hello
to solve this question, let's find the difference between the two numbers first
[tex]\text{change}=\text{ 400-350=50}[/tex]the percentage can be calculated as
[tex]\frac{50}{400}\times100=12.5\text{ \%}[/tex]from the calculation above, the percentage change is 12.5%
11 more than 4 times a number is 35. What is the equation and what is the solution?
Answer :
equation = 4x + 11 = 35
x = 6
Let the number be x
11 more than 4 times a number can be written mathematically
more than means addition
Since, the number is x
Therefore, 4 * x + 11 = 35
4x + 11 = 35
The equation is 4x + 11 = 35
To find x, collect the like terms
4x = 35 - 11
4x = 24
Divide both sides by 4
4x/4 = 24/4
x = 6
Therefore, the number is 6
Simplify each of the fractions. If there is no answer, enter "undefined."A. 4/12B. 0/8C. 16/0
Let's simplify the given fractions.
A.) 4/12 ; Simplified value = 1/3
[tex]\frac{4}{12}\text{ = }\frac{\frac{4}{4}}{\frac{12}{4}}\text{ = }\frac{1}{3}[/tex]B.) 0/8 ; Simplified value = 0
[tex]\frac{0}{12}\text{ = 0}[/tex]C.) 16/0 ; Undefined.
[tex]\text{ A fraction with a denominator of zero (0) is undefined.}[/tex]what are they different types of triangles and how can you tell the difference. if you don’t understand the question this is kinda what i’m talking about
7)
This triangle has two congruent sides, therefore it is an isosceles triangle.
Also, it has all angles smaller than 90° (acute angles), therefore it is an acute triangle.
8)
All three sides with different lengths, so it's a scalene triangle.
One angle is a right angle (the third angle is equal 180-30-60=90°), so it's an right triangle.
9)
All three sides are congruent, so it's an equilateral triangle.
All three angles are acute, so it's an acute triangle.
10)
All three sides with different lengths, so it's a scalene triangle.
One angle is greater than 90° (obtuse angle), so it's an obtuse triangle
11)
This triangle has two congruent sides, therefore it is an isosceles triangle.
Since the two base angles are 40°, the third angle is equal 180-40-40=100°, therefore the triangle is obtuse.
12)
All three sides with different lengths, so it's a scalene triangle.
All three angles are acute, so it's an acute triangle.
the area of a square can be represented by the expression x10. Which monomial represents a side of the square.x^2x^5x^20x^100
The given expression is
[tex]x^{10}[/tex]The side of the square is the square root of the are
[tex]s=\sqrt[]{x^{10}}=x^{\frac{10}{2}}=x^5[/tex]Hence, the answer is B.solve this question:. x² = -169
ANSWER
[tex]x\text{ = 13i or 13}\sqrt{-1}[/tex]EXPLANATION
We want to solve the equation:
[tex]x^2\text{ = -169}[/tex]To do this we will find the square root of both sides:
[tex]\sqrt{x^2}\text{ = }\sqrt{-169}[/tex]Because we can't find the square root of a negative number, we have to split the number:
[tex]\begin{gathered} x\text{ = }\sqrt{-1\cdot\text{ 169}} \\ x\text{ = }\sqrt{-1\text{ }}\cdot\text{ }\sqrt{169} \\ x\text{ = }\sqrt{-1\text{ }}\cdot\text{ 13} \\ x\text{ = 13}\sqrt{-1}\text{ or better written as 13i} \end{gathered}[/tex]Note: i is referred to as unit complex number.
what is the volume of the first container the bottom is 6inch and the height is 8inch
First: 226.19 in³
Second: 176.71 in³
1) Considering that these containers are cylinders we can find the volume by using this formula:
[tex]\begin{gathered} V_{\text{cylinder}}=\pi\cdot r^2\cdot h \\ \end{gathered}[/tex]2) Plugging the red one's data. Considering that 6, and 5 inches refer to the Diameter, then D=2r R= D/2 then the radi of those are
[tex]\begin{gathered} V_{\text{RED}}=\pi\cdot r^2\cdot h \\ V_{\operatorname{Re}d}=\pi\cdot(3)^2\cdot8 \\ V_{\text{red}}=72\pi\text{ }\approx226.19in^3 \\ \\ V_{\text{BLACK}}=\pi\cdot(\frac{5}{2})^2\cdot9 \\ V_{\text{BLACK}}=\frac{225}{4}\pi\text{ in³ }\approx176.71in^{^{3}} \end{gathered}[/tex]3) Hence, the answer is The Volume of the First container is approximately 226.19 in ³ and the Second one is approximately 176.71 in³
Find the original price given the total amount and tax rate.Total price: $128,500Tax rate: 5.5%Enter the correct answer in the box.
Let p be the original price, T be the total amount and r the tax rate. From this, we have:
T = (r+1)*p
(0.055+1)p = 128500
1.055p = 128500
p = 128500/1.055 = $121,800.95
Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distributionThe per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 108 pounds and a standard deviation of 37.9pounds. Random samples of size 17 are drawn from this population and the mean of each sample is determined.u(x) =. (Round to three decimal places as needed)Sketch a graph of the sampling distribution.
We have a population normally distributed with a mean of 108 pounds and a std deviation of 37.9 pounds.
The sample size is 17.
The sample mean is expected to be equal to the population mean, so it will be 108 pounds.
The standard error for this sample size can be calculated as:
[tex]\sigma_s=\frac{\sigma}{\sqrt[]{n}}=\frac{37.9}{\sqrt[]{17}}\approx9.192[/tex]Then, we have a sampling mean of 108 and a std. error of 9.192.
Most of the data (95%) should be within 2 std. error from the mean. This is between 90 and 126:
[tex]\begin{gathered} 108-2\cdot9.192\approx90 \\ 108+2\cdot9.192\approx126 \end{gathered}[/tex]Then, graph number C shows this condition: most of the data is within 90 and 126, with a mean of 108.
Answer:
μs = 108
σs = 9.192
Graph C is representing the sampling distribution.
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y = 980(1.08)
the change represent growth. And the rate of increase is 8%
An outdoor cylindrical fire pit has an interior radius of 28 in. Filling the fire pit with fireglass, will require 91 pounds of glass per cubic foot. How many will be needed to fill the pit to a depth of 3 inch? (Round to the nearest pound as needed.)
The Solution:
By formula, the volume of the cylindrical pit is given as below:
[tex]\begin{gathered} V=\pi r^2h \\ \text{ Where} \\ V=\text{volume of the pit} \\ r=\text{ radius of the pit=28 inches} \\ h=\text{ depth of the pit=3 inches} \end{gathered}[/tex]Converting inches to feet:
Recall that
[tex]undefined[/tex]Question 6Given the true/false statements are true (facts), select the best logical induction made from those statements:Betsy likes oranges. Jose does not like oranges. Benjamin likes oranges.A People only like orangesB) People do and do not like orangesPeople like apples and orangesD People like all fruit
The Solution:
Given the following statements:
Betsy likes oranges.
Jose does not like oranges.
Benjamin likes oranges.
It follows that:
People do and do not like oranges
Therefore, the correct answer is [option B]
I need help with this practice problem It asks to answer (a) & (b) Please separate (a) & (b) so I know which one is which
Solution:
Given:
[tex](3x^5-\frac{1}{9}y^3)^4[/tex]Using binomial theorem expansion, the sum in summation notation is;
[tex](x+y)^n=\sum ^n_{k\mathop=0}\begin{bmatrix}{n} & {} \\ {k} & \end{bmatrix}x^{n-k}y^k[/tex]Comparing this to the expression given,
[tex]\begin{gathered} x=3x^5 \\ y=-\frac{1}{9}y^3 \end{gathered}[/tex]Question a:
The summation notation is;
[tex]\begin{gathered} (x+y)^n=\sum ^n_{k\mathop{=}0}\begin{bmatrix}{n} & {} \\ {k} & \end{bmatrix}x^{n-k}y^k \\ \\ (3x^5-\frac{1}{9}y^3)^4=\sum ^4_{k\mathop{=}0}\begin{bmatrix}{4} & {} \\ {k} & \end{bmatrix}(3x^5)^{4-k}(-\frac{1}{9}y^3)^k \end{gathered}[/tex]Question b:
The expansion can be as shown below;
[tex]\begin{gathered} (3x^5-\frac{1}{9}y^3)^4=\sum ^4_{k\mathop{=}0}\begin{bmatrix}{4} & {} \\ {k} & \end{bmatrix}(3x^5)^{4-k}(-\frac{1}{9}y^3)^k \\ =^4C_0(3x^5)^4+^4C_1(3x^5)^3(-\frac{1}{9}y^3)+^4C_2(3x^5)^2(-\frac{1}{9}y^3)^2+^4C_3(3x^5)^{}(-\frac{1}{9}y^3)^3+^4C_4(-\frac{1}{9}y^3)^4 \\ =1(3x^5)^4+4(3x^5)^3(-\frac{1}{9}y^3)+6(3x^5)^2(-\frac{1}{9}y^3)^2+4(3x^5)^{}(-\frac{1}{9}y^3)^3+1(-\frac{1}{9}y^3)^4 \\ =81x^{20}-12x^{15}y^3+\frac{2x^{10}y^6}{3}-\frac{4x^5y^9}{243}+\frac{y^{12}}{6561} \end{gathered}[/tex]Therefore, the simplified terms of the expansion is;
[tex]81x^{20}-12x^{15}y^3+\frac{2x^{10}y^6}{3}-\frac{4x^5y^9}{243}+\frac{y^{12}}{6561}[/tex]Question 5 of 6Which values are equivalent to the fraction below? Check all that apply.11.В.A.31 1c.33OF 3-3
The question is given to be:
[tex]\frac{3^5}{3^8}[/tex]Applying the law of indices:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]Therefore, we have the expression to be:
[tex]\frac{3^5}{3^8}=3^{5-8}=3^{-3}[/tex]Recall the law of negative exponents:
[tex]a^{-m}=\frac{1}{a^m}[/tex]Therefore, the expression becomes:
[tex]3^{-3}=\frac{1}{3^3}=\frac{1}{3\times3\times3}=\frac{1}{27}[/tex]The expression is also equivalent to:
[tex](\frac{1}{3})^3[/tex]Since:
[tex](\frac{1}{3})^3=\frac{1^3}{3^3}=\frac{1}{27}[/tex]ANSWER
The correct options are OPTION C, OPTION E, and OPTION F.
One tennis ball can holds 3 balls. Jenna filled 5 cans and had 1 ball left over.Which equation could we use to find n, the number of tennis balls?Choose 1 answer:1)3+5+1=n2)5 X 3+1=n3)n x 5=1+3
N = the number of tennis balls
5 cans
1 ball left over
N = 5 x 3 + 1
N = 16 tennis balls
A textbook store sold a combined total of 252 chemistry and physics textbooks in a week. The number of chemistry textbooks sold was 78 more than the number of physics textbooks sold. How many textbooks of each type were sold?Number of chemistry textbooks sold:Number of physics textbooks sold:
We need to find the number of textbooks of each type that were sold.
Let's call C the number of Chemistry books and P the number of Physics books that were sold.
Since the store sold a combined total of 252, we have:
[tex]C+P=252[/tex]Also, the number of chemistry textbooks sold was 78 more than the number of physics textbooks sold:
[tex]C=78+P[/tex]Then, in order to find the value of P, we can replace C with 78+P in the first equation. We obtain:
[tex]\begin{gathered} 78+P+P=252 \\ \\ 78+2P=252 \\ \\ 78+2P-78=252-78 \\ \\ 2P=174 \\ \\ \frac{2P}{2}=\frac{174}{2} \\ \\ P=87 \end{gathered}[/tex]Now, we can use the above result to find C:
[tex]\begin{gathered} C=78+87 \\ \\ C=165 \end{gathered}[/tex]Therefore, the answers are:
• Number of chemistry textbooks sold:, ,165
• Number of physics textbooks sold:, ,87
In the election for class president. Sophie received 72 of the 160 votes. What precent of the votes did she receive?
Total number of votes Sophie received = 72
Total number of votes cast = 160
Percentage of votes received by Sophie = (72/160) x 100
= 45%
Therefore, Sophie received 45% of the total votes.
A tank is being filled with a liquid. L (t), given below, is the amount of liquid in liters in the tank after t minutes.L (t) = 1.25t + 73Complete the following statements.
To find (L(t))^-1, we replace t by [L(t)]^-1 and L(t) by t in the expression L(t) = 1.25t + 73
With this, we got: t = 1.25*(L(t))^-1 + 73, which implies [L(t)]^-1 = (t - 73)/1.25
B) If x = L(t), we got [L(x)]^-1 = (x - 73)/1.25 = (L(t) - 73)/1.25 = [(1.25t + 73) - 73]/1.25 = t
A) Therefore, [L(x)]^-1 is the the amount of time (in minutes) it takes to have x liter os liquid
C) And finally, if t = 125 we got: [L(125)]^-1 = (125 - 73)/1.25 = 41.6
A dilation maps (2,3) to (4,6).A) What is the scale factor of the dilation B) if (-6,3) is under tie sale dilation, what would it’s new coordinate be?
Given:
A dilation maps (2,3) to (4,6).
Required:
To find the scale factor and the new coordinate.
Explanation:
(a)
Scale factor = dimension of the new coordinate / dimension of the original coordinate.
So
[tex]\begin{gathered} =\frac{4}{2} \\ =2\text{ and} \\ =\frac{6}{3} \\ =2 \end{gathered}[/tex]Therefore scale factor is 2.
(b)
If (-6,3) is under the same dilation.
The new coordinate is
[tex]\begin{gathered} =2(-6,3) \\ =(-12,6) \end{gathered}[/tex]Final Answer:
(a) 2
(b) (-12,6)
Look at the steps and find the pattern.step 1step 2step 3How many dots are in the 5th step?dots
In step 1
You have 4 dots per vertical column and 4 columns
4+4+4+4=16
If you sum the dots you find 16 dots.
In step 2
You have 5 dots per vertical column and 5 columns
5+5+5+5+5=25 or 5 x 5=25 or 5^2=25
If you sum the dots you find 25 dots.
In step 3
You have 6 dots per vertical column and 6 columns
6+6+6+6+6+6=36 or 6 x 6=36 or 6^2=36
If you sum the dots you find 36 dots.
In step 4
You have 7 dots per vertical column and 7 columns
7+7+7+7+7+7+7=49 or 7 x 7=49 or 7^2=49
If you sum the dots you find 49 dots.
In step 5
You have 8 dots per vertical column and 8 columns
8+8+8+8+8+8+8+8=64 or 8 x 8=64 or 8^2=64
If you sum the dots you find 64 dots.
Answer 64 dots
Use a common denominator to find equivalent fractions for and Enter the correct fractions in the boxes. 1 6 8 9 5 6 1 +
The common denominator of both fractions is 12.
Once we have this we multiply the numerator and denominator of each fraction by 12. Then:
[tex]\frac{3}{4}\cdot\frac{12}{12}=\frac{36}{48}[/tex]and:
[tex]\frac{1}{6}\cdot\frac{12}{12}=\frac{12}{72}[/tex]log(x⁴+3x³) - log(X + 3 ) + log2 - log6 = 2logx . find the value of x
The given equation is
[tex]\begin{gathered} \log (x^4+3x^3)-\log (x+3)+\log 2-\log 6=2\log x \\ \log (\frac{x^4+3x^{3^{}}}{x+3})+\log \frac{2}{6}=\log x^2 \\ \log \frac{x^3(x+3)}{x+3}+\log \frac{1}{3}=\log x^2 \\ \log x^3+\log \frac{1}{3}=\log x^2 \\ \log \frac{x^3}{3}=\log x^2 \\ \frac{x^3}{3}=x^2 \\ x^3-3x^2=0 \\ x^2(x-3)=0 \end{gathered}[/tex]hence
[tex]x=0\text{ or x=3}[/tex]But x cannot be zero so x=3
So the value of x is 3
h
which expressions are equivalent to 3(2/3p + 3 - 1/3p - 5)
Let's simplify
open the bracket
[tex]2p\text{ + 9-p-15}[/tex]Rearrange
2p - p + 9 - 15
p - 6
The correct options are either the same values as this directly or options that will give the same values when simplified
They are;
p- 6
[tex]3(\frac{1}{3}p+\text{ 3-5)}[/tex]when you simplify this it becomes;
p - 6
[tex]3(\frac{1}{3}p-2)[/tex]when you simplify, it gives p - 6
First question, thanks. I believe there should be 3 answers
Given: The following functions
[tex]A)cos^2\theta=sin^2\theta-1[/tex][tex]B)sin\theta=\frac{1}{csc\theta}[/tex][tex]\begin{gathered} C)sec\theta=\frac{1}{cot\theta} \\ D)cot\theta=\frac{cos\theta}{sin\theta} \\ E)1+cot^2\theta=csc^2\theta \end{gathered}[/tex]To Determine: The trigonometry identities given in the functions
Solution
Verify each of the given function
[tex]\begin{gathered} cos^2\theta=sin^2\theta-1 \\ Note\text{ that} \\ sin^2\theta+cos^2\theta=1 \\ cos^2\theta=1-sin^2\theta \\ Therefore \\ cos^2\theta sin^2\theta-1,NOT\text{ }IDENTITIES \end{gathered}[/tex]B
[tex]\begin{gathered} sin\theta=\frac{1}{csc\theta} \\ Note\text{ that} \\ csc\theta=\frac{1}{sin\theta} \\ sin\theta\times csc\theta=1 \\ sin\theta=\frac{1}{csc\theta} \\ Therefore \\ sin\theta=\frac{1}{csc\theta},is\text{ an identities} \end{gathered}[/tex]C
[tex]\begin{gathered} sec\theta=\frac{1}{cot\theta} \\ note\text{ that} \\ cot\theta=\frac{1}{tan\theta} \\ tan\theta cot\theta=1 \\ tan\theta=\frac{1}{cot\theta} \\ Therefore, \\ sec\theta\ne\frac{1}{cot\theta},NOT\text{ IDENTITY} \end{gathered}[/tex]D
[tex]\begin{gathered} cot\theta=\frac{cos\theta}{sin\theta} \\ Note\text{ that} \\ cot\theta=\frac{1}{tan\theta} \\ cot\theta=1\div tan\theta \\ tan\theta=\frac{sin\theta}{cos\theta} \\ So, \\ cot\theta=1\div\frac{sin\theta}{cos\theta} \\ cot\theta=1\times\frac{cos\theta}{sin\theta} \\ cot\theta=\frac{cos\theta}{sin\theta} \\ Therefore \\ cot\theta=\frac{cos\theta}{sin\theta},is\text{ an Identity} \end{gathered}[/tex]E
[tex]\begin{gathered} 1+cot^2\theta=csc^2\theta \\ csc^2\theta-cot^2\theta=1 \\ csc^2\theta=\frac{1}{sin^2\theta} \\ cot^2\theta=\frac{cos^2\theta}{sin^2\theta} \\ So, \\ \frac{1}{sin^2\theta}-\frac{cos^2\theta}{sin^2\theta} \\ \frac{1-cos^2\theta}{sin^2\theta} \\ Note, \\ cos^2\theta+sin^2\theta=1 \\ sin^2\theta=1-cos^2\theta \\ So, \\ \frac{1-cos^2\theta}{sin^2\theta}=\frac{sin^2\theta}{sin^2\theta}=1 \\ Therefore \\ 1+cot^2\theta=csc^2\theta,\text{ is an Identity} \end{gathered}[/tex]Hence, the following are identities
[tex]\begin{gathered} B)sin\theta=\frac{1}{csc\theta} \\ D)cot\theta=\frac{cos\theta}{sin\theta} \\ E)1+cot^2\theta=csc^2\theta \end{gathered}[/tex]The marked are the trigonometric identities
To this function, does limit x approaching zero (without + or -) exist? Aside from that, is f(x) continuous at x=1?
Given:
[tex]f(x)=\begin{cases}{-\frac{1}{x},x<0} \\ {3,0\leq x<1} \\ {\sqrt{x}}+2,x\ge1\end{cases}[/tex]Required:
To find the limit exist if x approaching to 0.
Explanation:
As limit x approaching to 0,
[tex]\lim_{x\rightarrow0}f(x)=3[/tex]Therefore the limit exist.
[tex]\begin{gathered} \lim_{x\rightarrow1^{-1}}f(x)=\lim_{x\rightarrow1^{-1}}3 \\ \\ =3 \end{gathered}[/tex][tex]\begin{gathered} \lim_{x\rightarrow1^+}f(x)=\lim_{x\rightarrow1^+}\sqrt{x}+2 \\ \\ =\sqrt{1}+2 \\ \\ =1+2 \\ \\ =3 \end{gathered}[/tex]additional information is needed to prove that the triangles below are congruent select all options that would provide enough information to prove the triangles are congruent
we need that
AC=BD
CD=AB
with only these rwo conditions the triangles are congruent by SAS
because
the angle
is given
simplify 8(10m) product
the question request we simply an expression
[tex]8(10m)=8\times10m=80m[/tex]the answer to this question is 80m and this corresponds to option C
On a standardized exam, the scores are normally distributed with a mean of57 and a standard deviation of 10. Find the z-score of a person who scored 75on the exam.
data point = 75
mean = 57
standard deviation = 10
Replacing:
z = (75-57) /10 = 18/10 = 1.8
z score = 1.8
The table shows some input and output values: Which tables represent functions
In mathematics, a function[note 1] is a binary relation between two sets that associates every element of the first set to exactly one element of the second set.
In this case, the function corresponds to Only Table B.
Input Output
6 1
7 2
8 7
9 5
12.) You purchased a scooter for $6,800 when it was on sale for 30% off. What was the original price of thescooter?
SOLUTION:
Case: Percentages
Method:
The sale price after 30% off is $6800
Let the original price be 'x'
30% off means 70% of the original price
[tex]\begin{gathered} \frac{70}{100}\times x=6800 \\ 0.7x=6800 \\ x=\frac{6800}{0.7} \\ x=9714.2857 \end{gathered}[/tex]Final answer: (Nearest cents)
The original price was $9714.29
what is 9 / 4 without the decimal
Answer:
2¼
Explanation:
Given the fraction:
[tex]\frac{9}{4}[/tex]We have that:
[tex]9=(4\times2)+1[/tex]Therefore, writing it as a mixed fraction, we have:
[tex]9\div4=2\frac{1}{4}[/tex]