Use the distributive property to write an equivalent expression. 8(5m+5)

The equation that shows the power of a power property by obtaining the product of the exponents is given as follows:

(y^a)^b = y^(a x b).

Meaning that the lower right option is the correct option.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

A simple example is given as follows:

(2²)³ = 2^(2 x 3) = 2^6.

Hence the general format of the expression is presented as follows:

(y^a)^b = y^(a x b).

Which gives the correct option in the context of this problem, and the correct option is the bottom right option.

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The number of outfits Mariam can purchase is 7.

The inequality to represent the situation is 560 ≤ 349.02 + 27.40x.

Mariam has $560 to spend at a bicycle store for some new gear and biking outfits. The price list are as follows:

She plans to spend some or all of the money she has left to buy new biking outfits for $27.40 each.

The inequality that can be used to determine x, the number of outfits Mariam can purchase within her budget can be calculated as follows:

560 ≤ 275.67 + 3(16.32) + 24.39 + 27.40x

where

x = number of biking outfits

560 ≤ 275.67 + 3(16.32) + 24.39 + 27.40x

560 ≤ 275.67 + 48.96 + 24.39 + 27.40x

560 ≤ 349.02 + 27.40x

560 - 349.02 ≤ 27.40x

divide both sides by 27.40

210.98 ≤ 27.40x

divide both sides by 27.40

210.98 / 27.40 ≤ x

7.7 ≤ x

Therefore, the number of outfit he can purchase is 7.

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Answer:

Step-by-step explanation:

1

They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.

This type of decision making is known as bounded rationality. Bounded rationality acknowledges that people often make decisions based on incomplete and imperfect information but seek the best possible outcome. People use heuristics and mental shortcuts to make decisions and tend to satisfice, which means they settle on a satisfactory solution rather than searching for the optimal solution. This type of decision making is often used when the complexity of a problem is too great to be solved analytically.

Bounded rationality is a type of decision making which acknowledges that people often make decisions based on incomplete and imperfect information, and seek the best possible outcome using heuristics and mental shortcuts. They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.

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The flowers was 8 roses, 2 lillies and 2 irises in each of the identical bouquet.

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x represent the number of roses in each bouquet, y represent the lillies in each bouquet, and z represent the irises.

A florist must make 5 identical bridesmaid bouquets for a wedding. She has a budget of $160, hence:

Cost of flowers in each bouquet = $160/5 = $32

She wants 12 flowers in each bouquet, hence:

x + y + z = 12   (1)

She wants twice as many roses as the other two types of flowers combined, hence:

x = 2(y + z)

x - 2y - 2z = 0   (2)

Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each, hence:

2.5x + 4y + 2z = 32    (3)

From the equations:

x = 8, y = 2, z = 2

There was 8 roses, 2 lillies and 2 irises.

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Answer: g(f(10)) = g(√2x+5) = 6x-3

We need to substitute x = √2*10 + 5 into g(x) = 6x - 3

g(f(10)) = 6(√2*10 + 5) - 3 = 6√20 + 30 - 3 = 6√20 + 27

So g(f(10)) = 6√20 + 27.

The steps in the correct order to solve the equation: [tex]3\times 2^{(2t-5)} - 4 = 10[/tex] is given below and the solution to given equation is t = 3.625

Consider given equation: [tex]3\times 2^{(2t-5)} - 4 = 10[/tex]

We arrange the given steps in correct order to solve given equation.

Step 1:

Add 4 to each side of the equation.

⇒ [tex]3\times 2^{(2t - 5)} = 14[/tex]

Step 2:

Divide each side of equation by 3

⇒ [tex]2^{(2t - 5)} =\frac{14}{3}[/tex]

Step 3:

Take the log of each side of equation.

[tex]log 2^{(2t-5)} = log(\frac{14}{3})[/tex]

Step 4:

use the exponential property and write (14/3) in decimal form:

⇒ (2t - 5) log(2) = log(4.67)

Step 5:

Divide each side by log 2

⇒ 2t - 5 = log(4.67) / log(2)

Step 6:

Find the value of log(4.67) / log(2) and substitute  

⇒ 2t - 5 = 2.23

Step 7:

Add 5 to each side of the equation

⇒ 2t = 2.23 + 5

Step 8:

Simplify

t = 3.625

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Note if Tommy were to hire a car to drive 850 miles in 8 days under the price conditions given, it would cost him £575 to go with the cheaper company which is company B.

To compute the cheaper price, we need to work out how much it comes to if he went with either company.

Company A:

Daily Charge £20

Cost per mile 50p

Given that he goes 850 Miles ;

For 8 days,

His Total cost with Company A is

(20 x 8) + [ (50 *850)/100); recall that 100 pence (p) make 1 British Pound (£)

Thus, 160 + 425

= £585

Thus, to go with Company A, Tommy will spend £585

On the other hand, Tommy's Total cost with Company B is computed as follows;

Daily Charge £40

Cost per mile 30p

Total cost will come to: (40 x 8) + [(30 *850)/100)

= 320 + (25500/100)

= £575

Since Company will charge a total of £585 and Company B will charge a total of £ 575, we can conclude that the cheaper company is company B.

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Full Question:

Tommy wants to hire a car to drive 850 miles in 8 days how much would it cost him to hire a car from the cheaper side. See the attached for the pricing conditions.

To find the ratio equivalent to another ratio, divide both parts of the ratio by the same number. This will create a new ratio that is equal to the original ratio. For example, to find the ratio equivalent to a ratio of 4:6, divide both 4 and 6 by 2. This results in a new ratio of 2:3, which is equivalent to 4:6.

1. Start by identifying the ratio that you need to find the equivalent of.

2. Divide both parts of the ratio by the same number.

3. This will create a new ratio that is equal to the original ratio.

To find the ratio equivalent to another ratio, divide both parts of the ratio by the same number. This will create a new ratio that is equal to the original ratio.

To find the ratio equivalent to another ratio, divide both parts of the ratio by the same number. This will create a new ratio that is equal to the original ratio. For example, to find the ratio equivalent to a ratio of 4:6, divide both 4 and 6 by 2. This results in a new ratio of 2:3, which is equivalent to 4:6.

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The given expression 1 2/3+(-8 1/2) is equivalent to -41/6.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression is 1 2/3+(-8 1/2)

=5/3+(-17/2)

=5/3-17/2

Taking LCM 6

=(10-51)/6

=-41/6

Hence,

        The given expression 1 2/3+(-8 1/2) is equivalent to -41/6.

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Answer:

The length of the third side (Hypotenuse) is 7.1556411313

Step-by-step explanation:

In order to find the third side(Hypotenuse) we use a formula called the phytogorean theorem which was invented by a philosopher named Pythagoras.

[tex]a^{2} +b^{2} =c^{2}[/tex]

We now apply the given values to the equation

[tex]5.96^{2} + 3.96^{2} = c^{2}[/tex]

Squaring the numbers we get,

[tex]35.5216+15.6816 = c^{2}[/tex]

[tex]51.2032[/tex] [tex]= c^{2}[/tex]

We now find the root of the number to find the hypotenuse which is,

[tex]\sqrt{51.2032} = c[/tex]

[tex]7.1556411313 = c[/tex]

Hence ,  the length of the third side (Hypotenuse) is 7.1556411313

The information shows that f(4)=f(30) tells us that the weight of a particular female panda at 4 years old is the same as her weight at 30 years old.

It is a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable).

In this case, Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old.

The function illustrated shows that the weights are the same.

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1 is a universal factor. It is a factor of all numbers. The number itself is a factor of the number as it divides itself entirely.

A factor is a number that divides another number and leaves no remainder. In other words, if multiplying two whole numbers gives us a product, the numbers we are multiplying are factors of the product because they are divisible by the product. There are two processes for finding factors: multiplication and division.

For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 absolutely and 12 ÷ 6 = 2 absolutely. The other factors of 12 are - 1, 2, 4, and 12.

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The value of p, q, and r cannot be found without more information about what the variables represent and any equations or relationships that they may be a part of.

Please provide more context or information about the problem you are trying to solve.

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The 1 1/4 cups of sugar and 1 1/2 cups of flour used in making one batch, indicates that the number of cups of flour Lesley should use in the new batch of cookies, expressed as a mixed fractions is 1 1/5 cups

A mixed fraction consists of the sum of the quotient and the fraction of the remainder divided by the divisor, of a fraction which has a larger numerator than the denominator.

The amount of sugar and flour required to make one batch of cookies specified in mixed fractions are;

Amount of sugar = 1 1/4 cups

Amount of flour = 1 1/2 cups

The amount of sugar in the additional batch = 1 cup of sugar

The ratio of the quantities of the sugar and flour between original batch and the new batch is therefore;

Sugar in original batch/(Sugar in new batch) = (Flour in original batch)/(Flour in the new batch)

[tex]\frac{1\frac{1}{4} }{1} =\frac{1\frac{1}{2} }{y}[/tex]

Where;

y = The number of cups of flour required in the new batch

Cross multiplying, we get;

[tex]y \times 1\frac{1}{4} = 1\frac{1}{2}[/tex]

[tex]y = \frac{1\frac{1}{2} }{1\frac{1}{4} } = \frac{6}{5} =1\frac{1}{5}[/tex]

The number of cups of flour needed in the new batch is, y = 1 1/5 cups

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At a constant speed of 45 miles per hour it will take 0.71 hours for Darla to run her errands and get back home.

What is constant speed?

An object is considered to be moving at a constant speed when it covers the same distance in the same amount of time. When moving at a constant pace, an object covers a certain distance in a fixed amount of time.

Darla drives at a constant speed of 45 miles per hour.

She drives for y miles and it takes her x hours.

The number of miles Darla can drive in x hours is y = 45x.

Darla drives to the market, 14 miles from her house.

Then she drives to the post office, 3 miles from the market.

Then she drives back to her house, 15 miles from the post office.

Calculate Darla's total distance travelled -

14 + 3 + 15 = 32 miles

Now, substituting the value of y with 32 -

32 = 45x

x = 32/45

x = 0.71

Therefore, the time taken by Darla is 0.71 hours.

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Is associated with motor impairment but does not cause it

Autism is defined as the development of disability caused by differences in the brain.

People with autism often have problems with social communication and interaction, restricted or repetitive behaviors or interests, and also have different ways of learning, moving, or paying attention.

The study didn't explain the timeline of their findings, so we can conclude this research takes data at one time.

Research that doesn't take before and after exposure data cannot be used to derive causation since we can't prove that the condition happens after exposure.

But this study still can predict association by risk ratio or odds ratio depending on the study design.

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The trigonometric equation for the function with a period of 6 is [tex]f(x) = A sin (\frac{\pi}{3}t)[/tex].

The simplest definition of a trigonometric function is the function of an angle in a triangle, often known as a circular function. It implies that these trig functions can be used to determine the relationship between a triangle's angles and sides.

The general equation of the wave is given by the formula:

f(x) = A sin(wt)

Where, [tex]w = \frac{2\pi}{T}[/tex]

where, T is the time period.

Given that T = 6, substituting the value in the formula we have;

[tex]w = \frac{2\pi}{6}[/tex]

[tex]w = \frac{\pi}{3}[/tex]

Substituting the value of w in the general equation:

[tex]f(x) = A sin (\frac{\pi}{3}t)[/tex]

Hence, the trigonometric equations for the function with a period of 6 is [tex]f(x) = A sin (\frac{\pi}{3}t)[/tex].

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Answer:

(5n + 2.29n) + (5.82 + 7.67)

Step-by-step explanation:

According to the concept of differentiation the length of his shadow changing when he is 10 feet from the base of the light is 10 feet.

Here we have given that the height of man = 6 feet

And the Height of light is 15 feet

Then the Rate of walk by man is written as

=>dx/dt = 5 feet per second.

Here we have to find the rate at which the tip of his shadow is moving when he is 10 feet from the base of the light.

Here by using ratio of similar triangles we have write it as,

=> 15/y = 6/(y - x)

When we do the cross multiplication on it, then we get

=> 15(y - x) = 6y

=> 15y - 6y = 15x

=> 9y = 15x

When we dividing by 3 on both sides then we get

=> 3y = 5x

While we differentiating both sides with respect to t then we get

=> 3(dy/dt) = 5(dx/dt)

=> dy/dt = (5/3)(6)

When we simplify this one, then we get

=> dy/dt =  10 ft/s

Hence the rate at which the tip of his shadow is changing is 10 ft/s.

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When the volume of this sphere is [tex]$\frac{K \sqrt{6}}{\sqrt{\pi}}$[/tex], then the value of K is 8

As per the data given:

The length of the cube is 2 units.

First, we have to determine the surface area of the cube.

The formula for the surface area of the cube:

A = 6 (side × side)

A = 6 (2 × 2)

A = 6 (4)

A = 24 square units

The surface area of a cube is 24 square units.

Also given that the surface area of a cube and the surface area of a sphere is equal.

The formula for the surface area of the sphere.

A = 4π [tex]r^{2}[/tex]

Where r is the radius of the sphere.

4π [tex]r^{2}[/tex] = 24

π [tex]r^{2}[/tex] = 6

[tex]r^{2}[/tex] = [tex]\frac{6}{\pi }[/tex]

r = [tex]\sqrt{\frac{6}{\pi } }[/tex]

The radius of the sphere is [tex]\sqrt{\frac{6}{\pi } }[/tex]

Also given the volume of the sphere as [tex]$\frac{K \sqrt{6}}{\sqrt{\pi}}$[/tex]

Here we have to determine the value of K.

The volume of sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

Where r is the radius of the sphere.

[tex]\frac{4}{3} \pi r^{3}[/tex] =    [tex]$\frac{K \sqrt{6}}{\sqrt{\pi}}$[/tex]

[tex]\frac{4}{3} \pi (\sqrt{\frac{6}{\pi } }) ^{3} = \frac{K \sqrt{6} }{\sqrt{\pi } }[/tex]

[tex]\frac{4}{3} \pi {\frac{6}{\pi } }= K[/tex]

K = 4 × 2

K = 8.

Therefore the value of K = 8.

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The type of system of linear equations with infinitely many solutions is called a homogeneous system of linear equations.

A system of linear equations is a set of two or more equations with two or more variables that are related to each other. When a system of linear equations has an infinite number of solutions, it is called a homogeneous system of linear equations. This is because all the equations in the system are multiples of each other, so any solution of one equation is also a solution for all the other equations.

The type of system of linear equations with infinitely many solutions is called a homogeneous system of linear equations.

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From the given information, the value of x in the given table is 42.5.

To find the value of x, we can use the formula for the arithmetic mean (average) of a set of numbers:

Arithmetic mean = (sum of all numbers) / (number of numbers)

Given that the average score on the test is 62, we can use this information to find the sum of all the scores.

Given that number of students is 1,2,3 and 4 with scores of 40,55,70 respectively, we can use this information to find the sum of all the scores.

Sum of all scores = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x)

Now we can substitute the given average score and the number of students into the equation and solve for x.

62 = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x) / 10

620 = 40 + 110 + 210 + 4x

4x = 170

x = 42.5

So, the value of x is 42.5

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The complete question is -

ten students wrote a test, and the distribution of scores is shown in the frequency table. if the average (arithmetic mean) score is 62, what is the value of x?

Score - 40, 55, 70, x

Number of students - 1, 2, 3, 4

The percentage of oil that has leaked​ from the tank is 14.29%.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.

Given that,

The capacity of the tank = 49 litres.

Total litres of oil leaked = 7 litres.

Mathematically, the percentage for the amount of oil leakage in this tank is given by this formula:

Percentage = oil leakage/tank capacity *100

Substituting the given parameters into the formula, we have:

Percentage = 7/49 *100 =  14.29%

Thus, The percentage of oil that has leaked​ from the tank is 14.29%.

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No, it is not the same as receiving a 35% discount of all the $100 items.

A discount can be defined as the amount of money a seller deducts for their customers from the normal price of the products they are selling.

The percentage discount that is generally on products that are sold for the price of $100 = 35%

The additional discount Josh received were 25% and 10% which is a total of 35% which is different from the general discount.

Therefore, it is not the same as receiving a 35% discount of all the $100 items.

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Complete question:

Josh went into a store to buy a $100 item. There was a sale of 35% off all. The sales person gave Josh a 25% discount and then an additional merchandise.

10% discount. Is that the same as receiving a 35% discount? Prove your answer.

The probability of drawing exactly three face cards is given as follows:

0.0660 = 6.60%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Considering that a standard deck is composed of 52 cards, of which 12 are face cards, and 5 cards are taken, the values of the parameters are given as follows:

N = 52, k = 12, n = 5.

The probability of drawing exactly three face cards is P(X = 3), obtained as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,52,5,12) = \frac{C_{12,3}C_{40,2}}{C_{52,5}} = 0.0660[/tex]

The problem asks for the probability of drawing exactly three face cards.

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Answer:

Step-by-step explanation:

a) To find u1, we can use the term-to-term rule given in the problem:

Un+1 = U²₁ + 5

We know that u1 = 1, so we can substitute that into the equation:

u2 = 1² + 5 = 1 + 5 = 6

b) To find u2, we can use the same term-to-term rule and substitute the value of u1 (which is 6) into the equation:

u3 = 6² + 5 = 36 + 5 = 41

c) To find un, we can use the term-to-term rule and substitute the value of un-1 into the equation.

un = un-1² + 5

It's important to note that the value of n is not given so we can't calculate the value of un.

Therefore, u1 = 6, u2 = 41, and we can't calculate un without knowing the value of n.

Angle C is 70°

Angle A is 30°

Side AC is 12 cm.

Answer:

Step-by-step explanation:

21

Answer:

Sam bikes at a faster rate.  He can go 42.6 km in one hour while Alex is only able to go 39.6 km in the same amount of time.

Step-by-step explanation:

Alex's unit rate:

198/5 = 39.6 km per hour

Sam's unit rate:

298/7 = 42.6 km per hour rounded to the nearest tenths'