Mariam runs 7.5 miles in one hour How much distance will she cover in 3 hours

The value of y when x = 2 is 16/25 and when z = 6 is 200/36

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.

Given that, Y varies directly as x and inversely as the square of z and y=8 when x=25

That means, y ∝ x and y ∝ 1/z²

Let  constant of proportionality be k, then,

y = kx and y = k/z²

Now, finding k, when x = 25

8 = k25

k = 8/25

For x = 2,

y = 8/25X2

y = 16/25

Finding k when y = 5

8 = y/25

y = 200

Now, when z = 6

y = 200/36

Hence,  The value of y when x = 2 is 16/25 and when z = 6 is 200/36

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Answer:

£15 and £22

Step-by-step explanation:

let,the cost of one shirt be X and one jumper be y.Then according to question,

5x+4y=163-----(1)

also,

3x+2y=89------(2)

Now, multiplying eqn (2) by 2 and then subtracting from (1),we get

5x+4y=163

6x+4y=178

- - -

_________

-x=-15

:.x=15

Putting value of X in eqn (1),

5×15+4y=163

or,4y=163-75

or,y=88/4

:.y=22

Hence cost of one shirt is £15 and one jumper is £22.

The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.

Hence, The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.

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Answer:

D. Slope is 1

Step-by-step explanation:

Start at any point on the line. Go up 1 (rise of 1). Go right 1 (run of 1). You're on the line again.

slope = rise/run = 1/1 = 1

For an average intake of 2200 calories per day, the number of acres of land owned will be 2.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that, The function that models the number of calories consumed daily by a person owning x acres of land in a developing country is,

C(x)=270 ln (x+1)+1900

If an average intake of 2200 calories per day,

C(x)= 2200

2200=270 ln (x+1)+1900

2200-1900=270 ln (x+1)

270 ln (x+1)=2200-1900

270 ln (x+1)=300

ln (x+1)=300/270

ln (x+1)=1.11

(x+1)=ln⁻¹(1.11)

x+1=e¹¹¹

x=e¹¹¹-1

x=3.034-1

x=2.034≈2

Thus, for an average intake of 2200 calories per day, the number of acres of land owned will be 2.

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0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.

Given that,

Standard deviation (σ) = 5.2 oz

mean (μ) = 10 oz

Number of students (n) = 120

As we know,

P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ[tex]\sqrt{n}[/tex]}/σ])

                        = P (z > [{12.7 - 10[tex]\sqrt{120}[/tex]}/5.2])

                        = P (z > 1.86)

                        = 1 - P ( z < 1.86)

                        = 1 - 0.862394

                        = 0.137606

Thus, P( z > 12.7 oz.) = 0.137606

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Answer:

if the base is on the x-axis, the width of the rectangle is = xif the height is based on the parabola, the length = 7-x^2

the area of a rectangle = length * width

thus, area = x*(7-x^2)= 7x-x^3

in order to maximize the area, you would need to take the derivative of the area and set it equal to 0

Area = 7x-x^3Area' = 7 - 3x^2

7-3x^2 = 0thus, x = 1.5275

this x represents the x needed to create the largest possible area with the given parameters.

Thus:Width (x-axis) = 1.5275Length (y-axis) = 7 - (1.5275)^2 = 4.6667

Answer:

HL

Step-by-step explanation:

to solve this we first must see what is congruent

we see that both triangles are right triangles

that means that we can use HL (hypotenuse length) to solve

we must first see if HL works though

we see that the hypotenuses are both equal

that means that we can use HL

that is your answer

The graph that could be used to determine the possible variance levels that would result in an acceptable height is the third graph.

Fron the information, the required model height for the designed clothes should be less than or equal to 5 feet 10 inches. In this case, the equation for the variance in height is of the straight line form;

y = m·x + c

Where x is the height  in inches

Given that the maximum height allowable is 70 inches, when x = 0 we have;

y = m·0 + c = 70

Therefore, c = 70

Also when the variance = 0 the maximum height should be 70 which gives the x and y-intercepts as 70 and 70 respectively such that m = 1

The equation becomes;

y ≤ x + 70

Also when x > 70, we have y ≤ -x + 70   with a slope of -1

In this case, to graph an inequality, we will need to shade the area of interest which in this case of ≤ is on the lower side of the solid line.

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Answer:

see explanation

Step-by-step explanation:

the mistake is that a zero should be inserted to indicate the x - term

the standard form of a polynomial of degree 3 is

ax³ + bx² + cx + d

given

[tex]\frac{3m^3-2m^2-150}{m-4}[/tex]

there is no m- term in the numerator so a zero has to be inserted in its place, that is

4 | 3   - 2   0  - 150

     ↓    12   40  160

   ---------------------------

     3   10  40    10

Answer:

as a result you get approximately 2.8949 which in thousands of units is 2894 (rounded down since you can't have a fraction of a unit).

on dividing the given term we get

12.2105.

The three decimal places are :28.288< μ < 43.712

degree of freedom = 17-1 = 16

critical t value = 2.1199

lower limit = 36-2.1199*15/sqrt(17) = 28.288

Upper limit = 36+2.1199*15/sqrt(17) = 43.712

Answer:28.288< μ < 43.712

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Average rate of change for given function from x=4 to x=10 is -0.66

Average rate of change can be defined as slope of function between two fixed values of x. It can also be defined as change in function per unit or we can say as an average.

At x = 4 we have y = 8

At x = 10 we have y = 4

As y is nothing but value of function f(x) at x.

So, we can write them as f(4) = 8 and f(10) = 4

Average rate of change (from x = a to x=b) = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Using above formula of average rate of change and substituting for x=4 to x=10, we get

Average rate of change = [tex]\frac{4-8}{10-4} = \frac{-2}{3}[/tex]

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Answer:

A. No

B. Yes

C. No

Step-by-step explanation: To determine if each pair is a solution to the equation, substitute the x and y variables in the pairs for the corresponding variables in the equation. If the left and right sides are equal once you solve, you will know that the pair is a solution,

(9,1)   2(9)+7(1)=16    18+7=16    25=16    No

(8,0)    2(8)+7(0)=16    16+0=16    16=16    Yes

(0,0)    2(0)+7(0)=16    0+0=16    0=16    No

Answer: 1058000 tickets

Step-by-step explanation:

23000 x 46 = 1058000

1058000 tickets

Step-by-step explanation:

The expression 5x + 6y - 3x is equivalent to:

2x + 6y

This is because 5x and -3x can be combined by adding them together, which gives 2x.

The expression 5x + 6y - 3x is also equivalent to:

x + 6y - 3x

This is because 5x and -3x can be combined by adding them together, which gives x.

However, the expression 5x + 6y - 3x is not equivalent to:

2x - 3y

This is because the coefficient of the y term is 6, not -3.

The expression 5x + 6y - 3x is also not equivalent to:

x + y

This is because the coefficient of the y term is 6, not 1.

Answer:

You need to multiple

Step-by-step explanation:

The total cost of the topsoil needed to cover the layout will be

$(1.46 x 10⁻⁴)(15LB).

Given is that Joe must spread out topsoil to a depth of 15 inches over the entire yard. One truckload of topsoil costs $67.89 and contains 10 cubic yards of topsoil.

In 10 yards³ = 466,560.1 in³

Assume the length and breadth to be [L] inches and [B] inches. The height is 15 inches.

Volume of the layout will be -

V = (15 x L x B) in³

466,560.1 in³ of the topsoil costs $67.89.

1 in³ of the topsoil will cost $(67.89/466560.1)

(15 x L x B) in³ of the topsoil will cost -

$(67.89/466560.1) x (15LB)

(1.46 x 10⁻⁴)(15LB)

Therefore, the total cost of the topsoil needed to cover the layout will be

$(1.46 x 10⁻⁴)(15LB)

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Answer:

5.5

Step-by-step explanation:

earthquake is measured with the Ritcher Scale:

R (Magnitude) = ㏒base 10 (I)

where I = Intensity

thus,

R = ㏒ base 10 (316227.77)

R ≅ 5.5

Using the distance formula, [tex]JP=\sqrt{(0-4)^2+(1-(-2))^2}=\boxed{5}[/tex]

The equivalent fraction with a denominator of 100 will be;

⇒ 90 / 100

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The fraction is,

⇒ 9 / 10

Now,

Since, The fraction is,

⇒ 9 / 10

Hence, The fraction with denominator 100 is;

⇒ 9 / 10 = 9×10 / 10×10

             = 90/100

Thus, The equivalent fraction with a denominator of 100 will be;

⇒ 90 / 100

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The equation of vertical line passing through the point (4,-3) will be x = 4

And, The equation of horizontal line passing through the point (4,-3) will be y = - 3.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The horizontal and vertical lines passing through the point (4,-3).

Now,

Since, The horizontal and vertical lines passing through the point (4,-3).

Hence, The equation of vertical line passing through the point (4,-3) is the value of x.

So, We get;

The equation of vertical line is,

⇒ x = 4

And, The equation of horizontal line passing through the point (4,-3) is the value of y coordinate.

So, We get;

The equation of horizontal line is,

⇒ y = - 3

Thus, The equation of horizontal line is , y = - 3

And, The equation of vertical line is, x = 4

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An independent variable studied by using related samples in all conditions is called a within subjects factor.

An independent variable is defines as the variable that is modified or controlled in a scientific experiment. It reflects the rationale or cause for an outcome.

The variables that the experimenter adjusts to test their dependent variable are known as independent variables. A change in the independent variable has a direct effect on the dependent variable. The impact on the dependent variable is assessed and documented.

Examples of Independent Variables

A scientist is experimenting with the effect of light and dark on the behaviour of moths by turning on and off a light. The amount of light is the independent variable, while the moth's reaction is the dependent variable.

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5 x 3²⁴  bacteria will there be after one day.

What is exponents?

Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".

Consider what is actually happening in the question.

You begin with 5 bacteria, and after 1 hour it has tripled so you now have

5x 3=15.

Next hour, it triples again so you now have 5 x 3 x 3=45

You can see the pattern shows that the number of bacteria is multiplying every hour by a factor of 3. An exponent denotes how many times we are multiplying a number by itself, for example: 3⁴  means we are multiplying the number 3 a total of 4 times (3 x 3 x 3 x 3).

Therefore the question is requiring us to triple the number of bacteria every hour for 24 hours, which means we are multiplying by 3 a total of 24 times. This gives us:

n x 324 where n is the number of bacteria you begin with.

Since you begin with 1 bacteria, the solution is 5 x 3²⁴.

Hence 5 x 3²⁴  bacteria will there be after one day.

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When Bobby takes out a mortgage for $30 years at 4% interest with $835.48 in monthly payments, the total principal loan amount is $255644.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Here,

The interest paid per month=$835.48

Interest paid in 30 years=835.48*12*30

Rate of interest=4%=0.04

Time=30 years

Principal=I/RT

=(835.48*30*12)/(0.04*30)

=$250644

The principal loan amount is $250644 when Bobby takes out a mortgage for 30 years at an interest rate of 4% and his monthly repayments are $835.48.

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