Marta’s jump rope is 10 inches shorter than three times the length of David’s rope.

If both of their ropes lay together end to end, they measure 120 inches long. How long is each person’s jump rope?

Check the picture below.

[tex]\cfrac{24+x}{24}~~ = ~~\cfrac{36+12}{36}\implies \cfrac{24+x}{24}=\cfrac{48}{36}\implies \cfrac{24+x}{24}=\cfrac{4}{3} \\\\\\ 72+3x=96\implies 3x=24\implies x=\cfrac{24}{3}\implies x=8[/tex]

Answer:

Value Cars

Step-by-step explanation:

A1 Taxis: A 5-mile journey costs £15

15 divided by 5 = £3 per mile

Crazy Cabs: A 4-mile journey costs £13

13 divided by 4 =  £3.25 per mile

Value Cars: A 10-mile journey costs £28

28 divided by 10 = £2.80 per mile

Option A If the adage regarding the number 403, 043 is accurate, the three on the left is 100 times bigger than the three on the right.

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Answer:

The equation for babysitting can be written as y = 20x + 5, where y is the total cost and x is the number of hours.

The slope of the equation is 20, which represents the rate of change in the total cost (y) with respect to the number of hours (x).

The slope represents the rate at which the total cost changes for each unit change in the number of hours. In this case, for each hour of babysitting, the total cost increases by $20.

The y-intercept of the equation is 5, which represents the cost when x = 0, i.e. when there is no babysitting time.

The y-intercept represents the starting value of the total cost, in this case, the amount charged for babysitting even when there is no babysitting time.

Step-by-step explanation:

The number of people in a household with 2.5 pounds of waste are = 11

and we calculate this on the basis of question below

Predict the number of people in a household with 2.5 pounds of waste pounds of waste 0.27,1.41,2.19,2.83,2.19,1.81,0.85,3.05. In Home 2 3 3 6 4 2 1 5

pound    0.27  ,1.41,  2.19  ,2.83  ,2.19  ,1.81  ,0.85,  3.05  

people      2          3      3       6        4        2        1       5

so now the question is complete

in pound section we have to take care which value are greater than 2.5

so 2.83 and 3.05 is greater than 2.5 so here  number of people who's home have greater than 2.5 pound of waste are 6+6=11

and rest people who's home has less than 2.5 pound waste are 2+3+3+4+2+1=15

so final ans is 11.

so this question was in complete and this ans is valid for this Question only.

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Step-by-step explanation:

length = width + 6

the perimeter of a rectangle is

2×length + 2×width

by using the first equating as identity in the second we get

36 = 2×(width + 6) + 2×width =

= 2×width + 12 + 2×width = 4×width + 12

24 = 4×width

width = 6 m

length = width + 6 = 6 + 6 = 12 m

he dimensions of the rectangular room are 6 meters by 12 meters of the rectangular room is 6 meters longer than it is wide, and its perimeter is 36 meters by solving equations and geometric measurements.

Given that the room is 6 meters longer than it is wide, we can represent the width as W. Therefore, the length of the room would be W + 6.

The perimeter of a rectangle is calculated by adding all four sides, which in this case is given as 36 meters. We can express this as an equation:

Perimeter = 2 * (Length + Width)

Substituting the values, we get:

36 = 2 * (W + (W + 6))

Simplifying the equation further, we have:

36 = 2 * (2W + 6)

Dividing both sides of the equation by 2, we get:

18 = 2W + 6

Subtracting 6 from both sides, we obtain:

12 = 2W

Dividing both sides by 2, we find:

W = 6

Now that we have the width, we can calculate the length:

Length = Width + 6 = 6 + 6 = 12

Therefore, the dimensions of the rectangular room are 6 meters by 12 meters of the rectangular room is 6 meters longer than it is wide, and its perimeter is 36 meters by solving equations and geometric measurements.

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Answer:

Step-by-step explanation:

if 10,000/10, find 100drops by moving decimal place

100.00/0.10

so volume is 0.1 flOz

Answer:

Ten thousands

Step-by-step explanation:

20 x 1000 = 20,000 therefore, ten thousands

Answer:

1.6

Step-by-step explanation:

[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\\\=\frac{f(9)-f(1)}{9-1}\\ \\=\frac{15.8-3}{8}\\ \\=\frac{12.8}{8}\\ \\=1.6[/tex]

Answer:

1.  See below.

[tex]\textsf{2.} \quad \log_x256=\dfrac{1}{2}[/tex]

[tex]\textsf{3.} \quad x^6=1000000[/tex]

[tex]\textsf{4.} \quad \log_2\left(\dfrac{1}{64}\right)=x[/tex]

Step-by-step explanation:

Please note that this question is incorrect.  

I assume the question is missing an "x" term, since log₉27 ≠ -3.

Let's assume 27 should be "x":

[tex]\implies \log_9x=-3[/tex]

[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff b=a^c[/tex]

[tex]\implies x=9^{-3}[/tex]

If, however, the 9 is supposed to be "x":

[tex]\implies \log_x27=-3[/tex]

[tex]\implies x^{-3}=27[/tex]

Given exponential equation:

[tex]\sqrt{x}=256[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:[/tex]

[tex]\implies x^{\frac{1}{2}}=256[/tex]

[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies \log_x256=\dfrac{1}{2}[/tex]

Given logarithmic equation:

[tex]\log_x1000000=6[/tex]

[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies x^6=1000000[/tex]

Given exponential equation:

[tex]2^x=\dfrac{1}{64}[/tex]

[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies \log_2\left(\dfrac{1}{64}\right)=x[/tex]

Answer:

(9,7,10,8,7)

Step-by-step explanation:

range is the value of y.

No, AA Criterion should not be called the AAA Criterion, because we need only two angles to be equal to prove the similarity.

According to the AA triangle similarity criterion, two triangles are considered similar if their three angles are identical to one another. Equi-angular triangles are comparable in a nutshell.

Since just two pairs of angles must be equal in order for the third pair to be automatically equal thanks to the angle sum property of triangles, the proper term for this criterion would then be the AAA(Angle-Angle-Angle) criterion. However, we refer to it as the AA criterion instead.

Hence, no, because we need only two angles to be equal to prove the similarity.

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Answer: 11 (Or I'm wrong)

Step-by-step explanation: -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

The probability that Brad gets all five answers correct is 1/128.

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

true of false = 3

Multichoice = 2

So, the probability that Brad gets all five answers correct is (1/4)^2 * (1/2)^3 = 1/128.

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The sine function for a specified range of angles is shown graphically in the sine graph. A trigonometric graph's horizontal axis is the angle, which is typically denoted by the symbol, and the y-axis is the sine function of that angle.

To graph the sine function, we place the sine of each angle on the vertical y-axis and indicate the angles along the horizontal x axis.

The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: hypotenuse/perpendicular = sin. sin(n+2) = sin for each n.

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The exact binomial probability that the total number rolled will add up to 3 or less is 1/12.

The exact binomial probability that the total number rolled will add up to 3 or less is calculated as follows;

The total number that can be rolled with 2 dice is 2 to 12, with 7 being the most likely outcome (the sum of two dice has a maximum of 7).

The probability that the total number is 3 or less is the sum of the probabilities of rolling a 2 and a 1;

The probability P = (1/36) + (2/36)

P = 3/36

P = 1/12

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The diameter of the circle is 24 units.

In geometry, the circle is a curved and closed polygon whose boundary line is at equidistance from a point called the center.

A diameter is a line drawn through the circle's center and joining two points on its circumference. The diameter of a circle is twice its radius

The circumference of a circle is known as the circle's perimeter and is the distance a circle travels around its boundary line.

The formula for the circumference of a circle is given by

Here we have

The circumference of a circle is 75.4 units

Let 'r' be the radius of the circle

As we know Circumference of a circle = 2πr    

=> 2πr = 75.4

=> 2r(22/7) = 75.4

=> 2r = (75.4 × 7)/22  

=> 2r = [527.8]/22

=> 2r = 23.99  

=> 2r = 24 (approx)

Therefore,

The diameter of the circle is 24 units.

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The solution for the inequalities, y≥x+1​ is (0, 1) and (-1, 0).

and, solution for the inequalities, y≤x−3​ is (0, -3) and (3, 0).

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

y≤x−3​.........(1)

y≥x+1​.............(2)

If we solve the inequality using the graphical method we can see that the inequalities gives the parallel line.

Also, the solution for the inequalities, y≥x+1​ is (0, 1) and (-1, 0).

and, the solution for the inequalities, y≤x−3​ is (0, -3) and (3, 0).

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Answer:

8

Step-by-step explanation:

If my calculations are correct the third side is 8

The diagram that represent the distance and the journeys is added as an attachment

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

Using the above as a guide, we have the following:

Next, we create the diagram (see attachment)

The attached figure represents the required diagram

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Using the method of least squares, the faculty group obtained,  the estimated y-intercept of the line is For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000.

The relationship between the variables is calculated and represented as an equation in regression analysis. The dependent variable, independent variables, and line equation constants are all included in this equation. Variables may be related in ways that are linear, quadratic, polynomial, etc.

In this instance, the performance is the independent variable and the increase is the dependent variable. Simple linear regression is the name of the equation, which is shown as a straight-line equation.

Regression analysis makes use of the relationship between independent and dependent variables' relationship equation to forecast the values of the dependent variable y given the values of the independent variable x.

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If a ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. The fire travelled 31,968 meters.

Distance = d = v * t

Let v represent speed of the fire .

Where :

t = time elapsed in seconds = 20 * 60 = 1200 seconds

Using the tangent function:

d / v = tan(6°) - tan(4°)

Simplify this expression using the identity:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

Applying this to the above equation, we get:

d / v = (tan(6°) - tan(4°)) / (1 + tan(6°)tan(4°))

Using a calculator to evaluate the tangent values

d / v = 26.64 / v

d = 26.64 * v

Substituting the value of t, we get:

d = 26.64 * v

= 26.64 * 1200

= 31,968 meters (rounded to the nearest meter)

Therefore the fire travelled 31,968 meters.

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The complete question is:

A ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. Twenty minutes later the angle of depression was 6°. The fire travelled                         m (to nearest metre)

When converting 0.000056 into scientific notation, the decimal point will move 5 spaces to the right.

The resulting number in scientific notation would be 5.6 x 10^-5.

The function that represents the balance after t years is ,

FV = $470( 1.011)^4t

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

FV = Future value

P = Present value

R = interest rate

m = number of compounding

N = number of years

here, we have,

given that,

P = Present value= $470.

R = interest rate = 4.4%/4 =

m = number of compounding =4

N = number of years = t

FV = $470( 1.011)^4t

Hence,  The solution is, a function to represent the balance A in the account after t years is, FV = $470( 1.011)^4t

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The probability that a patient who has been diagnosed with cancer truly has the illness 0.406

It is known from prior experience that there is a 0.05 chance of choosing a cancer-positive adult over 40 in a certain area of the nation. What is the likelihood that an adult over the age of 40 will be given a cancer diagnosis if the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the probability of a doctor incorrectly diagnosing a person without cancer as having the disease is 0.06.

We wish to compute P(C | D) this time. Bayes rule is used in this process.

[tex]& P(C \mid D)=\frac{P(C n D)}{P(D)} \\\\& =\frac{P(C) P(D \mid C)}{P(C) P(D \mid C)+P\left(C^{\circ}\right) P\left(D \mid C^*\right)} \\\\& =\frac{0.05 * 0.78}{(0.05 * 0.78)+(0.95 * 0.06)} \\\\& =\frac{0.039}{0.039+0.057} \\\\& =\frac{0.039}{0.096} \\\\& =0.406[/tex]

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Answer:

Third option
q + d = 60

0.25q + 0.10d = 13.35

Step-by-step explanation:

Given q quarters and d dimes

Total number of coins = q + d and this must equal 60

Therefore q + d = 60

Since each quarter is 25 cents(or $0.25) and each dime is 10 cents($0.10)

Total value = 0.25q + 0.10d = 13.35

Correct set  of equations is the third option

Answer: The friends should choose the Raft Trip if they want to spend exactly $29.

The equation for the Raft Trip is 6n + 5 = 29. Solving for n, we get n = 4. This means that 4 people can participate in the Raft Trip for $29.

The other two activities, the Amusement Park and the Balloon Ride, have equations 14n = 29 and 30n + 40 = 29, respectively. Solving these equations, we find that neither of them allow exactly 4 people to participate for $29.

Step-by-step explanation:

The activity the friends should choose if they want to spend exactly $29 is Raft Trip

Number of people in the group= 4

Raft Trip:

6n + 5 = 29

6(4) + 5 = 29

24 + 5 = 29

Amusement Park:

14n = 29

14(4) = 29

56 ≠ 29

Balloon Ride:

30n - 40 = 29

30(4) - 40 = 29

120 - 40 = 29

80 ≠ 29

Hence, the friends should choose raft trip it they want to spend exactly $29

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The simplest form of the polynomial is (x²)-3x+1.

A polynomial is a mathematical expression consisting of constants, variables, and exponents. It can be written in the form of a polynomial equation, which is a mathematical equation with one or more variables.

In this example, we have two functions, f(x) and g(x). The polynomial of these two functions can be written in simplest form by combining the functions together.

The polynomial of f(x) and g(x) is written in simplest form as (x²)-3x+1.

This means that for any value of x, the polynomial will evaluate to the value given by the equation.

If x=2, then the polynomial will evaluate to (2(2)²)-3(2)+1=3.

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