write 7^3 × √ 7 as a single power of 7​

Answer:

he earns $500 from the lessons from both groups of students.

Step-by-step explanation:

To summarize:

There are 14 students in set R (piano students)

There are 10 students in set R (piano students) who are not in set S (saxophone students)

There are 11 students in set S (saxophone students)

There are 14 + 11 = 25 total students in both sets R and S

There are 4 students who are common to both R and S, that are taking saxophone for free

The music teacher will get $280 for the piano students

The music teacher will get $220 for the saxophone students.

So the total he earns is $280 + $220 = $500 from the lessons from both groups of students.

Price divided by size is the formula for calculating the price per square foot (in square feet). For instance, if a 2,000-square-foot property is being sold for $300,000, the price per square foot would be $150 if you took the overall price and divided it by the size.

What do you mean by rectangular area?

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The expressions that are sums or differences of two cube:

A. 64 + a¹²b⁵¹

B. –t⁶ + u³v²¹

C. 8h⁴⁵ – k¹⁵

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

The following phrases are sums or differences of two cubes:

A. 64 + a¹²b⁵¹

=4³+(a⁴b¹⁷)³

B. –t⁶ + u³v²¹

=(-t²)³+(uv⁷)³

C. 8h⁴⁵ – k¹⁵

=(2h¹⁵)³-(k⁵)³

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Answer:

Domain: [0, ∞)

Range: [√5, ∞)



Step-by-step explanation:

Find the domain by finding where the piecewise is defined. The piecewise range is the set of values that correspond with the domain.

Domain: [0, ∞)

Range: [√5, ∞)

hope that helps...

Answer: If Pedro starts reading at page 20 and reads at an average rate of 25 pages per hour, and Bella starts reading at the same time but starts at page 60 and reads at an average rate of 18 pages per hour,

We can use the formula: distance = rate x time

To find out when they will meet we need to find out when they are on the same page.

let's say t be the time in hours, Pedro will be reading t25 pages, and Bella will be reading t18 pages.

So we can write the equation: 20+t25 = 60+t18

Solving this equation we get t = 2

So, they will meet after 2 hours.

Pedro will be on page 20+225 = 70, and Bella will be on page 60+218 = 96

So they will meet at page 70 when Pedro reaches that page after 2 hours of reading, which means Bella will have read 26 pages more than Pedro on that point.

Step-by-step explanation:

The probabilities are 5/36 and 9/36, respectively, if the sum is bigger than 6 and if the amount is divisible by 5 or 6 (or both).

Probability theory is the study of how likely it is that an event will occur or that a statement is true. A number between 0 and 1, roughly 0 signifying how unlikely an event is to occur and 1, signifying certainty, is the probability of an event occurring. The likelihood or likelihood that a particular event will occur is expressed numerically as a probability. It is also possible to express probabilities as percentages between 0% and 100% or as percentages between 0 and 1. the percentage of all possible outcomes divided by the total number of events in a complete collection of equally likely alternatives that result in a specific occurrence.

given

It may take the following forms:

(4,6),(5,5),(5,6),(6,5),(6,6)

the likelihood that the total exceeds 9 is 1/36+1/36+1/36+1/36.

=5/36.

B) The following are some possible scenarios:

(1,4),(4,1),(3,3),(3,2),(4,2),(5,1),(1,5),(6,4),(4,6)

The likelihood that the number will be divisible by five, six, or both is

1/36 plus eight times

=9/36

Therefore, The probabilities are 5/36 and 9/36, respectively, if the sum is bigger than 6 and if the amount is divisible by 5 or 6 (or both).

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The length of GC could be 7.2 when Triangle GHC is similar to triangle JKC.

What is a triangle ?

Triangle can be defined in which it contains 3 sides and 3 angles and the sum of three angles is 180 degrees .

Given

Triangle GHC is similar to triangle JKC

JK = 15

KC = 20

JC = 18

GH = 6

SO,

△GHC ~ △JKC

we know that

(GH/GC) = (JK/JC)

(6/GC) = (15/18)

GC= 6 * 18 / 15

GC = 36 / 5

GC = 7.2

Hence , the length of GC could be 7.2 when Triangle GHC is similar to triangle JKC.

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Answer:

0.10 and 0.90 are the correct answers.

Step-by-step explanation:

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Jana's rode her bike 12 miles in 45 minutes, so Jana's rate per hour is 16 miles/hour.

Given that, Jana is training for a triathlon that includes a 112 mile bike ride.

What is the speed?

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Today she rode her bike 12 miles in 45 minutes.

Here, 45 minutes =45/60 =3/4

Speed =Distance/Time

= 12 ÷ 3/4

= 12 × 4/3

= 16 miles/hour

Therefore, Jana's rode her bike 12 miles in 45 minutes, so Jana's rate per hour is 16 miles/hour.

Answer: t/w

Step-by-step explanation: It's the reciprocal, so you have to flip both. 9/5 = w/t,   5/9 = t/w

There are only three correct equations for the area of the right triangle which are:

The area of a triangle is calculated by dividing the product of the base and height of the triangle.

base of the triangle = x

height of the triangle = x + 2

area of the triangle = 1/2(x)(x + 2)

so

1/2(x)(x + 2) = 24...(1)

1/2 is also 0.5, so the equation 0.5(x)(x + 2) = 24 is correct.

by cross multiplication, equation (1) becomes;

x(x + 2) = 48

x² + 2x = 48 {expand the left hand side}

x² + 2x - 48 = 0 {subtract 48 from both sides}

so the equation x² + 2x - 48 = 0 is correct.

Considering the last equation, x² + (x + 2)² = 100

x² + x² + 4x + 4 = 100

2x² + 4x = 100 - 4 {collect like terms}

2x² + 4x = 96 {divide through by 2}

x² + 2x = 48

x² + 2x - 48 = 0

so the equation x² + (x + 2)² = 100 is equivalent to the equation (1) and so is also correct.

Therefore, the equations 0.5(x)(x + 2) = 24, x² + 2x - 48 = 0, and x² + (x + 2)² = 100 are correct and can be used to find the length of sides for the right triangle.

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The function is  A = 120[tex](1.016)^{4t}[/tex] and the balance after 6 years is  $175.64.

What is compound interest?

The interest that is calculated using both the principal and the  interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Here the principal = $120

Rate of interest = 6.4%  = 6.4/100 = 0.064C. Then,

Now using compound interest formula then,

Amount A = P[tex](1+\frac{r}{n} )^{nt}[/tex]

Here n=4 compound quarterly

A = 120[tex](1+\frac{0.064}{4} )^{4t}[/tex]

=> A= 120[tex](1+0.016)^{4t}[/tex]

=> A = 120[tex](1.016)^{4t}[/tex]

The function is A = 120[tex](1.016)^{4t}[/tex]. Now years t = 6 then

=> A = A = 120[tex](1.016)^{4*6}[/tex] = 120[tex](1.016)^{24}[/tex]

=> A =  $175.64

Hence the function is  A = 120[tex](1.016)^{4t}[/tex] and the balance after 6 years is  $175.64 .

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The algebraic expression that she can use to represent the scenario would be = $x-25/2

Algebraic expression is defined as the expression that can be used to represent a constant algebraic number, variables, and the algebraic operations.

The amount of money Tamika and her friend sold their old toys= X dollars

The amount of money that Tamika had to pay back to her parents = $25

Therefore the remaining amount = X - 25

The amount of money that she divided between her friend and her = $ x-25/2

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If the correlation between 2 variables is 1.00, the standard error of estimate equals 0 statement is True.

The statistical measure of correlation, which is expressed as a number, describes the magnitude and direction of a relationship between two or more variables. A correlation between two variables does not, however, automatically mean that a change in one variable was what led to changes in the values of the other.

The two events are causally related, which means that causation demonstrates that one event is the result of the occurrence of the other event. It is also known as the cause-and-effect principle.

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The values of trigonometric functions are sinα = -10 and cotα =  -10/24.

What is the trigonometric functions?

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions[) are real functions that relate an angle of a right-angled triangle to ratios of two side lengths.

They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.

We have given,

tanα = -(24/10)  and π α < 2π

To Find: sinα =? & cotα = ?

 [tex]{\displaystyle \tan \theta ={\frac {\sin \theta }{\cos \theta }}=\cot \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cot \theta }}}\tan \theta ={\frac {\sin \theta }{\cos \theta }}=\cot \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cot \theta }}[/tex]

cotα =   -10/24

sinα = -10

Therefore, the values of trigonometric functions are sinα = -10 and  cotα =   -10/24.

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Answer:

y=2/5x+6

Step-by-step explanation:

work attached here

Answer:

The pharmacy has 8 pints of cough syrup and a prescription calls for 3/4 of a pint, so to find the number of full prescriptions that can be filled, you would divide 8 (the total amount of cough syrup) by 3/4 (the amount of cough syrup per prescription). This would be 8 / (3/4) = 8 * (4/3) = 8 * 1.33 = 10.67.

Therefore, they can fill 10 prescriptions, they will have 0.67 left.

Step-by-step explanation:

To compute the Laplace transform of a function, we use the integral definition , F(s) = L{f(t)} = ∫ f(t) e^(-st) dt.

What is integral definition ?

The integral definition of the Laplace transform is a mathematical method used to find the Laplace transform of a function. It is defined as,

F(s) = L{f(t)} = ∫ f(t) e^(-st) dt , Where F(s) is the Laplace transform of the function f(t), s is a complex variable known as the frequency domain variable, and t is the time domain variable.

Given the functions f(t) provided ,

f(t) = e^(-8t)sin(5t)

F(s) = L{e^(-8t)sin(5t)} = ∫ e^(-8t)sin(5t) e^(-st) dt = (5/(s+8+5i))(e^(-8-s)) - (5/(s+8-5i))(e^(-8-s))

f(t) = e^(-st)sinh(7t)

F(s) = L{e^(-st)sinh(7t)} = ∫ e^(-st)sinh(7t) e^(-st) dt = (7/(s^2+49))(e^(-s-7i)) - (7/(s^2+49))(e^(-s+7i))

f(t) = -7t cosh(5t)

F(s) = L{-7t cosh(5t)} = ∫ -7t cosh(5t) e^(-st) dt = (-7/s^2)(e^(-s-5)) - (7/s^2)(e^(-s+5))

f(t) = 9t sin(ut)

F(s) = L{9t sin(ut)} = ∫ 9t sin(ut) e^(-st) dt = (9/(s^2 + u^2))(e^(-su)) - (9/(s^2 + u^2))(e^(su))

Note that in all cases, we should check if the integral converges, and that the limits of integration are appropriate.

To compute the Laplace transform of a function, we use the integral definition , F(s) = L{f(t)} = ∫ f(t) e^(-st) dt.

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Answer:

60

Step-by-step explanation:

2(7)^2 -5(7) -3

2(49) -35 -3

98 -35 -3

63 -3

60

By using the recursive formula for the sequence, we will see that the second term is:

f(2) = -4

We know that the sequence is defined by the recursive formula:

f(1) = 3

f(n + 1) = -3*f(n) + 2

(notice that the formula is written incorrectly in the question, as it not completely defines a sequence).

We want to find the second term of the sequence, which is f(2).

Using the second part of the formula, we will get:

f(2) = -3*f(1) + 2

And we know that f(1) = 3

Then:

f(2)= -3*3 + 2

f(2) = -6 + 2 = -4

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Answer:

-35/24

Step-by-step explanation:

5/8 - (3 - 1/4) + 2/3 =

Distribute the negative sign to 3 and -1/4. When a negative sign is distributed to a negative number, that number becomes positive:

- (3 - 1/4)  ==> -3 + 1/4

5/8 - 3 + 1/4 + 2/3 =

Now multiply the equation by 24/24 = 1. Multiplying anything by 1 results in the same equation. For example, 8 * 1 = 8.

Also multiply the equation by 24/24 because 24 is the LCM (Least Common Multiple) of the denominators 8, 4, and 3: 8*3=24. 6*4=24.

(5/8 - 3 + 1/4 + 2/3) * 24/24 =

(5*24/8 - 3*24 + 1*24/4 + 2*24/3) / 24 = ==> multiply each term by 24 and

                                                                    divide the entire expression by 24

(120/8 - 72 + 24/4 + 48/3) / 24 = ==> simplify

(15 - 72 + 6 + 16) / 24 =

(-57 + 22) / 24 = -35/24                                      

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The value of the numerical expression 5/8 - (3 - 1/4) + 2/3 is -35/24.

When used to represent a quantity or a mathematical relationship, symbols and numbers are combined to form an expression in mathematics. It may contain exponents, brackets, variables, constants, and mathematical operations like addition, subtraction, multiplication, and division.

To simplify the expression 5/8 - (3 - 1/4) + 2/3, we need to follow the order of operations (also known as PEMDAS):

First, we need to simplify the expression inside the parentheses (3 - 1/4):

3 - 1/4 = 12/4 - 1/4 = 11/4

Next, we need to subtract 11/4 from 5/8:

5/8 - 11/4 = 5/8 - 22/8 = -17/8

Finally, we need to add 2/3 to the result:

-17/8 + 2/3

To add these two fractions, we need to find a common denominator. The least common multiple of 8 and 3 is 24, so we can rewrite the fractions with a denominator of 24:

-17/8 + 2/3 = (-51/24) + (16/24) = -35/24

Therefore, the value of the numerical expression 5/8 - (3 - 1/4) + 2/3 is -35/24.

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Answer:

[tex]a=7[/tex]

Step-by-step explanation:

The legs of an isosceles right triangle are congruent.

The Pythagorean Theorem may be used to calculate the length of side a: [tex]a^{2}[/tex] = 72 + [tex]b^{2}[/tex] = 49 + [tex]b^{2}[/tex]. When we solve for a, we obtain a = (49 + [tex]b^{2}[/tex]). As a result, the length of side an equals the square root of 49 multiplied by the square of side b.

The Pythagorean Theorem is a mathematical equation that asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle is equal to the sum of the squares of the other two sides. The Pythagorean Theorem is stated in equation form as [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex], where a and b are the lengths of the triangle's legs (the two sides that meet at a right angle) and c is the length of the hypotenuse.

In the given question,

a = 7 * sin(45°)

  = 7 * 0.707

  = 4.949

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Answer:

last

Step-by-step explanation:

last because isometry is a shape moving rotating or reflecting across but sides are same since square became bigger and rhombus thinner only triangle is left

Answer:

30%

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} & \sf Jazz&\sf Blues & \sf Ragtime & \sf Total\\\cline{1-5} \sf Adult & 14& 15&11 & 40\\\cline{1-5} \sf Children &36 &6& 18& 60\\\cline{1-5} \sf Total &50 &21 &29 & 100\\\cline{1-5}\end{array}[/tex]

From observation of the table:

To find the percent of the children surveyed that preferred ragtime music, divide the number of children that preferred ragtime music by the total number of children:

[tex]\begin{aligned}\implies \sf Percent&=\dfrac{\sf Children\;who\;preferred\;ragtime}{\sf Total\;children}\\\\&=\dfrac{18}{60}\\\\&=\dfrac{18 \div6}{60\div 6}\\\\&=\dfrac{3}{10}\\\\&=\dfrac{3 \times 10}{10 \times 10}\\\\&=\dfrac{30}{100}\\\\&=30\%\end{aligned}[/tex]

Answer: m∠ABC = 54° and m∠​DBC= 30°

Step-by-step explanation: To find the measures of each angle, you have to make it into an equation to solve for .

In this case, the equation is (3x + 3) + (6x - 1) = 83°

First you combine like terms. In this case the 3x and the 6x have to be combined. 3x + 6x = 9x. The 3 and -1 have to be combined as well. 3 - 1 = 2.

Now you have 9x + 2 = 83°

Subtract 2 from each side and you are left with 9x = 81°.

Now divide each side by 9 and you are left with x = 9.

Now that you know the value of x, you will have to apply it to the equation for each angle.

m∠ABC = 6(9) - 9 = 53

m∠ABC = 53°

m∠​DBC = 3(9) + 3 = 30

m∠​DBC = 30°

In conclusion, the measure of angle ABC 53° and the measure of angle DBC is 3°.

Hoped this helped!!

Answer:

m∠ABC = 54° and m∠​DBC= 30°

Answer:

4/7 = 12/g cannot be true, as the numbers on the right side of the equation are not related to the numbers on the left side of the equation and cannot be used to solve for the variable "g".

The correct way to solve for the variable in an equation like this is by cross-multiplying and simplifying the equation.

4/7 = 12/g

multiply both sides by 7g

4*g = 12

Divide both sides by 4

g = 3

So in this case the value of g is 3, but the given numbers 21 15 24 3 are not related to this equation.

Step-by-step explanation:

Answer:12/21

Step-by-step explanation:

cross-multiply 4/7 = 12/g so 4g = 84 . 4 x3 =12 7x3=21 So the answer is 12/21.

The total area under the density curve for X must be exactly 1.

The region below the density curve and above the values of X that make up the event is the likelihood of any event. There must be exactly one area under the density curve for all instances of X.

A Density Curve: What Is It?

The general shape of a distribution is depicted by a density curve. The percentage of all observations falling in a certain period is represented by the area under the curve and above any interval of values on the horizontal axis. A density curve's median is the location where the area to the left and right are equal.

A graph that displays probability is known as a density curve. All probabilities are represented by 100% of the curve's area under the curve. You can alternatively state that the area is equal to 1 because 100% is a decimal, which is how we typically express probabilities.

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the interest Bianca will collect is $3127.50.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

p = 3000

r =4.25%

t =1

S = 3000*4.25*1/100 = 127.50

Hence the interest Bianca will collect is $3127.50.

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