Lucy spent 2/4 of an hour riding her bike. She then spent 3 3/4
of an hour break playing video games. How much did she spend playing video games and riding a bike

We have prοven that the Prοduct Rule fοr expοnents wοrks, and that 4a and 4b are equivalent.

The prοduct rule οf expοnents states that when multiplying twο terms with the same base, yοu can add the expοnents. Specifically, [tex]a^m * a^n = a^{(m+n)[/tex].

Tο expand the expressiοn [tex]2x^3[/tex]  •[tex]5x^2[/tex] using the fact that expοnents are repeated multiplicatiοn, we can write:

[tex]2x^3[/tex] • [tex]5x^2[/tex]= (2 • x • x • x) • (5 • x • x)

Using the cοmmutative prοperty οf multiplicatiοn, we can rearrange the factοrs tο grοup the x's and the numbers:

[tex]2x^3[/tex] • [tex]5x^2[/tex] = 2 • 5 • x • x • x • x

[tex]= 10x^5[/tex]

Nοw, let's prοve why the Prοduct Rule fοr expοnents wοrks. The Prοduct Rule states that when multiplying twο expοnential expressiοns with the same base, we can add their expοnents:

[tex]a^m[/tex] • [tex]a^n = a^{(m+n)[/tex]

Tο see why this is true, let's cοnsider the repeated multiplicatiοn οf a base a with expοnent m and a base a with expοnent n:

[tex]a^m[/tex]• [tex]a^n[/tex] = (a • a • ... • a) • (a • a • ... • a)

We can cοmbine the twο grοups οf factοrs by using the assοciative prοperty οf multiplicatiοn:

[tex]a^m[/tex] •[tex]a^n[/tex] = [tex]a^{(1+1+...+1)[/tex]• (a • a • ... • a) (m times)

[tex]= a^{(m+n)[/tex] • (a • a • ... • a) (m times)

Using the fact that a tο the pοwer οf 1 is just a, we can simplify the expressiοn tο:

[tex]a^m[/tex] • [tex]a^n[/tex] [tex]= a^{(m+n)[/tex]•[tex]a^m[/tex]• [tex]a^n[/tex]

Dividing bοth sides by [tex]a^m[/tex] • [tex]a^n[/tex], we get:

[tex]1 = a^{(m+n)[/tex] / ([tex]a^m[/tex] • [tex]a^n[/tex])

Using the rule fοr dividing expοnential expressiοns with the same base, we get:

[tex]1 = a^{(m+n)[/tex] • [tex]a^{(-m)[/tex] • [tex]a^{(-n)[/tex]

Using the rule fοr adding expοnents with the same base, we can simplify the expressiοn tο:

[tex]1 = a^{(m+n-m-n)[/tex]

Simplifying further, we get:

[tex]1 = a^0[/tex]

Therefοre, we have prοven that the Prοduct Rule fοr expοnents wοrks, and that 4a and 4b are equivalent.

To learn more about the product rule of exponent, visit:

https://brainly.com/question/847241

#SPJ1

Answer:

21 sticks

Step-by-step explanation:

In order to solve an equation like this its best to count all the sticks each step and figure out the pattern

1st: 6 sticks

2nd: 11 sticks

3rd: 16 sticks

Now we notice that it adds 5 sticks each step so the 4th picture must have 21 sticks.

Hope this helps!

Brainliest and a like is much appreciated!

Answer: If Francesca's pedometer underestimates her step count by 4%, then the actual number of steps she walked can be found by dividing the pedometer reading by 0.96 (100% - 4% underestimation).

So, actual number of steps = 8,256 / 0.96 = 8,600.

Therefore, Francesca actually walked 8,600 steps.

Your welcome, comment on my answer, for anymore answers on questions.

Answer:

-4c-4

Step-by-step explanation:

The simplified expression for  6c + (-4) - 8c + (-2c) is -4 - 4c.

Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression is (Number/variable, Math Operator, Number/variable)

We have the expression, 6c + (-4) - 8c + (-2c)

Now, simplifying the expression as

6c - 4 - 8c - 2c

= -4 + c(6 - 8 - 2)

= -4 + c(-4)

= -4 - 4c

Thus, the simplified expression is -4 -4c.

Learn more about Expression here:

https://brainly.com/question/14083225

#SPJ5

Answer:

(a) 280

(b)  £26

Step-by-step explanation:

(a) 20 workers eat 2 biscuits a day.

20 × 2 = 40

Since there are 7 days a week, multiply the 40 x 7 to find how many biscuits are eaten each week.

40 × 7 = 280

280 biscuits are eaten every week.

(b) Now, divide 280 (the number of biscuits eaten each week) by 14 (the number of biscuits in a packet) to find how many packets are eaten weekly.

280 ÷ 14 = 20

Now you have the number of packets eaten each week, so you can determine the price spent on biscuits. Multiply 20 packets by the price per packet, which is £1.30.

20 × 1.30 = 26

The office spends £26 on biscuits each week.

Ashima will gain INR from selling the watch for INR, as the Cost Price of the watch is 1360 and the Selling Price is INR.

a. The Cost Price (CP) of the watch is the amount that Ashima paid to purchase the watch. In this case, Ashima sold the watch for 1350 and suffered a loss of 10. This means that the CP of the watch is 1350 + 10 = 1360.

b. To calculate her gain, we need to know the Selling Price (SP) of the watch. If she sells the watch for INR, then the SP of the watch is INR. The formula to calculate gain or loss is as follows:

Gain or Loss = SP – CP

In this case, the SP of the watch is INR and the CP of the watch is 1360. Applying the formula, Ashima’s gain is:

Gain = INR – 1360

= INR - 1360

Therefore, Ashima will gain INR from selling the watch for INR.

Learn more about Selling Price here:

https://brainly.com/question/13797424

#SPJ4

f the solutions to h(x) = 0 are x = -8 and 8, then the quadratic function must have factors of (x+8) and (x-8), since those are the values of x that make h(x) equal to zero. So, one possible quadratic function that could represent h is: h(x) = (x+8)(x-8) Expanding this out, we get: h(x) = x^2 - 64x + 64 So, the quadratic function that could represent h is: h(x) = x^2 - 64x + 64

Step-by-step explanation:

y = 3x + 10 the fixed charge is 10$ so our constant should be 10, there is a 3$ fee every day so x represents the days so we can multiply the amount of days with 3 to find the total amount paid in fees.

For example, if we hired a ladder for 3 days then

y = 3x + 10

= 3 x 3 +10

= 9 + 10

= 19$

So, we spent 19$ dollars in total cost

The time it will take to fill the tank is 1.256 hours and this it will take longer than an hour to fill the tank

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces.

The volume of the cylinder needs to be calculated first. Volume of a cylinder is expressed as ;

V = πr²h, where r is the radius and h is the height of the cylinder.

V = 3.14 × 30² × 160

V = 452160 cm³

Since 1litres = 1000cm³

452160cm³ = 452160/1000 = 452.16litres

The rate at which it is filled is 0.1 litres per second

therefore for a volume of 452.16litres

= 452.16/0.1 = 4521.6 sec

3600sec = 1 hour

therefore 4521.6 sec = 4521.6/3600 = 1.256hours.

Therefore it takes longer than 1 hour to fill the tank.

learn more about rate from

https://brainly.com/question/119866

#SPJ1

Special right triangles are triangles whose angles and side lengths have specific ratios that make them easier to solve without using complex trigonometry functions.

The two types of special right triangles are the 45-45-90 and 30-60-90 triangles trigonometry.

The 45-45-90 triangle, also known as an isosceles right triangle, has two congruent legs and a hypotenuse that is [tex]\sqrt{2}[/tex] times the length of a leg. The angles in this triangle measure 45 degrees, and the side lengths are in the ratio 1:1:[tex]\sqrt{2}[/tex]. This triangle is commonly found in constructions, as it is easy to create using a compass and straightedge.

The 30-60-90 triangle has angles that measure 30, 60, and 90 degrees, with the hypotenuse twice the length of the shortest side and the longer leg equal to the shortest side multiplied by [tex]\sqrt{3}[/tex]. The side lengths have ratio 1:[tex]\sqrt{3}[/tex]:2. This triangle is also commonly used in real-world applications, such as construction and engineering.

Knowing the ratios of the side lengths in these special right triangles can help simplify trigonometric calculations and make solving problems involving right triangles easier.

Learn more about trigonometry here:

https://brainly.com/question/29002217

#SPJ4

Answer:

Step-by-step explanation:

The sample proportion of encounters where a whale came within 985 feet of the bow is given by p-hat = 0.03, and the sample size is n = 85.

The mean of a sample proportion can be calculated using the formula:

μ = p

where p is the population proportion.

In this case, we do not have the population proportion, but we can use the sample proportion as an estimate of the population proportion. Therefore, the mean of the sample proportion is:

μ = p = p-hat = 0.03

So the mean of the sample proportion is 0.03.

Duane can expect to make a monthly payment amount of $506.18 over the 5-year term of his loan, including both the principal and the interest.

The monthly payment amount for Duane's MSRP vehicle purchase can be calculated using the following formula: ((MSRP - cash-back incentive) x interest rate) / (term in years x 12). In this case, the calculation is ((31,000 - 4,500) x 0.055) ÷ (5 x 12) = 506.18. Thus, Duane can expect to make a monthly payment of $506.18 over the 5-year term of his loan. This amount includes both the principal and the interest accrued on the loan. It is important to note that the monthly payment may change slightly due to the addition of taxes, registration fees, and other charges that may be included in the loan. Additionally, the amount of the monthly payment may vary slightly depending on the lender's terms and conditions.

Learn more about amount here

https://brainly.com/question/28970975

#SPJ4

In response to the query, we can state that Hence, a reduction dilation is the kind of dilation that happens when the scale factor is 1/4.

Dilation is a transform that modifies an object's size. Dilation is a technique used to increase or decrease objects. An picture that is an exact duplicate of the original shape is produced as a result of this change. There is, however, a significant fluctuation in the shape. Dilation should result in a distortion of the initial form.

Dilations are transformations that alter an object's size without altering its shape. When an object dilates by a scale factor of 1/4, its size is decreased by a factor of 1/4, or 0.25.

This implies that each dimension of the object—its length, breadth, and height—will be multiplied by 1/4, or 0.25. For instance, if the original item was 8 units long, the dilated version would be 2 units long (8 x 1/4 = 2). The dilated item would have a width of 1.5 units if the initial object had a width of 6 units (6 x 1/4 = 1.5).

Hence, a reduction dilation is the kind of dilation that happens when the scale factor is 1/4.

To know more about dilation in transformation geometry  visit:

https://brainly.com/question/10855880

#SPJ1

If a number from 0-9 is randomly selected and then a letter from a-d is randomly selected, the probability that the number 3 and a constant are selected is 0.1 or 10%.

There are 10 possible numbers that could be selected, ranging from 0 to 9, and 4 possible letters that could be selected, ranging from a to d.

To calculate the probability that the number 3 and a constant are selected, we need to determine how many outcomes satisfy this condition, and then divide that number by the total number of possible outcomes.

There is only one outcome where the number 3 and a constant are selected, which is if the number 3 is selected and any of the four letters (a, b, c, or d) are chosen. Therefore, the number of outcomes that satisfy this condition is 4.

The total number of possible outcomes is found by multiplying the number of possible numbers (10) by the number of possible letters (4).

Total number of possible outcomes = 10 x 4 = 40

Thus, the probability that the number 3 and a constant are selected is,

Probability = number of favorable outcomes / total number of possible outcomes

Probability = 4 / 40

Probability = 0.1

This means that out of all possible outcomes, 10% will result in the selection of the number 3 and any of the four letters.

To learn more about probability click on,

https://brainly.com/question/30818027

#SPJ4

As the area of the square is given 16/36 square feet for that the length of sides of the square is 4/6 feet.

A square is a quadrilateral with four sides. The length of each side is equal. The sum of angles in a square is 360 degrees.  Each angle in a square is a right angle.

Area of a square = side²

If the area of a square is given, in order to determine the length, find the square root of the area.

Thus, Area of square = 16 / 36 feet².

        s² = 16/36 feet²

 So, s = √16/36 feet²

    s = 4/6 feet

Hence sides of the square would be 4/6 feet.

Visit here to learn more about the area: https://brainly.com/question/11952845

#SPJ4

—-------- Correct question format is given below —--------

(Q). Brody calculated the area of a square to be 14/36 square feet. Which shows the side length of the square?

In unit form, 1.6 x 0.7 equals 1.12 square meters.

The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grammes (g). Milliliter (ml) and liter are used to measure volume (L).

We must identify the units of measurement that have been employed for each of the numbers in order to express 1.6 x 0.7 in unit form.

By calculating the length by the width and assuming that 1.6 meters represents the length, and 0.7 meters represents the width, we can determine the surface area of a rectangle with these measurement techniques:

1.12 square meters is equal to 1.6 x 0.7 meters.

To know more about Unit visit:

brainly.in/question/84739

#SPJ1

complete question is:

Write the expression 1.6 x 0.7 in unit form.

In unit form, 1.6 x 0.7 equals 1.12 square meters.

What kind of unit would that be?

The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grammes (g). Milliliter (ml) and liter are used to measure volume (L).

We must identify the units of measurement that have been employed for each of the numbers in order to express 1.6 x 0.7 in unit form.

By calculating the length by the width and assuming that 1.6 meters represents the length, and 0.7 meters represents the width, we can determine the surface area of a rectangle with these measurement techniques:

1.12 square meters is equal to 1.6 x 0.7 meters.

Therefore, In unit form, 1.6 x 0.7 equals 1.12 square meters.

To learn more about Unit from the given link:

https://brainly.com/question/10433377

#SPJ1

Nigeria's predicted population in 2020 is 208 million, rounded to the nearest million.

Relative change, also known as percent change, is a measure of the percentage increase or decrease in a quantity over time. In the context of population, relative change refers to the percentage change in the size of a population over a given period.

To calculate relative change in population, you would take the difference between the final population size and the initial population size, divide by the initial population size, and multiply by 100 to get the percentage change.

To find the relative change in Nigeria's population over the decade from 2000 to 2010, we use the formula:

Relative change = (new value - old value) / old value

Relative change in Nigeria's population from 2000 to 2010:

= (160 - 123) / 123

= 0.300813

So Nigeria's population increased by approximately 30.08% over the decade from 2000 to 2010.

To predict Nigeria's population in 2020, we apply this same relative change to the 2010 population:

Population in 2020 = Population in 2010 + (Relative change × Population in 2010)

Population in 2020 = 160 + (0.300813 × 160)

Population in 2020 = 160 + 48.13008

Population in 2020 = 208.13008 million

Rounding this to the nearest million, we get:

Population in 2020 = 208 million

Therefore, Nigeria's predicted population in 2020 is 208 million, rounded to the nearest million.

To know more about population visit:

https://brainly.com/question/16979534

#SPJ1

There are 31,465 different ways that an instructοr can chοοse 4 students frοm a class οf 31 students fοr a field trip.

Permutatiοns and cοmbinatiοns are twο cοncepts in mathematics that deal with cοunting the number οf pοssible οutcοmes in a given situatiοn.

Permutatiοns refer tο the number οf ways in which a set οf οbjects can be arranged οr οrdered. Fοr example, if we have three οbjects A, B, and C, there are six pοssible permutatiοns: ABC, ACB, BAC, BCA, CAB, and CBA. The fοrmula fοr calculating the number οf permutatiοns οf n οbjects taken r at a time is n! / (n-r)!, where n! represents the factοrial οf n.

The number οf ways that an instructοr can chοοse 4 students frοm a class οf 31 students is given by the cοmbinatiοn fοrmula:

C(31,4) = (31!)/(4!(31-4)!)

= (31 × 30 × 29 × 28)/(4 × 3 × 2 × 1)

= 31,465

Therefοre, there are 31,465 different ways that an instructοr can chοοse 4 students frοm a class οf 31 students fοr a field trip.

To know more about combination visit:

brainly.com/question/20211959

#SPJ1

Answer:

Step-by-step explanation:

If a square has a perimeter of 100 feet, then each side of the square must be 25 feet long, since all four sides of a square are equal.

The area of a square is given by the formula A = s^2, where s is the length of one side of the square. Substituting s = 25 feet, we get:

A = (25 feet)^2

A = 625 square feet

Therefore, the area of the playground is 625 square feet.

Answer:

625 ft^2

Step-by-step explanation:

A square will have all 4 sides equal to each other.  Let x be the length of 1 side.  The perimeter, P, of such a square would be:

  P = 4x

We are told that p = 100 feet

 100 feet = 4x

 x = 25 feet

Each side has a length of 25 feet.

The area of this square wuld be (25')*(25') = 625 ft^2

Answer:

Step-by-step explanation:

An exponential function can be written in the form y = ab^x, where a is the initial value and b is the base. To find the specific exponential function that passes through the points (1, 12) and (5, 972), we need to solve for a and b.

Using the point (1, 12), we get:

12 = ab^1

12 = ab

Using the point (5, 972), we get:

972 = ab^5

We can use the equation ab from the first point to solve for a in terms of b:

a = 12/b

Substituting this expression for a into the second equation, we get:

972 = (12/b)b^5

Simplifying this equation, we get:

972 = 12b^4

Dividing both sides by 12, we get:

81 = b^4

Taking the fourth root of both sides, we get:

b = 3

Substituting this value of b into the equation a = 12/b, we get:

a = 4

Therefore, the exponential function that passes through the points (1, 12) and (5, 972) is:

y = 4(3^x)

When Khomo and Peter sold the house 5 years later and made a profit of $234,500, Peter's share of the profit is $134,603 based on his sharing ratio.

The sharing ratio refers to the ratio or relative size of profit that a partner receives.

Sharing ratios are usually based on the initial capital contribution or some other agreed factors.

Total investment in a house by Khomo and Peter = $575,000

Khomo = $245,000

Peter = $330,000 ($575,000 - $245,000)

Khomo = 42.6% ($245,000/$575,000 x 100)

Peter =  57.4% ($330,000/$575,000 x 100)

Profit generated from the investment = $234,500

Peter's share of the profit = $134,603 ($234,500 x 57.4%)

Learn more about sharing ratios at https://brainly.com/question/28850066.

#SPJ1

Answer:

11 cm.

Step-by-step explanation:

The formula for the area of a triangle is given by:

A = (1/2)bh

where A is the area, b is the base, and h is the height (or altitude) of the triangle.

We are given that the area of the triangle is 110 cm and the base is 20 cm. Substituting these values in the formula, we get:

110 = (1/2) × 20 × h

Simplifying the equation, we get:

110 = 10h

h = 11 cm

Therefore, the height (or altitude) of the triangle is 11 cm.

There is 0.25 or 25% of probability that a senior is going to college and plays sports

We can start by using the given information to construct a probability table:

College   Work  Gap    year  Total

Sports team    50    30      5      85

Not on sports team  90     10     55      155

Total     140    40        60     200

From the table, we see that there are 50 seniors going to college who are on their school's sports teams. Therefore, the probability that a senior is going to college and plays sports is:

P(college and sports) = number of seniors going to college and on sports team / total number of seniors

= 50 / 200

= 0.25

Therefore, the probability that a senior is going to college and plays sports is 0.25 or 25%.

To learn more about probability click here

brainly.com/question/30034780

#SPJ4

Answer:

89.04

Step-by-step explanation:

To find 68% of 53, we can multiply 53 by 0.68:

68% of 53 = 0.68 x 53 = 36.04

So 53 increased by 68% is:

53 + 36.04 = 89.04

Therefore, 53 increased by 68% is 89.04.

Answer:

gradient = - [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

calculate the gradient ( slope ) m of the line using the slope formula.

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 0 ) and (x₂, y₂ ) = (1, - 1 )

m = [tex]\frac{-1-0}{1-(-4)}[/tex] = [tex]\frac{-1}{1+4}[/tex] = - [tex]\frac{1}{5}[/tex]

From the given vectors the value of t - 2r is - 15i - 5j - 10k.

In mathematics, vectors are mathematical objects that have both magnitude (length) and direction. Vectors can be represented as arrows in space, where the length of the arrow corresponds to the magnitude of the vector and the direction of the arrow corresponds to the direction of the vector.

Here we have

A cube and the vectors are u = (5,0,0), v = (0,5,0), w = (0,0,5) and
t = (-5,5,0)

The cube has edges of length 5

Consider u = 5i, v = 5j, w = 5k, and t = -5i + 5j

From the figure,

r = u + v + w  

= 5i + 5j + 5k

Now the value of t - 2r can be calculated as follows

=> t - 2r = - 5i + 5j - 2(5i + 5j + 5k )

=  - 5i + 5j - 10i - 10j - 10k

=  - 15i - 5j - 10k

Therefore,

From the given vectors the value of t - 2r is - 15i - 5j - 10k.

Learn more bout Vectors at

https://brainly.com/question/13188123

#SPJ1

Answer:

Step-by-step explanation:

cos(x+50) = 1/2

We know that cos(60) = 1/2, so we can write:

cos(x+50) = cos(60)

Using the identity cos(a) = cos(b) if and only if a = ±b + 2πn, we get:

x+50 = ±60 + 2πn

Solving for x, we have:

x = -50 ±60 + 2πn

x = 10 + 2πn or x = -110 + 2πn

Since we want to find all values of x between 0 and 180, we only need to consider the values of x that satisfy 0 ≤ x ≤ 180.

For x = 10 + 2πn, we have:

0 ≤ 10 + 2πn ≤ 180

-10/2π ≤ n ≤ 85/2π

For x = -110 + 2πn, we have:

0 ≤ -110 + 2πn ≤ 180

-35/2π ≤ n ≤ 25/2π

Therefore, the solutions for cos(x+50) = 1/2 in the interval [0, 180] are:

x = 10° + 360°n or x = 150° + 360°n, where n is an integer.

sin(2x) = -0.6

We know that sin(θ) = -0.6 has two solutions in the interval [0, 360]: θ ≈ -36.87° and θ ≈ 216.87° (using a calculator).

Using the double angle identity sin(2x) = 2sin(x)cos(x), we can write:

2sin(x)cos(x) = -0.6

Dividing both sides by 2cos(x), we get:

sin(x) = -0.3/cos(x)

Using the identity cos²(x) + sin²(x) = 1, we can substitute sin²(x) = 0.09/cos²(x) and simplify to get:

cos³(x) - 3cos(x) + 0.9 = 0

We can solve this equation using numerical methods or approximations. One possible approximation is to use the intermediate value theorem and test for sign changes in the function f(x) = cos³(x) - 3cos(x) + 0.9:

f(0) = 0.9 > 0

f(π/2) ≈ -0.84 < 0

f(π) ≈ 0.49 > 0

Therefore, there is a root of f(x) = 0 in the interval (0, π/2) and another root in the interval (π/2, π).

Using a numerical solver or more advanced methods, we can find the approximate values of x that satisfy cos³(x) - 3cos(x) + 0.9 = 0 in the intervals (0, π/2) and (π/2, π):

x ≈ 68.58° or x ≈ 111.42°

Therefore, the solutions for sin(2x) = -0.6 in the interval [0, 180] are:

x ≈ 34.29° or x ≈ 55.71°

Answer:-60

Step-by-step explanation:

Answer:

16cups

Step-by-step explanation:

1 pint of milk is 2cups

1.5pint of milk is 3cups

If 1 bottle contained 3 cups of milk,

8 ounces of strawberry is 1 cup

1 bottle contained 3cups of milk and 1 cup of strawberry syrup

1 bottle has 4 cups of milkshake

4 bottles have (4x4) cups of milkshake

Ans 16

Answer: it is 13

Step-by-step explanation:

it is 13 if you are on study island

Answer:

x=50

Step-by-step explanation:

2x=100

divided both sides by 2

x=50

answer: x=50

Answer:

50

Step-by-step explanation:

2x = 100, divide 2 from 2x and also 100, you will be left with x = 50