 2000.'' What is John's number?

Please answer correctly

Answer:

y^18

Step-by-step explanation:

(y^2)^5 x y^8

Assuming the x is multiplication

We know (a^b)^c = a^(b*c)

(y^2)^5 = y^(2*5) = y^10

We are multiplying this by y^8

We know a^b * a^c = a^(b+c)

y^10* y^8 = y^(10+8) = y^18

Assuming the x is a variable

We know (a^b)^c = a^(b*c)

(y^2)^5 = y^(2*5) = y^10

We are multiplying this by y^8

We know a^b * a^c = a^(b+c)

y^10* y^8 = y^(10+8) = y^18

This is multiplies by x

x y^18

Answer:

[tex]\Huge \boxed{xy^1^8}[/tex]

Step-by-step explanation:

Exponent rule: [tex]\displaystyle (a^b)^c=a^b^c[/tex]

[tex]\displaystyle y^2^\times^5[/tex]

Multiply.

[tex]\displaystyle 2\times5=10[/tex]

[tex]\displaystyle y^1^0^+^8[/tex]

Add.

[tex]\displaystyle 10+8=18[/tex]

[tex]\large \boxed{xy^1^8}[/tex], which is our answer.

Answer:

10 ≥ ⅛c + ¼d

Step-by-step explanation:

They budgeted up to 10 gallons of water, meaning that it CANNOT exceed 10. When turned around, you will see that everything is less than or equal to 10.

I am joyous to assist you anytime.

Complete question:

A small kennel has budgeted to provide 10 gallons of water for its animals. Each cat receive one eight of a gallon per day and each dog receives one fourth of a gallon per day . Which inequality correctly represent the scenario.

a. 10 < -1/8c - 1/4d

b.  10 ≤  1/8c + 1/4d

c  10 ≥ -1/8c - 1/4d

d. 10 ≥ 1/8c + 1/4d

Answer:

d. 10 ≥ 1/8c + 1/4d

Step-by-step explanation:

The kennel was budgeted to provide 10 gallons of water for its animals. The cat receives  1/8 of a gallon per day and each dog receive 1/4 of a gallon per day.

Since 10 gallons was budgeted for the animals the sum of the a gallon per day for the cat and dog will most likely not exceed 10 gallons. The animals will most likely consume less than the budgeted value or equals to the budgeted value.    

note that the sum of 1/8 of a gallon  for the cat and 1/4 of a gallon for the dog should be either less than 10 or equals to 10. This means  10 ≥ 1/8c + 1/4d .

Answer:

m∠1 = 50°

m∠2 =  130°

Step-by-step explanation:

The measure of the angle formed by 2 chords  that intersect inside the circle is 1/2 the sum of the chords' intercepted arcs.

m∠1 = (53+47)/2 = 50°

m∠1 + m∠2 = 180°   ⇒  m∠2 = 180 - m∠1 = 180 - 50 = 130°

The measure of angle 2 (θ2) is given as 312°. To determine the measure of angle 1 (θ1), additional information or context is needed as it is not provided directly in the question or accompanying information.

The question seems to be about finding the measures of angles angle 1 (θ1) and angle 2 (θ2) in a physics context, possibly related to momentum or forces. Given that Ø2 is provided as 312°, we can infer that this is the measurement of angle 2 (θ2). This angle is said to be in the fourth quadrant, which is consistent with the positive counterclockwise definition of angle measurement. For the measure of angle 1 (θ1), there's not enough direct information provided in the question or the reference information to determine its measure. More context or additional data would be necessary to solve for θ1. If the scenario is about a momentum conservation problem, the relationship between angles might be set by the conservation laws for linear momentum in the x and y directions. However, without additional information or clarification from the student's initial query, we would only be speculating on the measure of θ1.

the name of the plane is C. plane EGF

Answer:

(5/2 ,  3/2)

or

(2.5  , 1.5)

(These are the same point; just one is in fraction form and the other in decimal)

Step-by-step explanation:

I could be wrong but I think you want to solve the system

x+y=4

x-y=1

The cool thing about this system it is already set up for elimination (some people call it linear combination).  This means when you add the equations together, a variable will get eliminated allowing you to solve for the other.

x+y=4

x-y=1

----------Add equations.

2x+0=5

2x    =5

 x     =5/2

 x     =2.5

So plug in your x into either one of the equations and solve for y.

x+y=4

2.5+y=4

y=4-2.5

y=1.5

So the solution is (2.5 , 1.5)  or (5/2, 3/2).

Answer:

Its 7.7, 7, 0.6, -0.7

it's d, since the area of a circle is radius squared times pi

3.14×5^2= 78.4

Answer:

(1)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

We are looking for an equation of the form

y = 4x ± c ( since slope m = 4)

The only equation which fits the description is

y = 4x - 3 → (1)

Answer:

7c^2d-7c+4d-10

Step-by-step explanation:

Start off with the term that has c^2 in it. 5c^2d + 2C = 7c^2d, then since you have multiple choice, the d value differs between the two answer choices that have 7c^2d so you can do +3d +d to get +4d to get the fourth answer choice.

To check your work, you can add/subtract each term to see if you get 7c^2d-7c+4d-10

Final answer:

To find the mean absolute deviation (MAD) for the data set, calculate the mean, subtract it from each data value to find deviations, take the absolute values, and then find their mean. The MAD for the data set 12, 17, 16, 9, 18, 10, 9 is approximately 3.43.

Explanation:

To find the mean absolute deviation (MAD) for a given data set, we follow these steps:

Calculate the mean (average) of the data set.

Subtract the mean from each data value to find the deviations.

Take the absolute value of each deviation.

Find the average of these absolute values to determine the MAD.

The data set provided is: 12, 17, 16, 9, 18, 10, 9. First, let's calculate the mean:

(12 + 17 + 16 + 9 + 18 + 10 + 9) / 7 = 91 / 7 = 13

Next, we'll find the absolute deviations from the mean:

|12 - 13| = 1

|17 - 13| = 4

|16 - 13| = 3

|9 - 13| = 4

|18 - 13| = 5

|10 - 13| = 3

|9 - 13| = 4

Lastly, we calculate the mean of these absolute values:

(1 + 4 + 3 + 4 + 5 + 3 + 4) / 7 = 24 / 7 ≈ 3.43

The mean absolute deviation of the data set is approximately 3.43.

Final answer:

The mean absolute deviation of the data set is calculated by finding the mean, determining the absolute deviation of each value from the mean, and then taking the mean of those deviations. For this set, the mean absolute deviation is 3.43.

Explanation:

To find the mean absolute deviation, we follow these steps:

First, we calculate the mean of the data set: (12 + 17 + 16 + 9 + 18 + 10 + 9) ÷ 7 = 91 ÷ 7 = 13.

Next, we find the absolute deviation of each data point from the mean:

Add these absolute deviations: 1 + 4 + 3 + 4 + 5 + 3 + 4 = 24.

Finally, we find the mean of these absolute deviations: 24 ÷ 7 = 3.43 (rounded to the nearest hundredth).

The mean absolute deviation for the data set is 3.43.

Answer:

A) x greater than or equal to −3

Step-by-step explanation:

We have the following inequality:

7 − 9x − (x + 12) ≤ 25

Solving the inequation, we have:

7 − 9x − x - 12 ≤ 25

-10x ≤ 30

-x ≤ 3

x≥-3

Therefore the result is option A) x greater than or equal to −3

Answer:

B.

Step-by-step explanation:

7-9x - (x+12) ≤ 25

7 - 9x - x - 12 ≤ 25

-10x - 5 ≤ 25

-10x ≤ 25 +5

x ≥ 30/-10

x ≥ -3.

So, the incorrect answer is B.

Answer:

Isolate the variables in all cases. Note the equal sign, what you do to one side, you do to the other.

a) 3x = 18

Isolate the variable, x. Divide 3 from both sides:

(3x)/3 = (18)/3

x = 18/3

x = 6

b) 2x = 9

Isolate the variable, x. Divide 2 from both sides:

(2x)/2 = (9)/2

x = 9/2

x = 4.5

c) (x/5) = 7

Isolate the variable, x. Multiply 5 to both sides:

(x/5)(5) = (7)(5)

x = 7 * 5

x = 35

d) x/2 = 6.5

Isolate the variable, x. Multiply 2 to both sides:

(x/2)(2) = (6.5)(2)

x = 6.5 * 2

x = 13

~

a) 3x = 18

x = 6

____________

b) 2x = 9

x = 4.5

____________

c) (x/5) = 7

x = 35

____________

d) x/2 = 6.5

x = 13

____________

Have a great day!

Answer:

The measure of angle A is 51 degrees

Answer:

The measure of an angle A=[tex]1^{\circ}[/tex].

Step-by-step explanation:

We are given that an angle [tex]95^{\circ}[/tex] and two sides are 7  in and 9 in in a given figure.

We have to find the value of measurement of angle A.

To find the measurement of angle A we apply sine law.

Sine law:[tex]\frac{a}{sin \alpha}=\frac{b}{sin\beta}=\frac{c}{sin \gamma}[/tex]

Where  side a is opposite to angle [tex]\alpha[/tex]

Side b is opposite to angle [tex]\beta[/tex]

Side c is opposite to angle[tex] \gamma[/tex]

We are given an angle 95 degrees and opposite side of given angle is 9 in and the angle A is opposite to side 7 in.

Substituting the values then we get

[tex]\frac{9}{sin 95^{\circ}}=\frac{7}{sin A}[/tex]

[tex]\frac{9}{0.683}=\frac{7}{sin A}[/tex]

[tex] sin A=\frac{7\times 0.683}{9}[/tex]

[tex] sin A=\frac{4.781}{9}=\frac{4781}{9000}[/tex]

[tex] sin A=0.531[/tex]

[tex] A= sin^{-1}(0.531)[/tex]

[tex] A=0.56^{\circ}[/tex]

[tex] A= 1^{\circ}[/tex]

Hence, the measure of an angle A=[tex]1^{\circ}[/tex].

Answer:

A. By SAS only

Step-by-step explanation:

Side Side Side postulate (SSS) states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

In triangles ABC and AED:

So, SAS postulate can be applied.

SSS postulate cannot be applied, because it is not given that sides AB and AE are conruent.

Answer:

ΔABC and ΔAED are congruent to each other by SAS rule.

Step-by-step explanation:

We are given a figure in the question.

The figure shows that:

AC = AD, BC = ED, ∠BAC = ∠EAD

We are also given that triangle BCA is congruent to triangle EDA.

Now, we need to prove that triangle ABC is congruent to triangle AED.

We will use SAS criterion of congruence.

In ΔABC and ΔAED,

AC = AD, ∠BAC = ∠EAD, , BC = ED( all given in the figure)

Hence, the two triangles are congruent to each other by SAS rule.

Answer:

$60 a month is the answer

Step-by-step explanation:

$200 down payment leaves you with $300's to pay still. Divide the $300's by 5 and that leaves you with $60 a month.

Answer:

The common ratio is -3

Step-by-step explanation:

we know that

In a Geometric Sequence each term is found by multiplying the previous term by a constant called the common ratio

In this problem we have

-2,6,-18,54...

Let

a1=-2, a2=6,a3=-18,a4=54

a2/a1=6/-2=-3

a3/a2=-18/6=-3

a4/a3=54/-18=-3

Each term (except the first term) is found by multiplying the previous term by -3

therefore

we have a geometric sequence and the common ratio is -3

Answer:

2.5 gallons

Step-by-step explanation:

We need to go 100 miles

Write the proportion

Picking a point on the graph (40 miles, 1 gallon)

100 miles         40 miles

-------------- = -------------

x gallons         1 gallon

Using cross products

100 * 1 = 40 *x

Divide each side by 40

100/40 = 40x/4

2.5 =x

We need 2.5 gallons to go 100 miles

Answer: Based on the graph, the car requires 2.5 gallons of fuel to travel 100 miles.

Look at the picture below for help. The blue dot represents were the two points meet. We are trying to figure out how many gallons are for the 100 miles, 100 miles would be on the side that says distance (miles). That is were you start. Find point 100 on the distance (miles) side and just draw a straight line, stopping when you hit the black line on the graph. Once done, draw another line going straight down from the black line, and you get your answer of 2.5

Answer: 2.5

Hope it helps!

Answer:

1)all numbers less than -5 and greater than 5

Step-by-step explanation:

We are given

x<-5

and

x>5

So

Looking at both the inequalities one by one, The solution will consist of all the numbers that are less than -5 and greater than 5. The numbers between -5 and 5 will be excluded from the solution..

Hence,

1)all numbers less than -5 and greater than 5

is correct ..

The intersection of the sets {X|X<-5} and {x|x>5}, which represents numbers that fulfill both conditions, results in no real numbers, or the empty set.

The solution set of the given intersection of the two sets {X|X<-5} and {x|x>5} is defined as the set of numbers that fulfill both conditions: numbers less than -5 and numbers greater than 5.

However, there are no real numbers that can be both less than -5 and greater than 5 at the same time. Therefore, when these two sets intersect, the result is an empty set.

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The expression will be    [tex]\[ (-125) \cdot c^3 \][/tex]

The exponential form of the expression [tex]\((-5)(-5)(-5) \cdot c \cdot c \cdot c\)[/tex] can be calculated as follows:

First, simplify the multiplication of the negative numbers:

[tex]\[ (-5)(-5)(-5) = (-125) \][/tex]

Next, simplify the multiplication of the variables:

[tex]\[ c \cdot c \cdot c = c^3 \][/tex]

Now, combine the results:

[tex]\[ (-125) \cdot c^3 \][/tex]

The final exponential form of the expression is:

[tex]\[ (-125) \cdot c^3 \][/tex]

Here's a step-by-step explanation of the calculation:

1. Multiply the negative numbers:

[tex]\[ (-5)(-5) = 25 \][/tex]

  Multiply 25 by -5 again:

[tex]\[ 25 \cdot (-5) = -125 \][/tex]

2. Multiply the variables:

[tex]\[ c \cdot c = c^2 \]\\ Multiply \(c^2\) by c again:\\ \[ c^2 \cdot c = c^3 \][/tex]

3. Combine the results:

[tex]\[ (-125) \cdot c^3 \][/tex]

That's the final exponential form of the given expression.

Complete Question:

What is the exponential form of the following expression

(-5)(-5)(-5) •c•c•c

Answer:

y = 6x

Step-by-step explanation:

Find slope

Formula

0 - (-3) = 3

0 - (-1/2) = 1/2

Simplify

3/(1/2) = 6

y = 6x

y-intercept

The line crosses the origin, so the y-intercept is 0.

Answer

y = 6x

Answer: I know you prob don't need this answer anymore but this is for the people who look it up and need it.

Step-by-step explanation:

It's 2.1*10^-3

[tex]2.1 \times 10^{-3[/tex] is the scientific notation of the given number.

To write in scientific notation,

So, in scientific notation, 0.0021 is written as [tex]2.1 \times 10^{-3[/tex].

Learn more about Mathematical operations here:

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The little red lines on each side of the triangle mean that the sides are all equal.

A triangle that has all 3 sides the same is an equilateral triangle.

Because all the sides are identical all 3 inside angles are also identical.

180 / 3 = 60 degrees

The outside angle which is DEF would equal 180 - the inside angle.

DEF = 180 - 60 = 120.

The answer is D.

Answer:

120°

Step-by-step explanation:

It is an equilateral triangle, so all its sides and internal angles measure the same.

The sum of the internal angles of a triangle must be 180°, so each internal angle measures 60°.

The DEF angle is an external angle of that triangle, we can use the next property:

An external angle of a triangle is the sum of the internal angles opposed to it.

The two opposite angles to DEF are DCE and CDE:

DEF = DCE + CDE = 60 ° + 60 ° = 120°

Another way to find this same result is to notice that DEF + DEC total 180° since they form a straight line, and we know that DEC measures 60°

So:

DEF + DEC = 180 °

DEF = 180 ° - DEC

DEF = 180 ° -60 °

DEF = 120 °

Step-by-step explanation:

A = P (1 + r)^t

Given that P = $1,200,000, r = 0.1037, and t = 5:

A = $1,200,000 (1 + 0.1037)^5

A = $1,965,334.41

Round as needed.

Answer:

The forecasted sales for 2004 is $1965281.

Step-by-step explanation:

The annual sales in 1999 were = $1,200,000

Let geometric mean growth rate = r

we have now p = $1,200,000,

r = 10.37% or 0.1037

t = 5:

We have the formula Amt= [tex]p(1+r)^{t}[/tex]

Amt =[tex]1200000(1+0.1037)^{5}[/tex]

Solving this we get;

[tex]1200000\times1.63777=1965324[/tex]

A = $1,965,324

Answer:

[tex]\large\boxed{C.\ 75<x<110\ and\ 0<y\leq50}[/tex]

Step-by-step explanation:

x - the temperature

y - the number of people

the temperature is between 75 degrees and 110 degrees:

75 < x < 110

the room for 50 people:

0 < y ≤ 50

Answer:

C

Step-by-step explanation:

We know x is more than 75

75<x

and there is room for 50 people and we have to use y

0<y<110

  _^

The only possible answer is C hope this helps :)

Final Answer:

The probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.

Explanation:

To find the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F, we can use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed if the sample size is sufficiently large. In this case, we can assume a sample size of 19 is large enough.

Given:
- Population mean (μ) = 98.20°F
- Population standard deviation (σ) = 0.62°F
- Sample size (n) = 19
- Target sample mean (X) = 98.50°F

We need to do the following steps:

1. Calculate the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the sample mean.
  SEM = σ / √n

2. Calculate the Z-score for the sample mean of 98.50°F. The Z-score represents how many standard errors the value is away from the population mean.
  Z = (X - μ) / SEM

3. Use the Z-score to find the area to the left of it on the standard normal distribution, which represents the probability that the sample mean is less than 98.50°F.

Let's calculate each step:

1. Calculate SEM:
  SEM = σ / √n
      = 0.62 / √19
      ≈ 0.62 / 4.3589
      ≈ 0.1422

2. Calculate Z-score:
  Z = (X - μ) / SEM
    = (98.50 - 98.20) / 0.1422
    ≈ 0.30 / 0.1422
    ≈ 2.1095

3. Lastly, to find the probability that the sample mean is less than 98.50°F, we look up the Z-score in the standard normal distribution table (Z-table), use statistical software, or a calculator that provides the cumulative distribution function (CDF) for the normal distribution.

A Z-score of 2.1095 corresponds to a probability of about 0.9826 (using Z-table or a calculator).

Therefore, the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.

Among the options given, the closest to 0.9826 is 0.9826 itself. Hence, that is the correct answer.

Answer:

45

Step-by-step explanation:

Here are two ways of solving this problem.

Method 1:

Term 1 is 2.

Term 2 is 3.

Term 3 is 4.

Each term is 1 more than the term number.

The 44th term is 45.

Method 2:

Using the hint

Find the common difference: 5 - 4 = 1

The common difference is 1.

1st term + (common difference)(desired term - 1)

2 + 1(44 - 1) = 2 + 43 = 45

Answer: 45

Answer:

1/6

Step-by-step explanation:

(1/2)/3

To solve, note that there are 2 denominators in all. To solve, multiply the denominators together:

(1/2)/3 = 1/(2 * 3) = 1/6

1/6 is your answer.

~

Answer:

0.16

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Exact form: 1/6

Decimal form: 0.16

Answer:

x1/2

Step-by-step explanation:

Simplify the following:

(3 x1)/6

Hint: | In (x1×3)/6, divide 6 in the denominator by 3 in the numerator.

3/6 = 3/(3×2) = 1/2:

Answer:  x1/2

For this case we have the following expression:

[tex](x ^ {\frac {1} {6}}) ^ 3[/tex]

We have that by definition of properties of powers it is fulfilled that:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Now we have to, by applying the property:

[tex](x ^ {\frac {1} {6}}) ^ 3 = x ^ {\frac {3} {6}}[/tex]

Simplifying:

[tex]x ^ {\frac {3} {6}} = x ^ {\frac {1} {2}}[/tex]

Answer:

[tex]x ^ {\frac {1} {2}}[/tex]

Answer:

y = - 10x - 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here slope m = - 10, hence

y = - 10x + c ← is the partial equation

To find c substitute (- 1, 4) into the partial equation

4 = 10 + c ⇒ c = 4 - 10 = - 6

y = - 10x - 6 ← equation of line

Answer:

Option B

Step-by-step explanation:

Given:

total No. of students liking peas= 78

total no. of male students= 100

total number of students= 200

no. of male students liking peas= 42

Now we need to find are liking peas and being male independent or dependent events

P(likes peas)= 78/00

                    =0.39

                    =39%

P(likes peas/male) = 42/100

                                = 42%

as the two probabilities are not equal the two events are dependent.

Hence option B is correct: Dependent;

since these probabilities are not equal, the events are dependent!

Answer:

B

Step-by-step explanation:

In the Dependent case  the following relation must be satisfied:

p(a|b) = p(a∩b)/p(b)

Or, in terms of this problem:

p(like peas|male) = p(like peas∩male)/p(male)

The probabilities of this events are:

p(like peas|male) = 42/100 = 42%

p(like peas∩male) = 42/200 = 21%

p(male) = 100/200 = 50%

Therefore, the events are dependent

In the Independent case  the following relation must be satisfied:

p(a|b) = p(a)

or

p(like peas|male) = p(like peas)

p(like peas) = 78/200 = 39%

The equation is not satisfied.