Mathematics College

Hello, would you be able to help me with this?

Answers

Answer 1

Given: An expression

[tex]\sqrt{10}[/tex]

Required: To write the exponent form of the given expression.

Explanation: The square root of a number is the same as having an exponent of 1/2.

For example

[tex]\sqrt{36}=6[/tex]

And in exponent form,

[tex]\begin{gathered} \sqrt{36}=(36)^{\frac{1}{2}} \\ =(6^2)^{\frac{1}{2}} \\ =6 \end{gathered}[/tex]

Hence for the given expression, we can write it as

[tex]\sqrt{10}=(10)^{\frac{1}{2}}[/tex]

Final Answer: Option D is correct.

Related Questions

Hello I need help on this math questionYou can zoom in the picture

Answers

In this problem, we have the transformation

A(-3,4) -------> A'(-15,20)

The rule is

(x,y) -----> (5x,5y)

the answer is option b

geometry angels.PLS HELP I ONLY HAVE Until 10:00pm on 12/1 then I get a ZERO

Answers

We know that the angle 2 and the anlge 4 are equal because of oposite angles so:

[tex]4x-28=3x-9[/tex]

and we can solve for x so:

[tex]\begin{gathered} 4x-3x=-9+28 \\ x=19 \end{gathered}[/tex]

So:

[tex]\angle2=\angle4=3(19)-9=48º[/tex]

Now we also know that angle 1 and 3 are equal and the sum of the internal angles must be:

[tex]\begin{gathered} 360=2(48)+2(y) \\ \frac{360-96}{2}=y \\ y=132 \end{gathered}[/tex]

So angle 1 is equal to 132º

How would I multiply these two exponents?

Answers

The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.

A baseball team has home games on Wednesday and Saturday. The two games together earn $4920.00 for the team. Wednesday's game generates $880.00 less than Saturday's game. How much money did Wednesday's game generate?

Answers

Answer:

Wednesday's game generated $2020

Explanations:

Let the amount generated by Wednesday's game be x

Let the amount generated by Saturday's game be y

The two games together earn $4920 for the team. That is,

x + y = 4920....................(1)

Wednesday's game generates $880 less than Saturday's game

x = y - 880.................(2)

Make y the subject of the formula in equation (2)

y = x + 880..................(3)

Substitute equation (3) into equation (2)

x + x + 880 = 4920

x + x = 4920 - 880

2x = 4040

Divide both sides by 2

2x/2 = 4040/2

x = 2020

Wednesday's game generated $2020

help please to find the answer of the blanks

Answers

The associated matrix associated to the linear transformation is A = [tex]\left[\begin{array}{cc}5&-6\\1&- 3\\8&- 2\\0 & - 4\end{array}\right][/tex].

How to find the associated matrix associated to a linear transformation

Linear transformations are applications between two vector spaces that preserves the properties of vector addition and the product of a vector and a scalar. In this problem, we find the following linear transformation between the two bases:

W → V

(w₁, w₂, w₃, w₄) → v₁

Then, there is the following relationship:

V = A · W

Where A is the associated matrix. The matrix V has four rows and one column and the matrix W has two rows and one column. Then, by property of multiplication of matrices, the associated matrix has four rows and two columns. Then, the associated matrix is:

A = [tex]\left[\begin{array}{cc}5&-6\\1&- 3\\8&- 2\\0 & - 4\end{array}\right][/tex]

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10x3 thousands=?How many thousands are in the answer?

Answers

Given:

[tex]10\times3\text{ thousands}[/tex]

Required:

We need to find the number of thousands.

Explanation:

Multiply 10 and 3.

[tex]10\times3\text{ =30}[/tex][tex]10\times3\text{ thousands=30 thousands}[/tex]

The number of thousands is 30.

Final answer:

There are 30 thousands.

Describe a situation that can be modeled using the given simulation. 1 marble chosen from a bag containing 11 red marbles and 4 blue marbles a. Determine the probability of selecting a month from January through November and the month begins with the letter J. b. Determine the probability of surveying 11 people and 4 of them like playing checkers. c. Determine the probability of selecting a pair of tennis shoes from a shoe collection that contains 4 dress shoes and 7 tennis shoes. d. Determine the probability of selecting an apple from a basket that contains 11 apples and 4 oranges.

Answers

Answer:

Explanation:

A bag contains 11 red marbles and 4 blue marbles.

• The total number of marbles = 11+4=15

1 marble of any color is chosen random from the bag with a probability of 1/15.

A situation that can be modeled using such a situation must be one that also has a probability of 1/15.

In Option D,

4. Answer the following questions based on the information below:Han wants to build a dog house. He makes a list of the materials needed:• At least 60 square feet of plywood for the surfaces• At least 36 feet of wood planks for the frame of the dog house• Between 1 and 2 quarts of paintHan's budget is $65. Plywood costs $0.70 per square foot, planks of wood cost $0.10 per foot, andpaint costs $8 per quart.

Answers

Part A

The variable are;

Plywood, wood planks, quarts of paint

Part B

Let p represent Plywood

Let w represent Plank of wood

[tex]1

Part c

Let p represent Plywood

Let w represent Plank of wood

Let q represent quarts of paint

[tex]0.7p+0.1w+8q\leq65[/tex]

The balance of an account after t years can be found using the expression 4,500(1.75)^t where the initial balance was $4,500. By what percent does the account increase annually?

Answers

Solution

The Amount after t years is given by

[tex]A(t)=4500(1.75)^t[/tex]

The Percentage annual increase is

[tex]\begin{gathered} \frac{A(1)-A(0)}{A(0)}\times100\% \\ \Rightarrow\frac{4500(1.75)-4500}{4500}\times100\% \\ \Rightarrow0.75\times100\%=75\% \end{gathered}[/tex]

Hence, the account increase 75% annually

a real life situation for -2 × 4

Answers

How many miles of gas does my car travel if it used 2 gallons of gas with a speed of 4 mi/h?

A player hit a baseball from home plate 3 feet above the ground. The graph shows the height in feet of the baseball above the grounds as a quadratic function of x, the horizontal distance in feet of the baseball from home plate.What is the domain of this function?3≤x≤400≤y≤103≤y≤100≤x≤40

Answers

As the image attached shows, the horizontal distance reached by the ball is 40 feet.

Notice that the horizontal movement goes from 0 to 40, this means the domain is

[tex]0\leq x\leq40[/tex]

Since x-values are domain values.

Therefore, the right answer is the last choice.

4/5 × (12÷2+4)-1 what is the value of the expression

Answers

Given the expression

[tex]\frac{4}{5}\cdot(12\div2+4)-1[/tex]

To find the value of the expression you have to follow the order of operations:

- Parentheses

- Exponents

- Multiplication/Division

- Addition/ Subtraction

• First, you have to solve the operations inside the parentheses term:

[tex]12\div2+4[/tex]

Solve the division first and then the sum:

[tex]12\div2+4=6+4=10[/tex]

• Write the result on the original expression:

[tex]\begin{gathered} \frac{4}{5}\cdot(12\div2+4)-1 \\ \frac{4}{5}\cdot10-1 \end{gathered}[/tex]

• The next step is to solve the multiplication and finally solve the difference

[tex]\frac{4}{5}\cdot10-1=8-1=7[/tex]

The value of the expression is 7

M={z / z is an integer and -2

Answers

The given set in roster method is written as {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}.

Given that, M={x : x is an integer and 2 ≤ x ≤20.

What is roster method?

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

Now, the given set in roster method can be written as follows:

{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

Therefore, the given set in roster method is written as {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}.

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"Your question is incomplete, probably the complete question/missing part is:"

Write the given set in roster method: M={x : x is an integer and 2 ≤ x ≤20

The density of copper is 9.86 g/cm".
Work out the mass of the solid copper cuboid in kg
10 cm
3 cm
5 cm
Step by step

Answers

it’s 10 girl hey bye bye

How many gallons of the water are in the filled tank? You must show work with dimensional analysis using the above fact.

Answers

From the question, we can deduce the following:

Length = 5.6 meters

Width = 7.3 meters

Height = 4.5 meters

Where:

1 ft = 0.3048 m

1 cubic foot = 7.48 gallons

Let's find the amount of gallons of water in the tank if the tank is filled to 1 foot below the top of the tank.

Let's first sketch the tank.

We have:

Now, let's find the volume of the tank(total amount of water it can carry).

Apply the formula:

[tex]V=l\times w\times h[/tex]

Thus, we have:

[tex]\begin{gathered} V=5.6\times7.3\times4.5 \\ \\ V=183.96m^3 \end{gathered}[/tex]

Now, to find the amount of water presently in the tank since it is filled 1 ft below the top of the tank, we have:

[tex]\begin{gathered} V=5.6\times7.3\times(4.5-0.3048) \\ \\ V=5.6\times7.3\times4.1952 \\ \\ V=171.5m^3 \end{gathered}[/tex]

Therefore, the volume of the water in the tank is 171.5 cubic meters.

Now, let'c convert from cubic meters to gallons.

Where:

1 foot = 0.3048 m

[tex]1meter=\frac{1}{0.3048}=3.28\text{ feet}[/tex]

Thus, we have:

[tex]\begin{gathered} 1\text{ cubic meter = 3.28}^3=35.29\text{ cubic f}eet \\ \\ 171.5\text{ cubic meters = 171.5 x 35.29 = }6052.235\text{ cubic fe}et \end{gathered}[/tex]

Now, to convert from cubic feet to gallons, where:

1 cubci foot = 7.48 gallon

We have:

[tex]6052.235\times7.48=45273.86\text{ gallons}[/tex]

Therefore, there are 45273.86 gallons of water filled in the tank.

(1 point) The expression 64g4y2 64gʻy2 equals kg"ys where r, the exponent of g, is: and s, the exponent of y, is: and k, the leading coefficient is:

Answers

We are asked to find the final expression in exponent for, of the product of two radical expressions as shown below:

We will be addressing each factor at a time, first in the cubic root, and second in the square root.

Cubic root:

notice that the pure number (64) can be written as the perfect cube of the number 4 since 4^3 = 64. That means that a factor 4 will come out of the cubic root, and no factor 4 will be left in the root.

Now we are going to address the variables g and y which are inside the root, and try to find if they contain any perfect cube expression (perfect cubes will cancel out of the cubic root simplifying then the notation).

We notic that g^4 can be written as g^3 times g, so g^3 will come out of the cubic root as "g", and a factor "g" would be left inside the cubic root. Similarly, the factor y^2 cannot get out of the cubic root because it doesn't have a perfect cube in it.

We are then left with the following expression:

[tex]4g\sqrt[3]{g\cdot y^2}[/tex]

Now, we recall the property of fractional exponents associated with roots of a factor:

[tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]

Using this, the cubic root can be expressed as fractional exponents, as we show below:

[tex]4g\sqrt[3]{g\cdot y^2}=4g\cdot g^{\frac{1}{3}}\cdot y^{\frac{2}{3}}=4g^{\frac{4}{3}}\cdot y^{\frac{2}{3}}[/tex]

Now we proceed to simplify the expression with the square root. This is much simpler, since all factor inside can be written as perfect squares:

64 = 8^2

g^4 = (g^2)^2 (the double square of g)

y^2 is already a perfect square.

Therefore, the square root is simplified entirely and we are left with the following factors:

8 g^2 y

Now we combine via the multiplication what we found for the cubic root and what we found for the square root:

[tex](4\cdot g^{\frac{4}{3}}\cdot y^{\frac{2}{3}})\cdot(8\cdot g^2\cdot y)=32\cdot g^{\frac{10}{3}}\cdot y^{\frac{5}{3}}[/tex]

Therefore the power (r) of the factor g is the fraction: 10/3

The power (s) of the factor y is the fraction 5/3

and the constant number "k" is 32.

What is 30 percent of 120?

Answers

36
Explanation:
30/100 times 120 = 36

Answer:

30 percent of 120 is 36

Given: Ray BD bisects prove: <1 and <3 are supplementary

Answers

Let's begin by listing out the information given to us:

[tex]\begin{gathered} |BD|\text{ bisects }|EBC|\text{ into equal parts}\Rightarrow\angle1=\angle2 \\ \angle2\text{ is supplementary with }\angle3;\angle2+\angle3=180^{\circ} \\ \therefore\angle1+\angle3=180^{\circ} \end{gathered}[/tex]

lan and Matthew went shopping. lan spent $20 less than twice as much as Matthew spent. In total, they spent $130.

Answers

Using linear algebra, we concluded, the Mathew spent $50 and lan spent $80

What is Linear Algebra?

Vectors, matrices, vector spaces, and linear transformations are all topics covered in the mathematical field of linear algebra. Linear algebra is much better understood than other areas of mathematics, which are regularly stimulated by novel concepts and unresolved issues.

According to the question,

Let Mathew spent $x

lan spent = 2x - 20

Total money spent = $130

⇒ 2x - 20 + x = 130

⇒ 3x - 20 = 130

⇒ 3x = 150

⇒ x = 50

2x - 20 = 2(50) - 20

= 80

So, Mathew spent $50 and lan spent $80

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PLS HELP ME ASAP!!!!

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The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.

What is meant by data set?

A data set is a group of figures or values related to a specific topic. a list of words, numbers, or symbols, the values of which are frequently the outcomes of an investigation or observation. There are typically multiple variables in data sets.

A dataset is an organized group of data typically connected to a certain body of work. An organized collection of data kept as several datasets is called a database.

In an ordered data set, the median is the value in the middle. The mean is calculated by dividing the sum of all values by the total number of values. The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.

Therefore, the correct answer is option c) The northbound cars were generally faster because the median for the northbound cars is greater than the median for the southbound cars.

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The box and whisker plot summarizes the data collected on the number of Broadway tickets sold and the actual number of attendees at the plays. Which statement is TRUE about the statistics?
A.) The majority of the data values fall in the upper quartile for both sets of data.
B.) There were fewer tickets purchased than people attending the plays.
C.) The medians of the populations are the same.
D.) There were fewer attendees than purchased tickets.
The plot:

Answers

The true statement based on the information is that D. There were fewer attendees than purchased tickets.

Whet is a box and whisker plot?

A box and whisker plot is a graphical representation of variance in a set of data. A histogram analysis is sufficient in most circumstances, but a box and whisker plot can provide more detail while allowing different sets of data to be displayed in the same graph.

The box and whisker figure highlights data on the number of Broadway tickets sold and actual attendance at the performances. In this case, the graph shows that the number of tickets are more.

Therefore, the correct option is D.

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wildlife shelter in North Carolina is home to native species of birds. mammals, and reptiles. If cat chow is sold in 20 lb bags, what is the least number of bags of cat chow needed for one year at this shelter

Answers

At least 26 bags of cat chow is required for a period of one year to fulfil the demand at the wildlife shelter in North Carolina

Quantity of cat chow sold in each bag = 20 lb

Consumption in lb of cat chow per week in the wildlife shelter = 10 lb

Number of weeks in a year = 52 weeks

The total quantity of cat chow required for 52 weeks = Weekly consumption of cat chow*Number of weeks

= 10*52

= 520 lb

Number of bags required = Toal quantity of cat chow required for 52 weeks/ Quantity of cat chow sold in each bag

= 520/20

= 26 bags

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John took 30 minutes to bicycle to his grandmother’s house, a total of 2.5 kilometers. What was his speed in km/hr?

Answers

Answer:

5(km)/1(hr)

Step-by-step explanation:

You multiply the 30 minutes to make one hour, and with that, you also multiply the 2.5 kilometers to get 5. You multiply the 2.5 because we multiply both sides of an equation.

Uniform line movement.

We have that the data is:

Time (t) = 30 m = 0.5 h

Distance (d)= 2.5 km

Speed (v) = ?

Since it asks us for the speed in Km/h, we make a time conversion, from minutes to hours. Knowing that 1 hr = 60 minutes, then

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{30 \not{m}*\left(\frac{1 \ h}{60 \not{m})\right)=0.5 \ h } } \end{gathered}$}}[/tex]

To calculate the speed, divide the distance by the time. We apply the following formula:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{Speed=\frac{Distance}{Time} } \end{gathered}$}}[/tex]

We substitute our data in the formula and solve:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=\frac{d}{t} } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=\frac{2.5 \ km}{0.5 \ h} } \end{gathered}$}}[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=5 \ km/h} \end{gathered}$} }}[/tex]

Juan's speed was: 5 km/h.

In August, a giant panda named Lucky was born at the Silver City Zoo. In September, Lucky
weighed 3.07 pounds. Today, Lucky is weighed again and he is heavier than before. Now
Lucky weighs 10.81 pounds.
Use an equation to find the amount of weight Lucky gained between September and today.

Answers

Using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.

What is a Linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

So, in September, Lucky weighed = 3.07 pounds

Today's Lucky weighed = 10.81 pounds

The equation form is:

Let x = weight to find Lucky3.07 + x = 10.81This is a linear equation

So, now solve this linear equation and find 'x' as follows:

3.07 + x = 10.81=> x = 10.81 - 3.07=> x = 7.74

Therefore, using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.

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Write and solve an equation that represents the following math sentence.

Twenty-nine equals the sum of 11.5 and the quotient of a number and 2.5.

29 equals 11.5 plus m over 2.5; m = 43.75
29 equals 11.5 plus m over 2.5; m = 7
29 = 11.5 + 2.5m; m = 43.75
29 = 11.5 + 2.5m; m = 7

Answers

The algebraic expression which correctly represents the word phrase and it's solution are respectively; 29 equals 11.5 plus m over 2.5; m = 43.75.

What is the algebraic expression which correctly represents the given word phrase?

It follows from the task content that the algebraic expression of which represents the word phrase is to be determined.

First, the quotient of a number, m and 2.5 can be represented algebraically as; m/2.5.

Therefore, since; Twenty-nine equals the sum of 11.5 and the quotient of a number and 2.5, we have;

29 = 11.5 + (m/2.5)

The solution is therefore as follows;

29 -11.5 = (m/2.5)

17.5 = (m/2.5)

m = 2.5 × 17.5

m = 43.75.

Therefore, the correct answer choice is; 29 equals 11.5 plus m over 2.5; m = 43.75.

Answers

Given the following trigonometric expression:

[tex]sin^3x+cos^2x*sinx=?[/tex]

We will simplify the expression as follows:

First, taking sin (x) as a common

[tex]=sin\text{ }x*(sin^2x+cos^2x)[/tex]

Second, we will use the following trigonometric identity:

[tex]sin^2x+cos^2x=1\rightarrow(1)[/tex]

Finally, substitute the trigonometric identity number (1) into the given expression

[tex]=sin\text{ }x*1=sin\text{ }x[/tex]

So, the answer will be sin (x)

Find the value of f(4) for the func
f(x) = -3(x + 2)
f(4) = (Simplify your answer.)

Answers

Answer: f(4) = -18

Step-by-step explanation:

f(4) = -3(4 + 2)

= -3(6)

= -18

Vector A and B are at right angles and have the same initial point. Find the magnitude and direction from vector A of the resultant vector.

Answers

We need to find the magnitude and direction from vector A of the resultanr vector.

15. The life of a 9-volt battery is normally distributed with a mean of = 2000 hours and a standarddeviation of = 40 hours. What is the proportionof batteries with an average life of 2100 hours ormore? (enter the answer as a percent rounded tothe nearest hundredth as needed)

Answers

To answer this question we will use the following formula for the z-score:

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ where\text{ }x\text{ is the observed value, }\mu\text{ is the mean, and }\sigma\text{ is the standard deviation.} \end{gathered}[/tex]

Substituting = 2000h, = 40h and x=2100h we get:

[tex]z=\frac{2100h-2000h}{40h}.[/tex]

Simplifying the above result we get:

[tex]z=\frac{100h}{40h}=2.5.[/tex]

Using tables we get:

[tex]P(z<2.5)=0.99379[/tex]

Then:

[tex]P(z\geq2.5)=1-0.99379=0.00621.[/tex]

The above result as a percentage is:

[tex]0.621\%.[/tex]

Answer:

[tex]0.62\%.[/tex]

The area of a window measures 336 Square inches. If the window is 16 inches wide. How long is the window?

Answers

The window has a length of 21 inches

How to determine the length of the window?

From the question, we have the following parameters

Area of the window = 336 square inches

Width of the window = 16 inches

The area of the window is the product of its dimensions

So, we have

Area = Width of the window x Length of the window

Substitute the known values in the above equation

So, we have the following equation

336 = 16 * Length

Divide both sides by 16

Length = 21

Hence, the length is 21 inches