Algebraic models grade 12 math please write the answers without explaining thank you.
Answers
Explanation
let's remember this property of the exponent number
[tex]a^m\cdot a^n=a^{m+n}[/tex]Step 1
solve by applying the property. ( let the same base and add the exponents)
[tex]\begin{gathered} 6^4\cdot6^{-5} \\ 6^4\cdot6^{-5}=6^{4+(-5)} \\ 6^4\cdot6^{-5}=6^{-1} \\ \end{gathered}[/tex]hence, the answer is
[tex]d)6^{-1}[/tex]I hope this helps you
Related Questions
The perimeter of a triangle ABC is 100 cm.The length of AB is 45 cm and the length of BC is 32 cm.What is the length ofCA?
Answers
Recall that the perimeter of the triangle ABC is given by the following formula:
[tex]Perimeter=AB+BC+CA\text{.}[/tex]Substituting the given data we get:
[tex]100\operatorname{cm}=45\operatorname{cm}+32\operatorname{cm}+CA\text{.}[/tex]Solving the above equation for CA we get:
[tex]\begin{gathered} CA=100\operatorname{cm}-45\operatorname{cm}-32\operatorname{cm} \\ =23\operatorname{cm}\text{.} \end{gathered}[/tex]Answer: The length of CA is 23cm.
Find the surface area of a cylinder with a base radius of 6 ft and a height of 9 ft.Use the value 3.14 for n, and do not do any rounding.Be sure to include the correct unit.
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The surface area of the cylinder can be found below
[tex]\text{surface area=}2\pi r(r+h)[/tex]h = 9 ft
r = 6 ft
Therefore,
[tex]\begin{gathered} \text{surface area=2}\times3.14\times6(6+9) \\ \text{surface area=}37.68(15) \\ \text{surface area=}565.2ft^2 \end{gathered}[/tex]Identify the transformations for the function below. Check all that applyf (x) = 2(x – 3)^3 + 2DilationHorizontal ShiftVertical ShiftReflection
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The given function is,
[tex]f(x)=2(x-3)^3+2[/tex]The parent function of the given function can be identified as,
[tex]f(x)=x^3[/tex]A transformed function can be represented as,
[tex]f(x)=a(bx-h)^3+k[/tex]If k is a positive or a negative number, then function is shifted k units vertically.
So, comparing the equations, we find that in the given function k=2.
Hence, the function is vertically shifted.
A function f(x) is shifted h units horizontally if h is a positive or a negative number.
So, in the given function h=3.
Hence, the function is horizontally shifted.
If |a| >1 or 0<|a|<1, the function f(x) is dilated vertically by a scale factor of a units and if a is a negative number , the function is also reflected across the x axis.
In the given function, a=2.
So, f(x) is dilated, but not reflected.
If |b| >1 or 0<|b|<1, the graph of function f(x) is dilated by a scale factor of b units horizontally and if b is a negative number, the function is also reflected across the y axis.
In the given function, b=1.
So, f(x) is not dilated or reflected.
Hence, f(x) has undergone the transformations:
Dilation
Horizontal Shift
Vertical Shift
Weekly wages at a certain factory arenormally distributed with a mean of$400 and a standard deviation of $50.Find the probability that a workerselected at random makes between$500 and $550.
Answers
The Solution:
Step 1:
We shall state the formula for calculating Z-score.
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ \text{Where X}=5\text{00 ( for lower limit) and X=550 for upper limit.} \\ \mu=400 \\ \sigma=50 \end{gathered}[/tex]Step 2:
We shall substitute the above values in the formula.
[tex]\begin{gathered} \frac{500-400}{50}\leq P(Z)\leq\frac{550-400}{50} \\ \\ \frac{100}{50}\leq P(Z)\leq\frac{150}{50} \\ \\ 2\leq P(Z)\leq3 \end{gathered}[/tex]Step 3:
We shall read the respective probabilities from the Z score distribution tables.
From the Z-score tables,
P(3) = 99.9 %
P(2) = 97.7 %
Step 4:
The Conclusion:
The probability that a worker selected makes between $500 and $550 is obtained as below:
[tex]\text{Prob}(500\leq Z\leq550)=99.9-97.7\text{ = 2.2 \%}[/tex]Therefore, the required probability is 2.2 %
In Mr. Johnson’s third and fourth period classes, 30% of the students scored a 95% or higher on a quiz.Let be the total number of students in Mr. Johnson’s classes. Answer the following questions, and showyour work to support your answer.If 15 students scored a 95% or higher, write an equation involving that relates the number ofstudents who scored a 95% or higher to the total number of students in Mr. Johnson’s third andfourth period classes. Of the students who scored below 95% 40% of them are girls. How many boys scored below 95%?
Answers
Total number of students = scored below 95% + scored above 95% (I)
______________________________
Students scored below 95%
Scored below 95%* 0.40 = girls
Boys = total scored below 95% (100% - 40%)
Boys = total scored below 95% (60%)
Boys = total scored below 95% (0.6) (II)
__________________________________________
Can you see the updates?
_______________________________
30% of the students scored a 95% or higher on a quiz and 15 students scored a 95% or higher
Total number of students* 30 = 15
30%*n = 15
n= 15/ 0.3
n= 50
_____________________________
Replacing in (I)
Total number of students = scored below 95% + scored above 95%
50 = 15 + 35
Replacing in (II)
Boys = 15 (0.60) = 9
__________________________________________
Answer
9 of the students who scored below 95% are boys
The volume of a sphere is a function of it's radius, V=4/3* πr^3. evaluate the function for the volume of a volleyball with radius of 11.3 cm.Round to the nearest tenth.
Answers
Volume of sphere = 6040.9cm³
Explanation:
Volume of sphere = 4/3* πr³
radius = r = 11.3cm
if π = 3.14
[tex]\begin{gathered} \text{volume = }\frac{4}{3}\times3.14\times11.3^3 \\ \end{gathered}[/tex][tex]\begin{gathered} V\text{ = }\frac{4}{3\text{ }}\times3.14\times1442.897 \\ V=6040.929cm^3 \end{gathered}[/tex]Rounding to the nearest tenth:
Volume of sphere = 6040.9cm³
A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam.
a. What are the null and alternative hypotheses for addressing the research question, "are average test scores different between the different teaching methods?"
b. What are the degrees of freedom associated with the F distribution for evaluating these hypotheses?
c. Suppose the p-value for this test is 0.0168. What would you conclude? (Be sure to specify your significance level.)
Answers
a. The hypotheses are:
Null hypothesis: the average test scores are the same for the different teaching methods.
Alternative hypothesis: the average test scores are different for the different teaching methods.
b. To determine the degree of freedom for the F test: we must find two sources of variation such that we have two variances. The two sources of variation are: Factor (between groups) and the error (within groups) and add this up. Or use (N - 1). N is number in sample
c. With a p value of of 0.0168 and using a standard significance level of 0.05, we will reject the null hypothesis as 0.0168 is less than 0.05 and conclude that the average test scores are different for the different teaching methods.
Hence we get the required answer.
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The center of a circle and a point on the circle are given. Writecenter: (3,2), point on the circle: (4,3)
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Given:
The center of the circle is the point ( 3, 2 )
And the point on the circle is ( 4, 3 )
To write the equation of the circle, we need to find the radius
The radius = the distance between the center and the point on the circle
so, the radius is the distance between ( 3, 2) and ( 4, 3)
So,
[tex]\begin{gathered} r=d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ r=\sqrt[]{(4-3)^2+(3-2)^2^{}}=\sqrt[]{1+1}=\sqrt[]{2} \end{gathered}[/tex]The general equation of the circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h, k) is the coordinates of the center of the circle, r is the radius
So,
[tex]\begin{gathered} (h,k)=(3,2) \\ r=\sqrt[]{2} \end{gathered}[/tex]so, the equation of the circle will be:
[tex](x-3)^2+(y-2)^2=2[/tex]pls help I've had a bad day and I've been trying to figure this out forever
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the given expression is
4Ix-2I - 3
Can you help me with this assignment
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Those are vertical angles, therefore:
[tex]\begin{gathered} m\angle ONB=m\angle MNK \\ so\colon \\ m\angle ONB=85 \end{gathered}[/tex]Alex surveyed 60 student about their Vera zoo animals and made the circle graph of the results shown below
Answers
we can use the cross multiplication
we know that the full angle of a circle is 360° so the total angle corresponds to 60 students
so, what is 72 degrees?
[tex]\begin{gathered} 360\longrightarrow60 \\ 72\longrightarrow x \end{gathered}[/tex]where x is the number of students than said giraffes
[tex]\begin{gathered} x=\frac{72\times60}{360} \\ \\ x=12 \end{gathered}[/tex]the students than said giraffes are 12
the beginning of the question is "if the slope of..." please help
Answers
we know that
If two lines are parallel, then their slopes are equal
In this problem
mAB=mCD
substitute the given values
3/4=(x-2)/12
solve for x
multiply by 12 both sides
(x-2)=12(3/4)
x-2=9
x=9=9+2
x=11What are the zeroes of f(x) = x^2 + 5x + 6? (4 points)A) x = -2, -3B) x = 2,3C) x= -2,3D) x = 2, -3
Answers
You have the following function:
[tex]f(x)=x^2+5x+6[/tex]in order to find the zeros of the previous function, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a, b and c are the coefficients of the polynomial. In this case:
a = 1
b = 5
c = 6
replace the previous values of the parameters into the formula for x:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4(1)(6)}}{2(1)} \\ x=\frac{-5\pm\sqrt[]{25-24}}{2}=\frac{-5\pm1}{2} \end{gathered}[/tex]hence the solution for x are:
x = (-5-1)/2 = -6/2 = -3
x = (-5+1)/2 = -4/2 = -2
A) x = -2 , -3
Use the GCF to factor this expression.40x + 24y - 56
Answers
The given expression is,
[tex]40x+24y-56[/tex]The factors of 40, 24 and 56 are,
[tex]\begin{gathered} 40\colon2,4,5,8,10 \\ 24\colon2,4,3,8 \\ 56\colon2,4,7,8 \end{gathered}[/tex]The greatest common factor is therefore, 8.
Therefore, the given expression can be written as,
[tex](8\times5)x+(8\times3)y-(8\times7)[/tex]Taking 8 as common, we have,
[tex]8(5x+3y-7)[/tex]The figure below shows the graph of f’ , the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangentlines at x = 2 and x = 4.
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Solution
- The points of inflection of f(x) in a graph of f'(x) is gotten by just finding the points where the graph moves from increasing to decreasing, and also from decreasing to increasing.
- Thus, we have
- The points where the graph changes from increasing to decreasing is at point (2, 0) and the point where the graph moves from decreasing to increasing is (4, -2.5)
- Thus, the inflection points of the graph of f are at (2, 0), and (4, -2.5)
just need help and a simple way to solve this
Answers
ANSWER
The length of the third leg is
STEP-BY-STEP EXPLANATION:
The figure given is a right-angled triangle.
To find the third length of the triangle, we need to apply Pythagora's theorem
It states that
[tex]\begin{gathered} (Hypotenuse)^2=(opposite)^2+(adjacent)^2 \\ \end{gathered}[/tex]The third length of the triangle is the hypotenuse because it is the longest
[tex]\begin{gathered} (Hypotenuse)^2=4^2+2^2 \\ (Hypotenuse)^2\text{ = 16 + 4} \\ (Hypotenuse)^2\text{ = 20} \\ \text{ Take the squareroots of both sides} \\ \text{ }\sqrt[]{(Hypotenuse)^2\text{ }}\text{ = }\sqrt[]{20} \\ \text{Hypotenuse = }4.472 \\ \text{Hypotenuse }\approx\text{ 4.5} \end{gathered}[/tex]Hence, the length of the third leg is 4.5
A student has 5 pairs of plants, 2 shirts and 7 necklaces. He chooses one shirt, one pair of pants, and one necklace. How many different outfits could he make?
Answers
Answer:
70
Explanation:
By the rule of multiplication, we can calculate the number of different outfits as
5 x 2 x 7 = 70
pants shirts necklaces
Therefore, there are 70 different outfits
According to a pencil company's advertising campaign, 2 out of 3 students prefer the company's pencils to their competitor's pencils. A representative of the company went to a high school with 1479 students for alq & A session, and one of the students asked, "If this is true, in this high school, how many more students are there who prefer your pencils than students who prefer your competitor's pencils?" Help the company's representative come up with an answer. Assume that the company's claim is true.Part 1: How many of the students in the high school prefer the company's pencils? Part II: Out of 3 students, how many prefer the pencils of the company's competitor?Part III: How many of the students in the high school prefer the pencils of the company's competitor? Part IV: In the high school, how many more students are there who prefer the company's pencils than students who prefer their competitor's pencils?
Answers
Data:
2 of 3 students prefer the company's pencils to their competitor's pencils
high school with 1479 students
Part 1:You have 1479 students in total and know that 2 of 3 students prefer the company's pencils, then you multiply the toatl number of students by the factor 2/3
[tex]1479\cdot\frac{2}{3}=\frac{2958}{3}=986[/tex]Then, 986 students in the high school prefer the company's pencilsPart 2:Of 3 students 1 prefer the pencils of the company's competitorPart 3:Substract the number of students that prefer the company's pencils from the total of students:
[tex]1479-986=493[/tex]Then, 493 students in the high school prefer the pencils of the company's competitorPart 4:Substract the number of students who prefer the competitor's pencils fom the students that prefer the company's pencils:
[tex]986-493=493[/tex]Then, in the high school there are 493 students more that prefer the company's pencils than students who prefer their competitor's pencilsFind the equation of the line that has a slope of -2 and passes through point (-3 ,4)
Answers
Let's use the slope-point form to find the equation:
[tex]\begin{gathered} y-4=-2(x-(-3)) \\ \rightarrow y-4=-2(x+3) \\ \rightarrow y-4=-2x-6 \\ \rightarrow y=-2x-2 \\ \end{gathered}[/tex]Thereby, the equation of the line is:
[tex]y=-2x-2[/tex]Reason
A library has 144 books. A long
shelf can fit 100 books. A short shelf can fit 10 books.
The books that are left over can be put in a bin.
Draw two ways to sort books on a shelf.
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100 books can be kept in the long shelf and the 10 books can be kept in the short shelf.
The remaining 34 books can be kept in the bin.
Given, a library has 144 books. A long shelf can fit 100 books. A short shelf can fit 10 books.
The books that are left over can be put in a bin.
Now, we have to find the way to sort the books on a shelf.
So, we can put the books in this fashion,
100 books can be kept in the long shelf and the 10 books can be kept in the short shelf.
The remaining 34 books can be kept in the bin.
Hence, 100 books can be kept in the long shelf and the 10 books can be kept in the short shelf.
The remaining 34 books can be kept in the bin.
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Same took out a loan for 6200 that charges an annual rate of 8.6% compounded quarterly. Answer each part. Sent picture
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Given:
Sam took out a loan for 6200 that charges an annual rate of 8.6% compounded quarterly.
Required:
Find effective annual interest rate.
Explanation:
a).
We know compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Now,
[tex]undefined[/tex]b).
We know the effective annual interest rate
[tex]EAR=(1+\frac{i}{m})^m-1[/tex]EAR = Effective annual interest
i = Annual nominal rate of interest
m = No. of compounding periods in a year.
[tex]\begin{gathered} EAR=(1+\frac{0.086}{4})^4-1 \\ EAR=0.088813 \\ \text{ To find percentage multiply by 100 } \\ =0.088813\times100 \\ =8.8813\% \end{gathered}[/tex]Answer:
answered the question.
The function g(x) approaches positive infinity as x approaches positive infinity. The zeros of the function are -1,2 and 4. Which graph best represents g(x)?
Answers
Explanation
We are asked to select the correct option for which g(x) approaches positive infinity as x approaches positive infinity.
Also, the zeros of the function are -1,2 and 4.
The correct option will be
Sue, who is 5 feet tall, is standing at Point D in the drawing. The tip of her head is a point E. a tree in the yard is at point B with the top of the tree at point C. Sue stand so her shadow meets at the end of the trees shadow at point a Which triangles similar?How do you know?Find the height of the tree (This distance from B to C).
Answers
Which triangles are similar?
The triangle AED and the triangle ABC is similar.
How do you know?
Because all the angles are equal, the triangle AED and ABC have the same angle values, then they're similar.
Find the height of the tree (This distance from B to C)
We can use the relation of the similar triangle to find BC, we can write the equation
[tex]\frac{AB}{AD}=\frac{BC}{ED}[/tex]The only unknown value here is BC, then
[tex]\frac{24+8}{8}=\frac{\text{BC}}{5}[/tex]Now we solve it for BC!
[tex]\begin{gathered} \frac{32}{8}=\frac{BC}{5} \\ \\ 4=\frac{BC}{5} \\ \\ BC=4\cdot5 \\ \\ BC=20\text{ ft} \end{gathered}[/tex]Hence, the height of the tree is 20 ft
maurice read a research 10 pages that is 50 percent of the paper lenght what i the paper lenght
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we know that
10 pages -------> represent 50%
so
Multiply by 2 both sides
20 pages --------> 100%
therefore
the paper length is 20 pagesApply proportionRemember that the paper length represent the 100%
10/50=x/100
solve for x
x=10*100/50
x-20 pages100/50x-20 pagesHello, how are you? I would like you to help me solve this exercise, please!
Answers
Given
Formula for the length of an arc
[tex]\begin{gathered} Measureof\text{Arc of a circle=}\frac{\theta}{360}\times2\pi r \\ \\ \end{gathered}[/tex]Parameters;
[tex]\begin{gathered} \theta=?\text{ , r=1m} \\ \text{measure of arc =}\frac{\pi}{9} \end{gathered}[/tex]We can substitute into the formula
[tex]\begin{gathered} \frac{\pi}{9}=\frac{\theta}{360}\times2\times\pi\times1 \\ \\ \frac{\pi}{9}=\frac{2\theta\pi}{360} \\ \text{cross multiply} \\ 18\theta\pi=360\pi \\ divide\text{ both sides by 18}\pi \\ \frac{18\theta\pi}{18\pi}=\frac{360\pi}{18\pi} \\ \theta=20^0 \end{gathered}[/tex]Now, change to radian
[tex]\frac{\pi}{180}\times20^0=\frac{20^0\pi}{180^0}=\frac{\pi}{9}[/tex]The final answer
[tex]\frac{\pi}{9}[/tex]A card is drawn randomly from a standard deck of cards. You win $5 if the card is adiamond or a king. What is the probability that you will win 5 dollars?
Answers
EXPLANATION
Let name event A as the event of drawing a Diamond and let us name event B as the event of drawing an King.
Now, we are required to find P(A union B)
We know that P(A union B) = P(A) + P(B) - P(A intersection B) … (i)
Let's suppose there are 52 cards in a standard deck.
A standard deck of cards has 13 diamonds and 4 kings
We have P(A) = 13/52 = 1/4, P(B) = 4/52 = 1/13
A intersection B denotes the case of the King of Diamonds whose probability = 1/52
Now plugging in these values to equation (i) and simplifying, we obtain the required probability as P(A union B) = 1/4 + 1/13 - 1/52 = 4/13
The probability is 4/13 or 0.307 or 30.7%
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
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Answer:
I don't know the answer but I want to say something ...you can't just go around writing HELP!!! ILL GIVE 100 POINTS when your question only gives 5!!! it's just deceptive, if you want someone's help at least be honest! thank you for your time
Karmahhaze09 Can i have your number
Answers
Answer: irdk u yet so no
Step-by-step explanation:
Solve the equation for X. Round the answer to three decimal places. 4^x = 6
Answers
Answer:
c. x =1.293
Explanation:
To solve the expression, we will apply the properties of the logarithms, so
[tex]\begin{gathered} 4^x=6 \\ \log 4^x=\log 6 \\ x\log 4=\log 6 \\ x=\frac{\log 6}{\log 4} \\ x=1.293 \end{gathered}[/tex]Therefore, the value for x is
c. x =1.293
State if the triangles in each pair are similar. If so, state how you know they are similar andcomplete the similarity statement.1) 2)
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Triangles Similarity
For two shapes to be similar, two conditions must be satisfied:
* They must have the same angles.
* The side lengths must be in proportion
Let's focus on the image provided in problem 1.
We must try to find if the length sides of ABU and VWU are in proportion.
To do it, we find the ratio of the sides. If we find the same ratio of two pairs of sides, then the second condition is met.