The given angle is
[tex]\theta=-\frac{100}{\pi}[/tex]First, we have to transform this angle into degrees. We know pi=180°, so
[tex]\theta=-\frac{100}{180}=-\frac{50}{90}=-\frac{5}{9}=-0.56[/tex]The given angle is placed on the first quadrant.Assuming that the angle is starting on the positive x-axis.
Find the value of the following logarithms without using a calculator.(a) log319(b) log51(c) lne5(d) log0.00001
For this part, we can use the following properties:
[tex]\begin{gathered} \frac{1}{a^n}=a^{-n}\Rightarrow\text{ Property of the exponents} \\ \log _aa^x=x\Rightarrow\text{ Property of logarithms} \end{gathered}[/tex]So, applying the above property of exponents, we have:
[tex]\begin{gathered} \frac{1}{9}=\frac{1}{3\cdot3} \\ \frac{1}{9}=\frac{1}{3^2} \\ \frac{1}{9}=3^{-2} \end{gathered}[/tex]Now, applying the above property of logarithms, we have:
[tex]\begin{gathered} \log _3\frac{1}{9}=\log _33^{-2} \\ $$\boldsymbol{\log _3\frac{1}{9}=-2}$$ \end{gathered}[/tex]Part b)For this part, we can apply the following property of logarithms:
[tex]\log _a1=0[/tex]Then, in this case, we have:
[tex]\begin{gathered} a=5 \\ \log _a1=0 \\ \boldsymbol{\log _51=0} \end{gathered}[/tex]Part c)For this part, we can apply the following property of logarithms:
[tex]\ln e^x=x[/tex]So, we have:
[tex]\begin{gathered} x=5 \\ \ln e^x=x \\ $$\boldsymbol{\ln e}^{\boldsymbol{5}}\boldsymbol{=5}$$ \end{gathered}[/tex]Part d)For this part, we can rewrite 0.00001 like this:
[tex]\begin{gathered} 0.00001=\frac{0.00001}{1} \\ 0.00001=\frac{0.00001\cdot100,000}{1\cdot100,000} \\ 0.00001=\frac{1}{100,000} \\ 0.00001=\frac{1}{10\cdot10\cdot10\cdot10\cdot10} \\ 0.00001=\frac{1}{10^5} \\ 0.00001=10^{-5} \end{gathered}[/tex]Now, applying the above property of logarithms, we have:
[tex]\begin{gathered} a=10\text{ and }x=-5 \\ \log _aa^x=x \\ \log 0.00001=\log _{10}10^{-5} \\ $$\boldsymbol{\log 0.00001=-5}$$ \end{gathered}[/tex]which anwser shows the best approximation of [tex] \sqrt[]{26} [/tex]
Solution
[tex]\begin{gathered} \sqrt[]{26} \\ \text{simplifying }to\text{ decimal form} \\ =5.09901\ldots \end{gathered}[/tex]Answer: the best approximation is 5.1
Ethan and Michael played tablebasketball using wadded up bitsof paper and plastic cups. Eachbasket was worth 2 points.Ethan scored 18 points andMichael scored 24 points. Howmany goals did the boys scorealtogether?
Given:
Total score of Ethan, E=18 points.
Total score of Michael, M=24 points.
The score for each basket, N=2.
The total points scored by both boys is,
[tex]\begin{gathered} T=E+M \\ T=18+24 \\ T=42 \end{gathered}[/tex]Now, the number of goals scored by both boys is,
[tex]\begin{gathered} n=\frac{T}{N} \\ =\frac{42}{2} \\ =21 \end{gathered}[/tex]Therefore, the number of goals scored altogether by the boys is 21.
I tried solving this and I got the 2nd option. Is it correct?
Explanation
We are required to determine the double angle for sin 120°.
We know that the double angle identity states thus:
So. we have:
[tex]\begin{gathered} \sin2\theta=2\sin\theta\cos\theta \\ \sin120\degree=\sin2(60\degree)=2\sin60\degree\cos60\degree \\ \Rightarrow2(\frac{\sqrt{3}}{2})(\frac{1}{2})=\frac{\sqrt{3}}{2} \end{gathered}[/tex]Hence, the answer is:
[tex]\frac{\sqrt{3}}{2}[/tex]The second option is correct.
What linear equation represents the graph of a horizontal line, parallel to the x-axis, that travels through the point (0,4)? Use the grid or a piece of paper if needed. LY 2 1 X 5 2 2 0 1 2 3 4 1 -2
It's important to know that all horizontal lines can be represented as y = k, where k is a real number.
In this case, we know that the horizontal line passes through (0,4).
Therefore, the equation of the line is y = 4.I know the first part not sure of the 2nd
Given
The shell looks are a cone
Diameter is 5
Radius is half diameter which 2.5in
Slant length is 10in
Solution
The formula for the surface area of a cone
[tex]=\pi r(r+l)[/tex]Now, substitute the given parameters into the formula
[tex]\begin{gathered} =\pi2.5(2.5+10) \\ =31.25\pi \\ =98.17477\text{ in}^2 \end{gathered}[/tex]I need help with this problem it says find the missing value in the raitio table then write the equivalent ratios the table says boys:1 then □ girls 5 ! 10 . what's the equivalent ratios of 1 :□ and □ :□
Answer:
Equivalent ratios are 1:5 and 2:10
Step-by-step explanation:
We have the following ratios, and we can use proportional relationships to find the missing value:
[tex]\begin{gathered} \frac{1}{5}=\frac{x}{10{}} \\ x=\frac{10}{5} \\ x=2 \end{gathered}[/tex]The balance on a credit card, that charges a 15.5%APR interest rate, over a 1 month period is given inthe following table:Days 1-3:$200 (initial balance)Days 4-20: $300 ($100 purchase)Days 21-30: $150 ($150 payment)What is the finance charge, on the average dailybalance, for this card over this 1 month period?finance charge = $ [?]Round to the nearest hundredth.
Answer:
$3.10
Step-by-step explanation:
You want to know the finance charge on the average daily balance if the charge is 15.5% per year, and the balances were $100 for 3 days, $300 for 17 days, and $150 for 10 days.
Average daily balanceThe average daily balance is the sum of daily balances, divided by the total number of days:
adb = (3×200 +17×300 +10×150)/(3+17+10) = 7200/30 = 240
Finance chargeThe finance charge is ...
(r/12)(adb) = (0.155/12)(240) = 3.10
The finance charge is $3.10.
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Pls Pls Pls can you pls tell me what the parent function is?
The parent function of the given graph is y = |x| .
Let us consider finding the equation of the given graph.
the graph of the function is from the vertex is translated to the right by 2 units and the graph is translated downwards by 5 units.
So the graph of the function is : y = |x-2| - 5
The parent function of the graph will be y=|x| which is the basis of the given graph.
The absolute value of a number or variable is determined by a modulus function, which is defined. It produces the variable count's size. It is also known as an absolute value function. Whatever input was given to this function, the results are always positive.
Y = |x| is the formula. Similar to other simple processes, plotting these graphs involves defining the domain as all input values, such as x (all real numbers), and the range as all function values, such as y = f(x), which is equal to all input values and all positive real numbers other than 0.
Hence the parent function of the given graph is y = |x| .
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Does the set of ordered pairs {(-5, 0), (0, 1}, (5, 2), (10, 3), (15, 4)} represent a function? Why or why not?
Answer:
YES, it represents a function
Explanation:
For a relation to be a function, each member of the domain (input) must be matched to only one element in the range (output).
According to ordered pairs, we can see that the domain values are all unique as shown;
As you can see from the diagram, each input only has a unique corresponding co-domain (range). This shows that the ordered pairs represents a FUNCTION.
What values of c and d make the equation true?3/162x2y3 –3x+y{VoyaO c = 2, d = 2O c = 2, d = 4O c = 6, d = 2O c= 6, d = 4
we have the expression
[tex]\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d)}[/tex]Verify for each option
1) For c=2 and d=2
substitute
[tex]undefined[/tex]Dan’s income can be calculated as $20 times the number of hours worked (h) added to his overtime wages of $300. If you subtract $600 to pay a bill, his income totals $500. Which expression represents dance income?
Income:
$20 x number of hours = 20h
Add the overtime wages of $300
Dan's income= 2h+300
Subtract 600 to pay a bill:
2h+300-600
His income totals $500
2h+300-600 =500
Combine like terms:
2h-300 = 500
place and label the following numbers on the number line. draw your number line on paper
EXPLANATION
Drawing the numbers on the number line give us the following graph:
Solve the following formula for the indicated variable.L = 2nrh; solve for r.
To solve for the indicated variable;
[tex]L=2\pi rh[/tex]We shall solve for r as shown below;
[tex]\begin{gathered} L=2\pi rh \\ \text{Divide both sides by 2}\pi h\text{ to isolate the r variable;} \\ \frac{L}{2\pi h}=\frac{2\pi rh}{2\pi h} \\ \frac{L}{2\pi h}=r \end{gathered}[/tex]ANSWER:
Therefore, the solution is;
[tex]r=\frac{L}{2\pi h}[/tex]Which of the following is the graph of f(x) = |x+2|-3?
Answer:
Option D.
Explanation:
To know which is the correct graph, we need to replace one point of each graph and determine if the equation for f(x) is satisfied.
Then, for option A, point (-2, -1), we get:
f(x) = |x+2|-3
-1 = | -2 + 2| - 3
-1 = |0| - 3
-1 ≠ - 3
Since 1 and 3 are distinct, this is not the correct graph.
For option B, point (1, -2), we get:
f(x) = |x+2|-3
-2 = |1 + 2| - 3
-2 = |3| - 3
-2 ≠ 0
Since -2 and 1 are distinct, this is not the correct graph.
For option C, point (2, 3), we get:
f(x) = |x+2|-3
3 = |2 + 2| - 3
3 = |4| - 3
3 = 4 - 3
3 ≠ 1
Since 3 and 1 are distinct, this is not the correct graph.
For option D, point (-3, -2), we get:
f(x) = |x+2|-3
-2 = |-3 + 2| - 3
-2 = |-1| - 3
-2 = 1 - 3
-2 = -2
Therefore, option D is the correct answer.
The vertices of a y rectangle are 8 A(1,7), B (3,7). C(3, 1.5), and 6 D (1, 1.5). Find the perimeter and the area of 3 the rectangle.
Let us first find the measures of the sides.
Width
We can find the width calculating the distance between points A and B. Doing so, we have:
The distance on the y-axis is 0 as they have the same coordinate
The distance on the x-axis is 2 ( x2 - x1= 3 - 1 = 2)
So, the width of the rectangle is 2.
Length
We can find the length calculating the distance between points B and C. Doing so, we have:
The distance on the x-axis is 0 as they have the same coordinate
The distance on the y-axis is 5.5 ( y2 - y1= 7 - 1.5 = 5.5)
So, the length of the rectangle is 5.5.
Using the formula for the perimeter, we have:
P= 2L + 2W (P:perimeter, l: length, w:width)
P= 2*(5.5) + 2*(2) (Replacing)
P= 11 + 4 (Multiplying)
P=15 (Adding)
The perimeter is 15
Using the formula for the area, we have:
A=l*w (A:area, l: length, w:width)
A=(2)*(5.5) (Replacing)
A= 11 (Multiplying)
The area is 11
evaluate the expression and enter your answer below. 3x10+15-6^2
3*10 + 15 - 6^2
3*10 + 15 -36 (Raising 6 to the power of 2, because of the order of operations)
30 + 15 - 36 (Multiplying, because of the order of operations)
45 - 36 (Adding)
9 (Subtracting)
The answer is equal to: 9
The total volume of a tree increases 8% each year. What will its volume be after 7 years if it’s volume is 5 m³ now?
The volume of trees after 7 years if it’s volume is 5 m cube now is 8.57 m cube.
In the given question we have to find the volume be after 7 years if it’s volume is 5 meter cube now.
The increment in tree each year = 8%
At now the volume is 5 meter cube.
Time = 7 years
So the formula is used to find the volume after 7 years
A=P(1+ r/100)^n
A=volume after 7 years
P=now the volume of tree
n=time
Putting the values
A=5(1+ 8/100)^7
A=5((100+8)/100)^7
A=5(108/100)^7
A=5(1.08)^7
A=5×1.714
A=8.57
Hence, volume of trees after 7 years if it’s volume is 5 m cube now is 8.57 m cube.
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The population, P, of a species of fish is decreasing at a rate that is proportional to the population itself. If P=200000 when t=3 and P=150000 when t=4, what is the population when t=10?Round your answer to the nearest integer. Tries 0/99
The Solution:
Given:
[tex]\begin{gathered} P=200,000\text{ when }t=3 \\ \\ P=150,000\text{ when }t=4 \end{gathered}[/tex]Required:
Find P when t = 10.
Clearly, the proportion is an inverse proportion.
[tex]\begin{gathered} P=\frac{k}{t} \\ \\ Where\text{ k}=constant\text{ of proportionality.} \end{gathered}[/tex]Applying the given values:
[tex]\begin{gathered} 200000=\frac{k}{3} \\ \\ k=3\times200,000=600,000 \end{gathered}[/tex]This gives the formula:
[tex]P=\frac{600,000}{t}[/tex]Substitute t=10, and find P.
[tex]P=\frac{600,000}{10}=60,000[/tex]Answer:
The population is 60,000 when t = 10.
original price of pants is 2995 the discount is 10%
Ok,
Since we have that the price of the pants is $2995 and that represents the 100%.
In order to determine the total value since we get a 10% discount, we do as follows:
[tex]2995\to100\text{ \& x}\to10[/tex]We determine the 10%, multiplying the percentage we want to know (10%) times the total ammount of money the pants cost ($2995) and then divide by the total percentage (100%):
[tex]x=\frac{2995\cdot10}{100}\Rightarrow x=299.5[/tex]x represents our 10% and so we extract x from the total:
[tex]T=2995-299.5\Rightarrow T=2695.5[/tex]Therefore the total price to pay is $2695.5
what is this need to know Which model represents the product 6×34?
The model in the bottom-left represents the product 6×(3/4).
We are given two numbers. The first number is 6, which is a whole number. The second number is 3/4, which is a simple fraction. We need to represent the product of these two numbers in the form of the given models. The images of the models are attached below. The first number is already a whole number, so we can represent it with six whole horizontal blocks. The second number is a fraction, so we can represent it as 3 blocks out of 4, where 4 blocks combined represent the number 1. Hence, the bottom-left model represents the product.
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how do you draw a model to explain 3/4 x 24
3 / 4 x 24 = 3 x 6 = 18
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are (b) 2.3p – 10.1 = 6.49p – 4 and (c) 230p – 1010 = 650p – 400 – p
How to determine the equations with the same solution?The equation is given as
2.3p – 10.1 = 6.5p – 4 – 0.01p
Evaluate the like terms on the right-hand side
So, we have the following representation
2.3p – 10.1 = 6.49p – 4
The above equation is indicated in option (b)
Multiply through the equation by 100
So, we have:
100(2.3p – 10.1 = 6.5p – 4 – 0.01p)
Evaluate
230p – 1010 = 650p – 400 – p
The above equation is indicated in option (c)
Hence, the equations with the same solution are (b) and (c)
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Find the area under the Standard Normal Curve in-between z = -2.39 and z = 1.03Use the Normal table and give answer using 4 decimal places.
Recall that the area under the standard normal curve in-between z₁ and z₂ is:
[tex]P(z_1We know that:[tex]P(z_1Therefore the area under the Standard Normal Curve in-between z = -2.39 and z = 1.03 is:[tex]P(z<1.03)-P(z<-2.39).[/tex]From normal tables we get:
[tex]\begin{gathered} P(z<1.03)=0.84849, \\ P(z<-2.39)=0.0084242. \end{gathered}[/tex]Therefore the area under the Standard Normal Curve in-between z = -2.39 and z = 1.03 is:
[tex]0.84849-0.0084242=0.8400658\approx0.8401.[/tex]Answer: 0.8401.
Annie has 13 yards of string. She uses 12 1 yards to fix her backpack. About how much string does she have left? 9 10
Annie will be left with 0.9 yd of string with her.
What is subtraction?In maths, to subtract means to take away from a group or a number of things.
Given that, Annie had a string of 13 yd, and she used 12.1 yd of the string for her backpack.
The length of string left with her after using for backpack = 13-12.1 = 0.9 yd
Hence, Annie will be left with 0.9 yd of string with her.
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Factor out the GCF in the polynomial.32x - 24 =
The Solution:
The given expression is
[tex]32x-24[/tex]To factor out the Greatest Common Factor of the above expression, we have
[tex]8(4x-3)[/tex]So, the Greatest Common Factor is 8.
Simplify. (Assume all variables represent positive numbers.)✓32a5b15Need Help?Watch ItAdditional MaterialseBook
We have the next expression
[tex]\sqrt[]{32a^5b^{15}}[/tex]In order to simplify we will factorize the expression in a next way
[tex]\sqrt[]{4\cdot4\cdot2\cdot a^4\cdot b^{14}\cdot b}[/tex][tex]\sqrt[]{4}\cdot\sqrt[]{4}\cdot\sqrt[]{2}\cdot\sqrt[]{a^4}\cdot\sqrt[]{b^{14}}\cdot\sqrt[]{ab}[/tex]Then we simplify the results
[tex]2\cdot2\cdot a^2\cdot b^7\cdot\sqrt[]{2ab}[/tex][tex]4a^2b^7\sqrt[]{2ab}[/tex]the simplification is
[tex]4a^2b^7\sqrt[]{2ab}[/tex]I need help with this question its on arithmetic growthanddecay , been stuck on it for many days and i need help! pleasep
We are given the following information about the arithmetic sequence
First two rows = 27 chairs
Last two rows = 114 chairs
Common difference = 3 chairs
Recall that the general formula for an arithmetic sequence is given by
[tex]a_n=a_1+(n-1)d[/tex](a) Let us substitute the given values into the above formula and solve for n
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ 114=27_{}+(n-1)\cdot3 \\ 114-27=_{}(n-1)\cdot3 \\ 87=_{}(n-1)\cdot3 \\ \frac{87}{3}=_{}n-1 \\ 29=_{}n-1 \\ 29+1_{}=_{}n \\ 30=n \end{gathered}[/tex]There are 30 rows of chairs.
(b) Let us find the number of chairs in the 13th and 30th row.
i) 13th row:
Substitute n = 13
[tex]\begin{gathered} a_{13}=27_{}+(13-1)\cdot3 \\ a_{13}=27_{}+12\cdot3 \\ a_{13}=27_{}+36 \\ a_{13}=63 \end{gathered}[/tex]There are 63 chairs in the 13th row.
ii) 30th row:
Substitute n = 30
[tex]\begin{gathered} a_{30}=27_{}+(30-1)\cdot3 \\ a_{30}=27_{}+29\cdot3 \\ a_{30}=27_{}+87 \\ a_{30}=114 \end{gathered}[/tex]There are 114 chairs in the 30th row.
i need help with math
The true statement for the angles formed by the three parallel roads are-
∠EBC measure x°; then ∠BED = 180 - x°.∠HEF has the same measure as ∠x°.Sum of ∠GHE and ∠HED = 180°.What is termed as the transversal?A transversal is a line that connects two lines in same plane at two different points with in geometry. A transversal intersection with two lines generates a variety of angles in pairs, including consecutive interior angles, corresponding angles, and alternate angles.For the given question,
There are 4 roads, three are parallel to each other and one is the transversal.
Thus, the relation of the angles formed as-
∠EBC measure x°; then ∠BED = 180 - x°.(supplementary angles).∠HEF has the same measure as ∠x°.(corresponding angles)Sum of ∠GHE and ∠HED = 180°.(supplementary angles).Thus, the correct relation between the set of angles are found.
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What is the solution to the equation 7c+5= 9(c- 3)?ROc=2Oc=4Oc=11Oc= 16
ANSWER:
16
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]7c+5=\: 9\mleft(c-\: 3\mright)[/tex]We solve for c:
[tex]\begin{gathered} 7c+5=9c-27 \\ 9c-7c=27+5 \\ 2c=32 \\ c=\frac{32}{2} \\ c=16 \end{gathered}[/tex]The solution of the equation is that c equals 16