Steve stopped for a drink of water when he had completed 60% of his jog. He had traveled 3 miles. What is the total distance Steve jogged?

2 miles
3 miles
4 miles
5 miles
6 miles

The number of pencils he paid for is 15.

He bought some pencils for N60.00.

If he had paid N1 less for each pencil, he could have bought 5 more pencils.

Let

x = cost of each pencil that amount to N60.00

y = number of pencil

Therefore,

xy = 60

y = 60 / x

(y + 5)(x - 1) = 60

(60 / x + 5)(x - 1) = 60

60 - 60 / x + 5x - 5 = 60

- 60 / x + 5x  + 55 = 60

- 60 / x + 5x = 60 - 55

- 60 / x + 5x = 5

- 60 + 5x² / x = 5

5x = -60 + 5x²

5x² - 5x  - 60 = 0

x² - x - 12 = 0

x² + 3x - 4x - 12 = 0

x(x + 3) - 4(x + 3) = 0

(x - 4)(x + 3)

Hence,

x = 4 and x = -3

We can only use positive value.

xy = 60

y = 60 / 4

y = 15

Therefore, he paid for 15 pencils.

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Answer:

12 more days

Step-by-step explanation:

Every time cheeseburger will be served: 4th day, 8th day, 12th day, 16th day

Every time pizza wil be served: 6th day, 12th day, 18th day

Since 12 is a common number, every 12 days both cheeseburgers and pizzas will be served

Answer:

x = 7

Step-by-step explanation:

The probability that exactly 7 individuals are dropouts out of 35 is 0.0033288.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Given,

Probability of dropouts=p= 6%= 0.06

Probability of not dropouts=q=1-p=1-0.06=0.94

n=35

We use the probability mass function of binomial distribution, as there are only two possible outcomes for the given situation. If the individual is dropout or not a dropout.

P(X=x)= nCr x p^r x q^(n-r)

P(X=7)= 35C7x(0.06)^7x(0.94)^28

P(X=7)=6724520x(0.06)^7x(0.94)^28

P(X=7)=0.00332889

Therefore, the probability of exactly 7 of them are dropouts is 0.00332889.

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The statements The range of the distribution is around 60 cm and

the center of the distribution is around 180 cm are true.

Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.

In the given statements

There are no outliers in this distribution.

The shape of the boxplot is fairly symmetric.

The range of the distribution is around 60 cm.

The center of the distribution is around 180 cm.

The statement "The range of the distribution is around 60 cm" is true.

The range is the spread of your data from the lowest to the highest value in the distribution.

In the given graph

Range=200-140

=60

So it is true.

The center of the distribution is around 180 cm is also true.

Hence the statements The range of the distribution is around 60 cm and

the center of the distribution is around 180 cm are true.

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The area of the region consisting of all the points Charlyn can see during her walk is equal to, A = 4840 km.

Charlyn is walking around the boundary of square A, which is 55 km long, and she has a horizontal vision of 11 km.

So as she walks around the square of 55 km, let there be another square B which lies outside square A, which is created due to her 11 km field of vision.

length of sides of square B = 55+(2×11) which is equal to 77 km.

And as she walks around the square of 55 km, let there be yet another square C which lies inside square A, which is created due to her 11 km field of vision.

length of sides of square C = 55-(2×11) which is equal to 33 km.

The area that Charlyn can see throughout her walk is equal to,

A = Area of square B - Area of square C.

The area of square B = Side² = 77² = 5929.

The area of square C = Side² = 33² = 1089.

A = 5929 - 1089.

A = 4840 km.

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Answer:

[tex]\displaystyle y = \frac{-2}{7}[/tex]

Step-by-step explanation:

   To solve, we will isolate the variable.

   Given:

-12/7 = 6y

   Divide:

[tex]\displaystyle \frac{\frac{-12}{7} }{6} =\frac{6y}{6}[/tex]

   Simplify the right side:

[tex]\displaystyle \frac{\frac{-12}{7} }{6} =y[/tex]

   "Keep, change, flip" on the left side:

[tex]\displaystyle \frac{-12}{7} *\frac{1}{6} = y[/tex]

   Multiply:

[tex]\displaystyle \frac{-12*1}{7*6}= y[/tex]

[tex]\displaystyle \frac{-12}{42}= y[/tex]

   Simplify and reflexive property:

[tex]\displaystyle y = \frac{-2}{7}[/tex]

_______________

I'm reading your question

___________________

According to the Pythagorean theorem

Hypotenuse ^2 = Side 1 ^2 + Side 2 ^2

The hypotenuse is the case (Square 1 )

area of the sqaure= side of the square^2

________________________

That means the area of 1 is = area of square 2 + area fo square3 (J is false)

_______________________________

We are not sure about the relation between square 2 and 3 just the addition is the square 1 (F and H we have no certainty)

______________________________

G is true

______________________________

Answer

G

A) 4/5 or 0.8

B)7

C)1/81

Answer:

m/1 = 87

m/2 = 93

Step-by-step explanation:

m1 and m2 need to have an angle of 180

so 180-87 = 93

The solution of 0.125x +1 -0.25x < -3 is x > 32

Difference between equality and inequality equations

Both mathematical phrases, equations and inequalities, are created   by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.

The given expression is,

0.125x +1 - 0.25x < -3

subract the x value,

0.125x  - 0.25x + 1 < -3

-0.125x + 1 < -3

-0.125x < -3 - 1

-0.125x < -4

Now, if on both the sides the signs are -ve then change the inequality sign, like this

x > 4 / 0.125

x > 32

Hence, The solution of 0.125x +1 -0.25x < -3 is x > 32

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Answer:

Slope = (15/14)

Step-by-step explanation:

(3, 0), (-11, -15)

(x₁, y₁)  (x₂, y₂)

        y₂ - y₁        -15 - 0        -15            15

m = ------------ = ----------- = ----------- = ---------

        x₂ - x₁        -11 - 3          -14            14

I hope this helps!

Answer:

She worked Seven (7) hours.

Step-by-step explanation:

$112.75 is the total

she earned $62 in tips which doesn't count because the questions asked for how long she worked.

Adding tips would make the equation unreliable because how long people work doesn't really affect how much tips you get. You maybe getting 50 bucks of tips in the first and 40 in the next.

solving steps: (where x = number of hours worked)

7.25x + 62 = 112.75 <<<the true equation based on the story

7.25x = 112.75 - 62

7.25x = 50.75

x = 50.75 ÷ 7.25

x = 7

Seven (7) hours worked.

Answer:

1/5

Step-by-step explanation:

I multiplied 2 * 7, which is 14. Then, I multiplied 7 * 10 which equals 70. Then, I divided 14/70 by 14. The answer is 1/5.

The probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8 is 53/99

The greatest number that can be formed by the two wheels is 99

Let event A be multiple of 4

Multiples of 4 between 1 to 9 is 4,8

Probability that at least one wheel land at a multiple of 4 is

[tex]\frac{2}{9} + \frac{2}{9}[/tex] = 4/9

Let event B be first value greater than 9

P(B) = 9/99 = 1/11

P(A∩B) = 0

Probability of at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8

P(A∪B) = P(A) + P(B) - P(A∩B)

= 4/9 + 1/11 - 0

= [tex]\frac{4(11)}{9 (11)} + \frac{1 (9)}{11(9)}\\\\ \frac{44 + 9}{99}\\\\ \frac{53}{99}[/tex]

Therefore, the probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8 is 53/99

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Answer:

50cm is equivalent to 500km

Have a good one!

Answer:

140

Step-by-step explanation:

Based on the yards of fabric used by Jan for the quilt squares, the total fabrics used by Jan was 1 ¹ / ₅₆ yards

The yards of fabric used by Jan were 7 / 8 of a yard and 1 / 7 of another yard.

The total yards used by Jan can be found by adding these fractions up. To add both fractions, you first need to find the common denominator of 8 and 7 which is 56.

Then the numerators can be found by dividing 56 by the denominator and then multiplying the numerator by the result.

Fraction 7 / 8 yards:

= 56 / 8 x 7

= 49 / 56

Fraction 1 / 7:

= 56 / 7 x 1

= 8 / 56

The total number of yards used is:
= 49 / 56 + 8 / 56

= 57 / 56

= 1 ¹ / ₅₆ yards

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Check below, please

1) The way to tackle this problem, is by dividing those numerators by the denominators so we can get the decimal form of each fraction, and count the marks to plot them.

2) Let's divide them:

So now, we can plot them:

Thus, this the answer.

Answer:

Step-by-step explanation:

Let the amount invested at 9% be x.

Then the amount invested at 7% is 10000 - x.

The amount of interest after one year is $780.

Set up equation to represent this:

Amount invested at 7% is:

Answer:

Milan invested:

Step-by-step explanation:

Given information:

Let x be the amount invested in Account A.

Therefore, the amount invested in Account B is (10000 - x).

Simple Interest Formula

I = Prt

where:

Create two equations using the given information:

[tex]\begin{aligned}\textsf{Interest: Account A} &= x \cdot 0.09 \cdot 1\\& = 0.09x\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Interest: Account B} &= (10000 - x) \cdot 0.07 \cdot 1 \\& = 0.07(10000 - x)\\& = 700-0.07x\end{aligned}[/tex]

As the total interest earned was $780, set the sum of the two found equations to 780 and solve for x:

[tex]\begin{aligned}\implies 0.09x+700-0.07x&=780\\0.02x+700&=780\\0.02x&=80\\x&=4000\end{aligned}[/tex]

Therefore, Milan invested:

Domain and Range of a Function

The domain of a function f is the set of values of the input (or independent) variable, often called x. The range is the set of values of the output (or dependent) variable, often called y, or f(x).

The function shown in the image has a shape that opens up to infinity (marked with the two arrows). This means that x can have any real value from minus infinity to plus infinity, that is, all real numbers.

Now for the range, we can see not every value of y belongs to the function. The graph decreases down to the vertex of the parabola that is located at (3,-12). This means that from y=-12 and up, the function exists, but not below this value.

Summarizing:

Domain: All real numbers

Range: y ≥ -12

Using the concept of Application of Derivatives(A.O.D),we got 4.79 inches will be the square size for making the volume of candy box maximum.

A candy box is made from a piece of a cardboard that measures 43 × 23 inches.

Let squares of equal size will be cut out of each corner with the measure of x inches.  

Therefore, measures of each side of the candy box will become

Length = (43 - 2x)

Width   = (23 - 2x)

Height  = x

Now we have to calculate the value of x for which volume of the box should be maximum.

Volume (V) = Length×Width×Height

 =>V = (43 -2x)×(23 - 2x)×(x)

 =>V= [(43)×(23) - 46x - 86x + 4x²]×x

 =>V= [989 - 132x + 4x²]×x

 =>V= 4x³- 132x² + 989x

Now we find the derivative of V and equate it to 0

[tex]\frac{dV}{dx}[/tex]= [tex]12x^{2} -264x+989[/tex]=0

Now we get values of x by quadratic formula

x=(264±[tex]\sqrt{264^{2}-4.12.989 }[/tex] )/24

=>x=(264±[tex]\sqrt{69696-47472}[/tex])/24

=>x=(264+√22224)/24, and x=(264-√22224)/24

=>x=(264+149.07)/24 and x=(264-149.07)/24

=>x=17.212                  and x=4.79

Now we test it by second derivative test for the maximum volume.

[tex]\frac{d^{n}V }{dx}[/tex]=24x-264

For x = 17.212

[tex]\frac{d^{n}V }{dx}[/tex]=(24×17.212)-264=413.088-264=149.088

This value is > 0 so volume will be minimum.

For x = 4.79

[tex]\frac{d^{n}V }{dx}[/tex]=(24×4.79)-264= -149.04

-149.04 < 0, so volume of the box will be maximum.

Therefore, for x = 4.79 inches volume of the box will be maximum.

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(Complete Question) is

A candy box is made from a piece of cardboard that measures 43 by 23 inches. Squares of equal size will be cut out from  each corner. The sides will then be folded up so that to form a rectangular box. What size square should be cut from each corner so that to obtain maximum​ volume?

Answer:

there are 378 students

Step-by-step explanation:

you can see this as a simple proportion.

You know that the 100% of the seats are 1080 and you need to know the 35% of the seats, so you do:

[tex] \frac{1080}{100} = \frac{x}{35} [/tex]

so you do

x = 35 * 1080 ÷ 100 which gives 378

The distance between Ashely’s house and the public library is of 7.8 miles.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between these two points is given by the following rule:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the Cartesian plane, with the hypotenuse representing the distance between them.

In the context of this problem, the coordinates of her house and of the library are given as follows:

Hence the distance is calculated as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]D = \sqrt{(10 - 4)^2+(7 - 2)^2}[/tex]

D = sqrt(61)

D = 7.8 miles, as each unit on the plane represents one mile.

The problem states that each unit on the plane represents one mile and the image gives their position on the plane.

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Answer:

w = (4/35)

Step-by-step explanation:

-1/5 = -1/2w - 1/7

+1/7              +1/7

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

-2/35 = -1/2w

÷-1/2      ÷-1/2

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

4/35 = w

Extra:

-1(7)      1(5)

------- + -------

5(7)      7(5)

  -7        5          -2

------- + ------- = -------

 35        35        35

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

 -2         -1

------- ÷ -------

 35         2

 -2        -2          4

------- × ------- = -------

 35         1          35

I hope this helps!

Yes, her strategy was correct.

When compared to operations involving just two numbers, solving an arithmetic expression that includes multiple operations like addition, subtraction, multiplication, and division is more difficult. A two-number operation is simple, but how do you work out an expression with brackets as well as multiple operations, as well as how to make a bracket simpler? Let's review the BODMAS rule as well as discover how brackets can be made simpler. For Bracket, Order, Division, Multiplication, Addition, and Subtraction, the acronym BODMAS is used. The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, as well as Subtraction, is also known as BODMAS in some areas. Thus, the following figure illustrates the order in which BODMAS and PEMDAS operate.

Simplification is done following BODMAS rule.

266-39 gives 227.

Hence, her strategy was correct.

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We need to identify the true statement for every polynomial P with degree n.

The degree n of a polynomial is the exponent of the highest power of x in that polynomial. For example, the polynomial

has degree 3, since the highest power of x has exponent 3.

Thus, if the degree is n, then the highest power is n (not n-1). Therefore, (a) is False.

About the number of solutions to P(x) = 0, it can equal the number of the polynomial degree. For some polynomials, the solutions can repeat, so the number of solutions will be less than n. For some of them, the solutions may not belong to the real numbers.

As an example, for P(x) = x²+4, we have:

The above polynomial has degree 2 and 2 solutions. Therefore, (b) is False.

Each turning point is where the graph of the polynomial P(x) changes from decreasing to increasing or vice versa. The graph of any polynomial of degree n has at most n-1 turning points.

Therefore, (c) is True.

We can see that (d) is False from the following example:

the line P(x) = x+1 has degree n = 1 and n = 1 x-intercept, which is its zero x = -1.

Answer:

c) The graph of P has at most n-1 turning points

Applying power rules, the equations that is true when x = 10 but false when x = -10 is given as follows:

x³ = 10000.

The behavior of the exponents of 10 is different for even and for odd exponents, as follows:

In this problem, we have two exponents, as follows:

We want different results for the power when x = 10 and when x = -10, hence the correct option will involve the odd exponent 3.

The third power of 10 is calculated as follows:

10³ = 10 x 10 x 10 = 100 x 10 = 1000.

Hence the equation that is true for x = 10 and false for x = -10 is:

x³ = 10000.

As when x = -10, the result is:

(-10)³ = (-10) x (-10) x (-10) = 100 x (-10) = -1000.

The options are given by the image at the end of the answer.

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