Answers
a)
[tex]e^{\ln (\sqrt[]{5})}[/tex]Simplify
[tex]\ln (\sqrt[]{5})=\frac{1}{2}\ln (5)[/tex]So, we have
[tex]e^{\frac{1}{2}\ln (5)}[/tex]Apply the exponent law
[tex]\begin{gathered} (e^{\ln (5)})^{\frac{1}{2}} \\ e^{\ln (5)}=5,\text{ therefore} \\ 5^{\frac{1}{2}}=\sqrt[]{5} \end{gathered}[/tex]Answer:
[tex]\sqrt[]{5}[/tex]b)
[tex]e^{\ln (\frac{1}{\pi})}[/tex]Applying the properties of logarithms
[tex]\begin{gathered} \frac{1}{\pi} \\ \end{gathered}[/tex]Answer:
[tex]\frac{1}{\pi}[/tex]c)
[tex]10^{\log (15)}[/tex]Applying the properties of logarithms
[tex]=15[/tex]Answer: 15
Related Questions
Tiny Tim is given a problem where he is told to solve for× in the given right triangle. He sets up the equationto solve for x. Did Tiny Tim set up the problem correctly?Explain in at least 3 sentences.
Answers
The given triangle is a right-angles triangle. To solve the problem, Tim has to follow the steps below:
Step 1: Identify the sides of the triangle:
Step 2: Apply the cosine ratio since we have the adjacent and hypothenuse sides
[tex]\cos \theta\text{ = }\frac{adjacent}{hypothenuse}[/tex]Hence:
[tex]\cos \text{ 40 = }\frac{8}{x}[/tex]Answer:
Tiny Tim did not set up the problem correctly. To solve the problem, he should use the cosine ratio because in the diagram, the adjacent side is given and the hypothenuse side is required. He should not use the tangent ratio.
whats 10 times 2 i do not know
Answers
10 times 2 is equal to:
[tex]10\cdot2=20[/tex]Layla has 2 pairs of shoes and 3 pairs of socks. If each pair of socks and shoes are equally likely to be chosen, which is the best simulation to show the probability of choosing eny combination
Answers
Since we have 2*3= 6 possible scenarios, the equivalent situation would be to throw a coin and spin a spinner with 3 sections, since with that experiment, we also have 2*3=6 possible outcomes
To best estimate the quotient in scientific notation, what number should replace m?6.33 x 10°* 3x 10"1.79 x 10°
Answers
When you have a diision of numbers in scientific notation you have to know that first you divided the bases like any other division in this case:
[tex]\frac{6,33}{1,79}[/tex]and then you must substract the exponents; in this case
[tex]9-5[/tex]So the answer is:
[tex]3,5x10^4[/tex]The m is 4You rake leaves to earn extra cash. You charge clients $10 an hour. On average, you work 20 hours a week. You are thinking about increasing your hourly rate by 15%. If you do begin charging your clients more what will be the difference in how much money you earn each week?
Answers
In this case the answer is very simple . .
Step 01:
Data
Initial earnings
1 hour ===> $10
20 hours / week
New earnings
+ 15% hour
$10 * (1.15)
Step 02:
Inicial earnings
[tex]\frac{10\text{ \$}}{\text{hour}}\cdot\frac{20\text{ hour}}{\text{week}}=\text{ 200 \$ / we}ek[/tex]New earnings
[tex]\frac{10\cdot\text{ (1.15) \$}}{\text{hour}}\cdot\frac{20\text{ hour}}{\text{week}}\text{ = }230\text{ \$ / w}eek[/tex]The difference would be:
New earnings - Inicial earnings = $ (230 - 200) = $30
The answer is:
The difference in money you will earn is $ 30.
Chandler and Gabe went to the candy store. Chandler bought 6 pieces of fudge and 4 jawbreakers for a total of $5.30. Gabe bought 3 pieces of fudge and 10 jawbreakers for a total of $4.25. How much did each type of candy cost?
Answers
Answer:
The cost of 1 piece of fudge, f = $0.75
The cost of 1 piece of jawbreaker, j = $0.2
Explanation:
Let the cost of 1 piece of fudge = f
Let the cost of 1 piece of jawbreaker = j
Chandler bought 6 pieces of fudge and 4 jawbreakers for a total of $5.30.
[tex]6f+4j=5.30[/tex]Gabe bought 3 pieces of fudge and 10 jawbreakers for a total of $4.25
[tex]3f+10j=4.25[/tex]Next, solve the two equations simultaneously:
[tex]\begin{gathered} 6f+4j=5.30\ldots(1) \\ 3f+10j=4.25\ldots(2) \\ \text{Multiply (1) by 10 and (2) by 4.} \\ 60f+40j=53 \\ 12f+40j=17 \end{gathered}[/tex]Subtract:
[tex]\begin{gathered} 48f=36 \\ f=\frac{36}{48} \\ f=0.75 \end{gathered}[/tex]Substitute f to solve for j:
[tex]\begin{gathered} 6f+4j=5.30\ldots(1) \\ 6(0.75)+4j=5.30 \\ 4j=5.30-6(0.75) \\ 4j=5.30-4.5 \\ 4j=0.8 \\ j=\frac{0.8}{4} \\ j=0.2 \end{gathered}[/tex]We conclude that:
• The cost of 1 piece of fudge, f = $0.75
,• The cost of 1 piece of jawbreaker, j = $0.2
Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers. f(x)=x−−√+2, g(x)=x2+9
Answers
We have the next functions
[tex]\begin{gathered} f(x)=\sqrt[]{x}+2 \\ g(x)=x^2+9 \end{gathered}[/tex]For f(g(x))
[tex]f(g(x))=\sqrt[]{x^2+9}+2[/tex]For g(f(x))
[tex]\begin{gathered} g(f(x))=(\sqrt[]{x}+2)^2+9 \\ g(f(x))=x+4\sqrt[]{x}+4+9 \\ g(f(x))=x+4\sqrt[]{x}+13 \end{gathered}[/tex]ANSWER
[tex]f(g(x))=\sqrt[]{x^2+9}+2[/tex][tex]g(f(x))=x+4\sqrt[]{x}+13[/tex]9-41. A. Describe the solid formed by the net below. What are its dimensions (length, width, and height)?B. On graph paper, carefully draw the net of a similar solid using your enlargement ratio. Then cut out your net and build the solid (so that the gridlines end up on the outside the solid) using scissors and tape. (1) 1 (2) 2 (3) 3 (4) 4 C. How does the volume change when a three-dimensional solid is enlarged or reduced to create a similar solid? For example, if a solid’s length, width, and depth are enlarged by a linear scale factor of 10, then how many times bigger does the volume get? What if the solid is enlarged by a linear scale factor of r? Explain.
Answers
Part A
The solid formed by the net has a bottom and a top face which are rectangles with a width of 3 and a length of 4.
Also, it has four lateral faces which are rectangles: two with a length of 4 and a width of 2, and the other two with a length of 3 and a width of 2.
Notice that the width of the lateral faces corresponds to the height of the solid.
Thus, the solid is a rectangular prism, with dimensions:
• length: 4
,• width: 3
• height: 2
Part B
A similar solid with an enlargement ratio of 2 changes the length, width, and height of the solid to: 8, 6, 4.
For an enlargement ratio of 1, the dimensions stay the same.
For an enlargement ratio of 3, each dimension is multiplied by three.
For an enlargement ratio of 4, each dimension is multiplied by four.
Part C
The volume of a rectangular prism is the product of its three dimensions. So, when we enlarge each of its dimensions by a linear scale factor of 10, the volume is changed as follows:
[tex]\begin{gathered} \text{new Volume}=10(length)\times10(w\imaginaryI dth)\times10(he\imaginaryI ght) \\ \\ \text{new Volume}=10(length)\times10(w\imaginaryI dth)\times10(he\imaginaryI ght) \\ \\ \text{new Volume}=10\times10\times10(length)\times(w\imaginaryI dth)\times(he\imaginaryI ght) \\ \\ \text{new Volume}=1000\text{ \lparen original Volume\rparen} \end{gathered}[/tex]Therefore, the volume increases 1000 times.
And if the solid is enlarged by a linear scale factor of r, we have:
[tex]\begin{gathered} \text{new Volume}=r(length)\times r(w\imaginaryI dth)\times r(he\imaginaryI ght) \\ \\ \text{new Volume}=r(length)\times r(w\imaginaryI dth)\times r(he\imaginaryI ght) \\ \\ \text{new Volume}=r\times r\times r(length)\times(w\imaginaryI dth)\times(he\imaginaryI ght) \\ \\ \text{new Volume}=r^3\text{ \lparen original Volume\rparen} \end{gathered}[/tex]Therefore, the volume increases by a factor of r³.
10 The model below shows Jonathan's rate of pay by hours. How much will he get paid for the greatest number of hours shown on the model below? S105 $?
Answers
From the model, we notice that for three hours Jonathan earns $105. This means that he earns $35 (105 divided by 3) per hour.
Now, we have in total 10 hours in the model, hence he will earn a total of $350 (35 times 10).
A basketball player makes 6 out of 10 free throws. Based on her results, how manyof her next 35 free throws will she not make?
Answers
From the information given, the basketball player makes 6 out of 10 free throws. This means that the probability that she will make a throw from a number of free throws is
6/10 = 3/5
Recall, total probability is 1
The probability that she will not make a throw from a number of free throws is
1 - 3/5 = 2/5
Thus, if she has 35 free throws, the number of throws that she will not make is
2/5 x 35
= 14
She will not make 14 throws
A major supplier has 427 transformers on back order. On the same day they receive 1,000 transformers, they have additional transformer orders placed for 27, 150, 310, and 36. How many transformers are left in stock after filling all orders?
Answers
We have that the total transformers is 427 + 1000 = 1427.
Then, if we substract the transformer orders, we get:
[tex]1427-27-150-310-36=904[/tex]therefore, there are 904 transformers left in stock
Question
1. decrease 28 by 125%
correct answers gets a REWARD!!!!
Answers
The result of the statement " The decrease 28 by 125% " is -7
The number = 28
The decreased percentage = 125%
The percentage is defined as the number or ratio that can be represented as the fraction of 100. The percentage can be denoted as writing the percentage sign "%" after the number
125% of 28 = 28×(125/100)
= 3500/100
= 35
The decrease 28 by 125% = 28 - 125% of 28
Substitute the values in the equation
The decrease 28 by 125% = 28 - 35
= -7
Hence, the result of the statement " The decrease 28 by 125% " is -7
Learn more about percentage here
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For each equation, choose the statement that describes its solution.
If applicable, give the solution.
3(y+2)+y=4(y-1)+9
5(u+1)-u=4(u-1)+9
Answers
ANSWER
The first equation has no solution
The second equation has infinitely many solutions
STEP-BY-STEP EXPLANATION:
From the question provided, you are given the following equations
3(y + 2) + y = 4(y - 1) + 9
5(u + 1) - u = 4(u - 1) + 9
To find the values of y and u, we need to solve the equations independently
[tex]\begin{gathered} 3(y\text{ + 2) + y = 4(y - 1) + 9} \\ \text{open the parentheses} \\ 3\cdot\text{ y + 3 }\cdot\text{ 2 + y = 4}\cdot y\text{ - 4 }\cdot1\text{ + 9} \\ 3y\text{ + 6 + y = 4y - 4 + 9} \\ \text{Collect the like terms} \\ 3y\text{ + y + 6 = 4y + 5} \\ 4y\text{ + 6 = 4y + 5} \\ 6\text{ = 5} \\ \text{Hence, the equation has no solution} \end{gathered}[/tex][tex]\begin{gathered} 5(u\text{ + 1) - u = 4(u - 1) + 9} \\ \text{Open the parentheses} \\ 5\cdot\text{ u + 5}\cdot1\text{ - u = 4}\cdot u\text{ - 4}\cdot1\text{ + 9} \\ 5u\text{ + 5 - u = 4u - 4 + 9} \\ \text{Collect the like terms} \\ 5u\text{ - u + 5 = 4u + 5} \\ 4u\text{ + 5 = 4u + 5} \\ 5=\text{ 5} \\ \text{Hence, this equation has infinite }solutions \end{gathered}[/tex]?ОАОвосODWhich graph represents theparabolic equation(x - 2)^2 = 12(y - 3)?DoneA-2ОУБ1wN1(2,3)(2,0)23 4(2,3)2(5,3)St.5A5.66B-3О0(-1,3)0-1:УБLOID10(2,6)(2,3)3(2,3)С3A
Answers
Solution:
Given:
[tex](x-2)^2=12(y-3)[/tex]Using a graph plotter, the graph of the parabolic equation showing its y-intercept and vertex is shown;
I need help with these math questions extraneous solution #9
Answers
given the function
[tex]4x-17=\frac{15}{x}[/tex]solving for x
[tex]x(4x-17)=15[/tex][tex]4x^2-17x=15[/tex][tex]4x^2-17x-15=0[/tex][tex]4x^2-20x+3x-15=0[/tex][tex]2^2x(\frac{2^2*x^2}{2^2*x}-\frac{2^2*5x}{2^2*x})+3(\frac{3x}{3}-\frac{3*5}{3})=0[/tex][tex]2^2x(x-5)+3(x-5)=0[/tex][tex](x-5)(2^2x+3)=0[/tex][tex](x-5)(4x+3)=0[/tex]then
[tex](x-5)=0[/tex][tex]x=5[/tex]and
[tex]4x+3=0[/tex][tex]4x=-3[/tex][tex]x=-\frac{3}{4}[/tex]x = 5
x = -3/4
what numbers equal 10
Answers
Answer:
Step-by-step explanation:
I need help with this practice I’m having a tough time completing it
Answers
Explanation
We are given a function that shows the relationship between the temperature and the number of minutes to be
[tex]f(x)=-19sin(\frac{7}{3}x+\frac{1}{6})-3[/tex]I have I have two patterns and I need to find the correct equation
Answers
First pattern
The number of squares in the first term is 3
The second term is 5
The third term is 7
So this pattern increased by 2
The rule of any pattern increased by a constant number is
y = a + (x-1)d, where
a is the first term
d is the constant difference
x is the position of the term
So a = 3
and d = 2
The equation is
y = 3 + (x - 1)2
Multiply 2 by the bracket
y = 3 + 2x - 2
Add the like terms
y = 2x + 1
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I don't understand how to do this equation. The string is 108 inches. The string is cut into 3 pieces. One piece is 2 inches longer than the shortest piece., and the longest piece is 4 inches longer than the shortest piece. How long is the longest piece?
Answers
Start by sketching the situation, dividing the string into 3 pieces
Call the shortest piece as x
Then since the other pieces are a reference to the shortest side we can call them as:
[tex]\begin{gathered} x+2 \\ x+4 \end{gathered}[/tex]Then, add them to the sketch
If we add together the 3 pieces they must be equal to the initial length of the string
[tex]x+(x+2)+(x+4)=108[/tex]Simplify the left side of the equation
[tex]\begin{gathered} 3x+6=108 \\ \end{gathered}[/tex]Solve the equation for x
[tex]\begin{gathered} 3x+6-6=108-6 \\ 3x=102 \\ x=\frac{102}{3} \\ x=34 \end{gathered}[/tex]The shortest piece is 34 inches long.
The longest piece is 4 inches longer than the shortest, then,
[tex]34+4=38[/tex]The longest piece is 38 inches long.
Find the equation of the line that passes through negative 3 and negative 3 and that is parallel to X - to Y equals negative 7
Answers
The given equation is
[tex]x-2y=-7[/tex]First, we find the slope of the given equation.
[tex]\begin{gathered} -2y=-7-x \\ y=\frac{-7-x}{-2} \\ y=\frac{7}{2}+\frac{x}{2} \end{gathered}[/tex]Remember that the slope is the coefficient of x. So, the slope of the given line is 1/2.
Since the new line must be parallel, then its slope is also 1/2.
According to the problem, the new line passes through (-3, -3). Let's use the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=\frac{1}{2}(x-(-3)) \\ y+3=\frac{1}{2}x+\frac{3}{2} \\ y=\frac{1}{2}x+\frac{3}{2}-3 \\ y=\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]Therefore, the equation of the new parallel line is[tex]y=\frac{1}{2}x-\frac{3}{2}[/tex]find the slope of the line y= 5/2x + 7/5
Answers
The line equation in general form is written as,
y = mx + b .........(1)
Here, m is the slope and b is the y-intercept.
The given equation of line,
[tex]y=\frac{5}{2}x+\frac{7}{5}[/tex]is of the form of the general equation (1).
So equating the coefficients, we can see that,
[tex]\text{slope, m = }\frac{5}{2}[/tex]Alan is a paleontologist who collects dinosaur fossils. He keeps each fossil in a cube - shaped box with edges that are 1/2 ft long. Alan keeps the boxes in a storage bin. The storage bin is a right rectangular prism that is 2 1/2 ft. long, 2 ft. wide, and 2 ft. tall. How many boxes can Alan keep in the bin?
Answers
In order to answer this question, we need to find the volume of one cubic box and the volumeof the storage bin.
The volume of the cubic box is given by
[tex]V_c=(\frac{1}{2})^3[/tex]which gives
[tex]V_c=\frac{1}{8}ft^3[/tex]On the other hand, the volume of the storage bin is given by
[tex]V_s=2\frac{1}{2}\times2\times2[/tex]but we need to convert first the mixed fraction form into a simple fraction form, that is
[tex]2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{5}{2}[/tex]then, its volume is
[tex]\begin{gathered} V_s=\frac{5}{2}\times2\times2 \\ V_s=10ft^3 \end{gathered}[/tex]Now, we need to compare our last volume with the volume of the cubic box, that is,
[tex]\frac{V_s}{V_c}=\frac{10}{\frac{1}{8}}=80[/tex]this means that Alan can keep 80 cubic boxes into the storage bin
Expressed the relation below as a table can I get some help with this please
Answers
The question shows a relation with three values.
When an ordered pair is given, it is given in the form (x, y).
Therefore, the pair (1, 13) means:
[tex]x=1,y=13[/tex]If we were to arrange the 3 pairs into a table, we have:
Therefore, the answer is 0.
In the scale drawing below, each side is.38 cm long. Use the scale factor shown. What is the perimeter of the actual object? I cm - 6.5 m O A. 12.35 m O B. 52.25 m C. 42 m D. 61.75 m
Answers
The scaled perimeter of the polygon is,
[tex]\begin{gathered} P=5\times0.38 \\ P=1.9\text{ cm} \end{gathered}[/tex]The expression to calculate the actual perimeater is,
[tex]\text{Actual Perimeter=P}\times Scale\text{ factor.}[/tex]Here, scale factor is 6.5 cm.
[tex]\begin{gathered} \text{Actual Perimeter=1.9}\times6.5 \\ =12.35\text{ cm} \end{gathered}[/tex]Thus, the actual perimeter of the polygon is 12.35 cm.
Answer: 12.35 m
Step-by-step explanation:
Can you please help me with this problem and can you please solve the question using proportion
Answers
"Percent" or "%" means "out of 100" or "per 100",
Therefore we can write this problem as:
[tex]\frac{29}{36}=\frac{x}{100}[/tex]Where x is the percent of carpenters who showed up.
We can solve this for x:
2900 = 36x
x = 2900/36
x = 80.6%.
which of the following functions has a graph in which the vertex and axis of symmetry are to the left of the vertex and axis of symmetry of the graph of f (x) =(x - 1)^2+ 1 select all that apply
Answers
Input data
The vertex and axis of symmetry are to the left of the vertex
in a race, the-second place finisher crossed the finish line minutes after the winner. The third-place finisher was minutes behind the second-place finisher. The third-place finisher took minutes. How long did the winner take? Do not include units (minutes) in your answer
Answers
EXPLANATION
Let's see the facts:
First winner take 1 minutes
Second winner ---->
I'll send the question.
Answers
Add 6 to both sides
[tex]\begin{gathered} 1+6=\frac{x}{2}-6+6 \\ 7=\frac{x}{2} \end{gathered}[/tex]Multiply both sides by 2 to find x
[tex]\begin{gathered} 7\times2=\frac{x}{2}\times2 \\ 14=x \end{gathered}[/tex]The value of x = 14
Answer A
The stem-and-leaf plot shows the number of text messages Hal received each day for two weeks.
Answers
From the step and leaf plot, we can generate the actual number of text messages Hal received:
[tex]10,\text{ 22, 24, 24, 24, 25, 30, 32, 32, 33, 34, 44, 46, 51}[/tex]Mode of the data: Value with the highest frequency
[tex]\text{Mode = 24}[/tex]Median of the data: value that lies at the center of the distribution
[tex]\begin{gathered} \text{Median = }\frac{30\text{ + 32}}{2} \\ =\text{ 31} \end{gathered}[/tex]Difference between the median and the mode :
[tex]\begin{gathered} =\text{ Median - Mode} \\ =\text{ 31 - 24} \\ =7 \end{gathered}[/tex]Correct option : third option
The Apps 'R' Us store charges 1.09 per app Susan downloaded 2 apps on Friday and 3 apps on Saturday. How much did she spend?
Answers
The Apps 'R' charges 1.09 dollars per app. Susan downloaded 2 apps on friday and 3 apps on saturday . Altogether she will spend
[tex]\begin{gathered} on\text{ friday = 1.09}\times2\text{ = }2.18\text{ dollars} \\ on\text{ saturday = 1.09}\times3=3.27\text{ dollars} \\ total=3.27+2.18=5.45\text{ dollars} \end{gathered}[/tex]