joe gets a new pair of running shoes. if he runs 1 mile each day in week 1 and adds 1 10 mile to his daily routine each week, what is the total mileage on joe's shoes after week 21?

Step-by-step explanation:

Graph: y=−2x is a linear equation in slope-intercept form: ... The x-intercept is the value of x when y=0 , and the y-intercept is the value of y when x=0 .

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Answer: 15

Step-by-step explanation:

Let the number of sandwich sold be a

Let the number of drinks sold be b

The following can be formed as.an equation from the question:

5a + 2b = 230 ....... i

a + b = 55 ....... ii

Multiply equation i by 1

Multiply equation ii by 5

5a + 2b = 230 ........ iii

5a + 5b = 275 ........ iv

Subtract iv from iii

-3b = -45

b = 45/3

b = 15

The number of drinks sold were 15

Answer:

A. The graph is reflected across the x-axis and stretched vertically by

a factor of 2.

Step-by-step explanation:

Transformations

For a > 0

\(f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.\)

\(f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.\)

\(f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.\)

\(f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.\)

\(a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}.\)

\(f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}.\)

\(-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.\)

\(f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.\)

Given functions:

\(f(x)=|x|\)

\(g(x)=-2|x|\)

The series of transformations that take function f(x) to function g(x) are:

1.  Reflection across the x-axis:

\(-f(x)\implies g(x)-|x|\)

2.  Vertical stretch by a factor of 2:

\(-2f(x) \implies g(x)=-2|x|\)

Therefore, the area of the quarter circle of radius 8 cm is 16π square centimeters (or approximately 50.2655 square centimeters if we use a decimal approximation for π).

A circle is a two-dimensional shape that is defined as the set of all points that are a fixed distance (called the radius) from a central point (called the center) in a plane. It is one of the most basic geometric shapes and is often used in a variety of mathematical and scientific contexts. One important thing to note about circles is that they are symmetrical: any line passing through the center of a circle divides the circle into two halves that are mirror images of each other. Circles are commonly used in a variety of contexts, including geometry, trigonometry, physics, engineering, and many other fields. They are also used in everyday life, such as in the design of wheels and other circular objects, the calculation of the areas of circular fields or gardens, and the measurement of circular objects like plates and bowls.

Here,

The formula for the area of a quarter circle is given by:

A = (1/4)πr²

where A is the area of the quarter circle, r is the radius of the circle, and π is the mathematical constant pi (approximately 3.14159).

In this case, the radius of the quarter circle is 8 cm, so we can substitute this value into the formula and simplify as follows:

A = (1/4)π(8 cm)²

A = (1/4)π(64 cm²)

A = 16π cm²

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Step-by-step explanation:

sorry..if it is wrong..I tried...........

Answer:

Step-by-step explanation:

The graph is that of the basic absolute value function y = |x|, except that the vertex (0, 0) has been translated 4 units to the right and 7 units down.

On calculating, the 40% of 84 is found to be 33.6.

Given is that to find the 40% of 84.

Assume that the 40% of 84 is equivalent to [x]. Then, we can write -

x = (40/100) x 84

x = 4/10 x 84

x = 8.4 x 4

x = 33.6

Therefore, on calculation, the 40% of 84 is equivalent to 33.6.

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Answer:

the answer is A

B, C, D is false

The true sentence is,

⇒ 8.565 < |-13.23|

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

Given that;

All the expressions are,

A) 8.565 < |-13.23|

B) 7/8 < 0.78

C) 4/11 < - 4.11

D) 23.5 < 2 3/5

Now, From A;

A) 8.565 < |-13.23|

RHS;

|-13.23| = 13.23

Hence, It is true.

Thus, The true sentence is,

⇒ 8.565 < |-13.23|

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Answer:

27 inches

Step-by-step explanation:

i think this is the answer

Answer:

.7 I your answer to your question hope it's help

Answer:

\(\frac{7}{10}\)

Step-by-step explanation:

35/50 -->    \(\frac{7}{10}\)
divide 35 by 5 = 7
divide 50 by 5 = 10

The answer is x=6x +2

Using the binomial distribution, it is found that there is a 0.037 = 3.7% probability that Adina's friend correctly identifies each of the 3 cups of water.

For each water, there are only two possible outcomes, either it is correctly identified, or it is not. The probability of a water being correctly identified is independent of any other water, hence the binomial distribution is used to solve this question.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that each of the 3 cups is correctly identified is P(X = 3), hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 3) = C_{3,3}.(0.3333)^{3}.(0.6667)^{0} = 0.037\)

0.037 = 3.7% probability that Adina's friend correctly identifies each of the 3 cups of water.

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Answer:

Step-by-step explanation:

Answer:

1: draw a line across the circle, but not through point O

2: place the two points on the edge of the circle so that the space in between is about 1/3 of the circle. Label C and D.

3: draw two lines out from point O to the edge of the circle. 45 is half of 90. this means you can draw a 90 degree angle and divide it in half and remove the extra line. Label these E and F.

Using the triangle inequality theorem, the largest possible whole-number length for the third side is 4.

The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides.

So, for a triangle with sides of length 1, 4, and x (where x is the length of the third side), we have:

1 + 4 > x

4 + x > 1

1 + x > 4

Simplifying these inequalities, we get:

5 > x

x > 3

x > -3 (this inequality is always true)

The largest possible whole-number length for the third side is 4, since it is the largest integer that satisfies the above inequalities.

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The jam recipe that has more strawberry flavour would be recipe A with 1 cup of sugar to 6 cups of strawberries.

A recipe is defined as the a structured list that contains all the substances that are used for the preparation of a meal.

Strawberries = 3 cups

sugar = 1/2

Therefore 1 cup of sugar = 6 cups of strawberries

Strawberries = 5 cups

sugar = 1

Therefore 1 cup of sugar = 5 cups of strawberries

It can be concluded that jam recipe that has more strawberry flavour would be recipe A with 1 cup of sugar to 6 cups of strawberries.

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If the height of a triangle is 2 cm more than base and the area of the triangle is 10 cm then the height is, 7 cm

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

The area of a triangle is given by the formula:

Area = (base x height) / 2

We are given that the area is 10 cm² and that the height is 2 cm more than the base.

Let's call the base "b".

Then, the height is "b + 2".

We can substitute these values into the area formula:

10 = (b x (b + 2)) / 2

Expanding the right side:

10 = (b² + 2b) / 2

Multiplying both sides by 2:

20 = b² + 2b

Subtracting b² from both sides:

20 - b² = 2b

Factoring the left side:

(10 - b)^2 = b²

Taking the square root of both sides:

|10 - b| = b

Adding b to both sides:

10 = 2b

Dividing both sides by 2:

5 = b

So, the base of the triangle is 5 cm and the height is b + 2 = 5 + 2 = 7 cm.

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Answer:

36

Step-by-step explanation:

\(3^{2}\) = 9 (3x3)

\(3^{3}\) = 27 (3x3x3)

9 + 27 = 36

The equation used for solving the value of x will be 2x+4x+10+6x-10 = 180 and value of x is 15.

A common property of all kinds of triangles is the angle sum property. The angle sum property of triangles is 180°. This means that the sum of all the interior angles of a triangle is equal to 180°.

Given a triangle with interior angles 4x+10, 6x-10 and 2x

According to the angle sum property of a triangle,

2x+4x+10+6x-10 = 180

x = 15

Hence, The equation used for solving the value of x will be 2x+4x+10+6x-10 = 180 and value of x is 15.

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Answer:  Robbie pay in twelve months $1080 .

$92.47 more Robbie pay and 9.36 %(Approx) Robbie pay.

Step-by-step explanation:

As given

Robbie Morse has a $47,500 insurance policy.

The annual premium is $987.53.

Robbie pays $90.00 monthly.

First find out the Robbie pay in twelve months .

Robbie pay in twelve months = 12 × 90

                                                 = $ 1080

Second find out how much more does Robbie pay .

Robbie pay extra = Robbie pay in twelve months -  annual premium

                            = $ 1080 - $987.53

                            = $92.47

Therefore the $92.47 more Robbie pay .

Third find out the what percentage does Robbie pay .

Formula

Robbies pay more = $92.47

Annual premium = $987.53

Put in the above

Percentage = 9.36 % (Approx)

9.36 %(Approx) Robbie pay.

The length of the side x is derived to be √2/2 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

The right triangle is also an Isosceles having same base angles so;

x² + x² = 1²

2x² = 1

x² = 1/2

x = √(1/2) {take square root of both sides}

x = 1/√2

x = √2/2 {rationalize}

Therefore, the length of the side x is derived to be √2/2 using the Pythagoras rule.

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The value of logy will be 7.457.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

Given that log x is twice log y

So,

logx = 2 logy

logx = logy² ( by property of log)

x = y²

Now given that x = 3 × 10⁶

So,

y² = 3 × 10⁶

y = 1732.5

Now,

Logy will be

log1732.5 = 7.457

Hence "The value of logy will be 7.457".

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Answer:

exact form-512/7

decimal form-73.1

Mixed number form-73 1/7

Step-by-step explanation:

Line of symmetry is just splitting an object in half, if you fold this object onto itself over this line the sides should be equal.

" Give 2 examples and describe the symmetry in as much detail as possible."

If we separated an elephant using reflectional symmetry each side would have 1 ear, 2 legs, half a tail, half a trunk, and 1 eye.

If we separated a lamp using reflectional symmetry each side would have half a lamp shade, half a lamp base, half a light blub.

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The differential equations that are not separable among the given options are II. \(\(\frac{d^{2} y}{d x^{2}}=3 x y+\frac{d y}{d x}\)\) and III. \(\(\frac{d y}{d x}=y^{2}+y x\).\)

To determine if a differential equation is separable, we need to check if it can be written in the form \(\(M(x)dx + N(y)dy = 0\), where \(M(x)\)\) is a function of \(\(x\) only and \(N(y)\)\) is a function of \(\(y\)\) only.

In the first equation, \(\(\frac{dy}{dt} = \frac{1+t}{yt}\),\) we can rearrange it as \(\(y\frac{dy}{dt} = \frac{1+t}{t}\).\) By multiplying both sides by \(\(dt\), we get \(ydy = \frac{1+t}{t}dt\),\) which shows that it is separable. Therefore, the first equation is separable.

In the second equation, \(\(\frac{d^{2} y}{d x^{2}}=3 x y+\frac{d y}{d x}\),\) we have a second derivative and a first derivative term on the right-hand side. This equation cannot be rearranged into the form \(\(M(x)dx + N(y)dy = 0\)\) with functions of \(\(x\) and \(y\)\) only. Hence, the second equation is not separable.

In the third equation, \(\(\frac{d y}{d x}=y^{2}+y x\),\) we have both \(\(y^2\) and \(yx\)\) terms on the right-hand side. Again, this equation cannot be expressed in the form \(\(M(x)dx + N(y)dy = 0\)\) with functions of \(\(x\) and \(y\)\) only. Therefore, the third equation is not separable.

In summary, among the given differential equations, the second equation \(\(\frac{d^{2} y}{d x^{2}}=3 x y+\frac{d y}{d x}\)\) and the third equation \(\(\frac{d y}{d x}=y^{2}+y x\)\) are not separable, while the first equation \(\(\frac{d y}{d t}=\frac{1+t}{y t}\)\) is separable.

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Answer:

$26

Step-by-step explanation:

What I did first divided the 64 dollars by 8 and we get 8 . ( Save the 8 for later)

Now we divide 272 by 8 which is 34.

Now we take away 8 from 34 which is 26 because they used those 8 dollars to buy them however we take away from the profit to see its raw form.

Step-by-step explanation:

No of people likes tea = 4000

No of people like coffee = 4500

Total = 8500

No of people don't like tea and coffee = 2500

No of people like tea and coffee = 8500 - 2500 = 6000

Answer:

500

Step-by-step explanation:

n(t)=4000

n(c)=4500

n(tea only )= 4000-x

n(coffee only )= 4500-x

n(coffee and tea )= x

note...using Venn diagram ..all together must add up to 9000

(4000-x)+(4500-x) +x = 9000

..............

...........collect like terms

9500-9000 = x

x = 500

In general, higher confidence levels provide wider confidence intervals.

What is the concept of confidence level and confidence interval?

Confidence level:

The confidence level refers to the long term success rate of the method , that is , how often this type of interval will capture the parameter of interest.

Confidence interval:

A specific confidence interval gives a range of plausible values for the parameter of interest.

As the confidence level increases, the width of confidence interval also increases.

A larger confidence level increases the chance that the correct value will be found in the confidence interval. This means the interval is larger.

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Answer:

\((17a-1)(x+1)\)

Step-by-step explanation:

Given: Expression is \(17ax+17a-x-1\)

To factor: the given expression

Solution:

Take \(17a\) common from the first two terms and \(-1\) from the last two terms.

\(17ax+17a=17a(x+1)\)

and

\(-x-1=-(x+1)\)

So,

\(17ax+17a-x-1=17a(x+1)-1(x+1)\\=(17a-1)(x+1)\)

Therefore,

\(17ax+17a-x-1=(17a-1)(x+1)\)