The number of 3 digit combinations possible for the six digit wheel combination lock is; 216 combinations.
Combinations and selections.It follows from the task content that the number of possible 3 digit combinations for the six digit wheel as required is to be determined.
The number of possible selections in a given sample space is defined by the combination which defines the situation.
On this note, each digit from the 3 digit combinations could be any of the six digits on the wheel.
Therefore, the number of possible combinations is; 6 × 6 × 6 = 216 combinations.
Ultimately, the number of possible combinations is; 216 combinations.
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Lines PQ and Rs are parallel. Find y. P(2, -5); Q(5, 6); R(3, -1); S(6, y)y = ?
To answer this question it is necessary to find the equation of the given lines
Find the equation for PQ. To do it, find the slope of the equation:
[tex]m=\frac{6-(-5)}{5-2}=\frac{11}{3}[/tex]Now, use the point slope formula to find the equation of the line:
[tex]\begin{gathered} y-6=\frac{11}{3}(x-5) \\ y=\frac{11}{3}x-\frac{55}{3}+6 \\ y=\frac{11}{3}x-\frac{37}{3} \end{gathered}[/tex]Parallel lines have the same slope, it means PQ and RS have the same slope, then RS has a slope of 11/3
Use the point slope formula to find the equation of the line RS:
[tex]\begin{gathered} y-(-1)=\frac{11}{3}(x-3) \\ y+1=\frac{11}{3}x-11 \\ y=\frac{11}{3}x-12 \end{gathered}[/tex]Now, use this equation to find y when x is 6 (which corresponds to point S):
[tex]\begin{gathered} y=\frac{11}{3}x-12 \\ y=\frac{11}{3}(6)-12 \\ y=22-12 \\ y=10 \end{gathered}[/tex]y has a value of 10.
Identify the rate, base, and portion.
21% of what number is 57?
Question content area bottom
Which values are given? Select the correct choice below and fill in any answer boxes in your choice. (Type an integer or a decimal. Do not perform the calculation.)
A.The base is (enter your response here) and the portion is (enter your response here). The rate is not given.
B.The rate is (enter your response here % ) and the portion is (enter your response here). The base is not given.
C. The rate is (enter your response here %) and the base is (enter your response here).
Given:
21% of what number is 57
Let the number = x
So, 21% of x = 57
so, the rate = 21%
and the base = x
and the portion = 57
So, the base is not given
so, the answer will be option B
B) the rate is 21% and the portion is 57. the base is not given.
Angles of Polygons The figure below is a pentagon whose interior angles have the same measure.What is the sum of the measures of these 5 angles?
Given the number of sides of a pentagon:
Number of sides = 5
Let's find the sum of the measures of the 5 equal angles.
To find the sum of the measures of interior angles of a polygon, apply the formula:
[tex]S=(n-2)*180[/tex]Where:
n is the number of sides = 5
Thus, we have:
[tex]\begin{gathered} S=(5-2)*180 \\ \\ S=(3)*180 \\ \\ S=540^o \end{gathered}[/tex]Therefore, the sum of the interior angles of the pentagon is 540 degrees.
ANSWER:
540°
3-4 Ch 8 L 5-7 Test (modified) Is the given value a solution of the inequality? 2 + m > 10 m = 7
2 + m > 10
substituting with m = 7, we get:
2 + 7 > 10
9 > 10
which is false, because 9 is less than 10
How many square feet of outdoor carpet willwe need for this hele??3 ft2 ft2 ft
total square feet:
[tex]4\times12=48\text{ ft}[/tex]square feet 1:
Identify the center and the radius of the circle.(x - 1)^2+ (y + 3) = 4
We are given the following equation of a circle.
[tex]\mleft(x-1\mright)^2+(y+3)^2=4[/tex]The standard form of the equation of a circle is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]Comparing the given equation with the standard form we see that
[tex]\begin{gathered} h=1 \\ k=-3 \\ r^2=4 \\ r=\sqrt[]{4} \\ r=2 \end{gathered}[/tex]Therefore, the center of the circle is
[tex]C=(h,k)=(1,-3)[/tex]Therefore, the radius of the circle is
[tex]r=2[/tex]I really need help with number 9 find the value of x that makes abcd a parallelogram.
Given:
The adjacent angles of a parallelogram are 78 and x+10.
To find:
The value of x.
Explanation:
We know that,
The sum of the adjacent angles in a parallelogram is supplementary.
So, we can write,
[tex]\begin{gathered} 78+x+10=180 \\ x+88=180 \\ x=180-88 \\ x=92 \end{gathered}[/tex]Thus, the value of x is 92.
Final answer:
The value of x is 92.
23,000,000 in scientific notation.
Answer:
2.3 x 10⁷
Explanation:
A number is said to be in scientific notation when it is written in the form:
[tex]\begin{gathered} A\times10^n \\ \text{where:} \\ \text{A is between 1 and 10} \\ n\text{ is an integer} \end{gathered}[/tex]Given the number: 23,000,000
The number has 8 digits before the decimal point.
Therefore, in standard notation we have:
[tex]23,000,000=2.3\times10^7[/tex]Determine if the triangles are similar, if similar state how
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Triangle YXZ
Triangle AXB
Similar Triangles = ?
Step 02:
Similar Triangles
AB || YZ
The Side-Splitter Theorem:
AB || YZ ===> XY/ YA = XZ / ZB
The answer is:
The triangles are similar, by the Side-Splitter Theorem.
x=-3
f(x)= -2
f’(x)=2
g(x)=3
g’(x)=-1
h(x) = g(x)/2f(x)
Find h'(-3)
Answer: [tex]-1[/tex]
Step-by-step explanation:
Using the quotient rule,
[tex]h'(x)=\frac{2f(x)g'(x)-2g(x)f'(x)}{(2f(x))^2}\\\\h'(3)=\frac{2f(3)g'(3)-2g(3)f'(3)}{(2f(3))^2}\\\\=\frac{2(-2)(-1)-2(3)(2)}{2(-2)^2}\\\\=-1[/tex]
FIVE STAR®
The cost associated with a school dance is $300 for a venue rental and $24 for each couple
that attends. This can be represented by the expression 300 + 24x.
a. Define all the variables and terms is this scenario. That means tell us what x, 24x, and
300 represent
Answer:
300 -- venue cost24 -- cost for each couplex -- the number of couples24x the cost associated with all couple300+24x -- the total cost for the danceStep-by-step explanation:
Given the scenario that cost is $300 for the venue and $24 for each couple attending a dance at that venue, you want to know the meaning of the variables and terms in 300 +24x.
ComparisonYou can compare the terms, coefficients, and variables in the given expression with the parts of the problem statement.
300 is a constant term that corresponds to "$300 for a venue rental'24 is a coefficient that corresponds to "$24 for each couple"x is a variable representing the number of "couple that attends"24x is a term representing the cost associated with "$24 for each couple that attends"That is, the cost associated with the number of people attending is $24 times the number of couples: 24x. The expression 300+24x is the total of the fixed venue cost and the per-couple costs
FIRST OPTIONS ARE THE NUMBER OF CONVERTIBLES SOLD BY PLATO CARSTHE REVENUE FROM SALES OF CONVERTIBLE CARS BY PLATO CARSTHE REVENUE FROM SALES OF SEDANS BY PLATO CARSTHE TOTAL SALES REVENUE OF PLATO CARS SECOND OPTIONS 0.1070.2250.290.33
Given:
The number in the highlighted cell is 18.
The total sales revenue of pluto cars is 80.
To find the relative frequency from the sales of sedans by Plato cars to the total sales revenue of Plato cars:
The formula for relative frequency is,
[tex]\begin{gathered} RF=\frac{subgroup\text{ fr}equency}{\text{Total frequency}} \\ =\frac{18}{80} \\ =0.225 \end{gathered}[/tex]So, the relative frequency is 0.225.
Hence, the answer is,
The number in the highlighted cell is 18. The relative frequency from the sales of sedans by Plato cars to the total sales revenue of Plato cars is 0.225
Question 8 According to a textbook, this is a challenging question; according to me, it is the easiestquestions, among the easy questions!Suppose that the equations ax + by = c, where a, b, and c are real numbers, describes a directvariation. What do you know about the value of c?That c is
The Solution:
Given the equation below:
[tex]ax+by=c_{}[/tex]We are asked to say what we know about the value of c.
From the above equation, it is clear that:
c is a variable that depends on the values of the variables x and y.(where a and b are possibly constants.
A helicopter pilot sights a landmark an an angle of depression of 34°. The altitudeof the helicopter is 1,748 feet. To the nearest foot, what is the horizontal distancefrom the helicopter to the landmark?
For the question, we will be making a sketch showing the features in the question.
From the sketch and the question, the angle of depression = 34 degrees
The helicopter height above the ground (altitude) = 1,748 ft
L represents the landmark
x = horizontal distance from the helicopter to the landmark
To solve the question, we need to bring out the right triangle from the sketch
Angle e = 34 degrees (alternate to the angle of depression given)
To get x, we make use of the trigonometrical ratio of tan
[tex]\begin{gathered} \tan \text{ }\theta=\frac{opposite}{adjacent} \\ \text{From the right triangle, the opposite = 1748} \\ \text{The adjacent = x} \\ \theta=34^0 \\ \tan \text{ 34 =}\frac{\text{1748}}{x} \\ \text{Making x the subject of the formula, we have} \\ x=\frac{1748}{\tan 34} \\ x=\frac{1748}{0.6745} \\ x=2591.55 \end{gathered}[/tex]Therefore, the horizontal distance from the helicopter to the landmark to the nearest foot is 2592 feet.
A polynomial function with degree 5 can have a maximum of how many turning points? It would be 5 right?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
polynomial function
Step 02:
turning points:
The maximum number of turning points of a polynomial function is always one less than the degree of the function.
5th degree polynomial function and has 4 turning points.
The answer is:
5th degree polynomial function and has 4 turning points.
QUESTION 6Emily has enrolled in a first year math class. The course has 5 assignments each worth 2%, 3 tests worth 20% and 2 tests worth 15%. Emily thus far has completed 3 assignments scoring: 72%, 84%, and 58%. In addition to the assignments, Emily has completed 2 tests: Test 1 (worth 20%) she scored 85% and Test 2 she scored 68% (worth 15%). What is Emily's current grade? Keep the answer in percent and round to the tenth if necessary. Do not input the percent (%) into the answer.
ANSWER:
76.8
STEP-BY-STEP EXPLANATION:
Given:
3 Assignments (2%)
1. 72%
2. 84%
3. 58%
1 Test (20%)
85%
1 Test (15%)
68%
We can calculate Emily's current grade using the weighted average principle, just like this:
[tex]p=\frac{\sum ^{}_{}x_i\cdot w_i}{\sum ^{}_{}w_i}[/tex]In this case, the value of x are the scores and w are the percentages associated with that value, we replace:
[tex]\begin{gathered} g=g=\frac{72\cdot2\%+84\cdot2\%+58\cdot2\%+85\cdot20\%+68\cdot15\%}{2\%+2\%+2\%+20\%+15\%} \\ g=\frac{72\cdot0.02+84\cdot0.02+58\cdot0.02+85\cdot0.2+68\cdot0.15}{0.02+0.02+0.02+0.2+0.15} \\ g=\frac{31.48}{0.41} \\ g=76.78 \\ g\cong76.8\% \end{gathered}[/tex]Therefore, Emily's current grade is 76.8%.
20. Two teachers measured the shoe size of each of their students. The datawere used to create the box plots shown.Mrs. Norris's Class567891011121314Shoe SizeMrs. Ganger's Class5 6+87111213149 10Shoe SizeBased on the data, which statement about the results must be true?The average shoe size is the same for both classes.The shoe sizes 6 and 13 are outliers for both classes.© Mrs. Norris's class and Mrs. Ganger's class have the sameinterquartile range.© The median shoe size for Mrs. Norris's class is greater than forMrs. Ganger's class.
The correct answer is the last sentence.
"The median shoe size for Mrs. Norris's class is greater than for
Mrs. Ganger's class".
I need help with #1 of this problem. It has writings on it because I just looked up the answer because I’m confused but I want to know the answer and how to do it with work provided please
In the figure below
1) Using the theorem of similar triangles (ΔBXY and ΔBAC),
[tex]\frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC}[/tex]Where
[tex]\begin{gathered} BX=4 \\ BA=5 \\ BY=6 \\ BC\text{ = x} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \frac{4}{5}=\frac{6}{x} \\ \text{cross}-\text{multiply} \\ 4\times x=6\times5 \\ 4x=30 \\ \text{divide both sides by the coefficient of x, which is 4} \\ \text{thus,} \\ \frac{4x}{4}=\frac{30}{4} \\ x=7.5 \end{gathered}[/tex]thus, BC = 7.5
2) BX = 9, BA = 15, BY = 15, YC = y
In the above diagram,
[tex]\begin{gathered} BC=BY+YC \\ \Rightarrow BC=15\text{ + y} \end{gathered}[/tex]Thus, from the theorem of similar triangles,
[tex]\begin{gathered} \frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC} \\ \frac{9}{15}=\frac{15}{15+y} \end{gathered}[/tex]solving for y, we have
[tex]\begin{gathered} \frac{9}{15}=\frac{15}{15+y} \\ \text{cross}-\text{multiply} \\ 9(15+y)=15(15) \\ \text{open brackets} \\ 135+9y=225 \\ \text{collect like terms} \\ 9y\text{ = 225}-135 \\ 9y=90 \\ \text{divide both sides by the coefficient of y, which is 9} \\ \text{thus,} \\ \frac{9y}{9}=\frac{90}{9} \\ \Rightarrow y=10 \end{gathered}[/tex]thus, YC = 10.
What is the measure of ∠N, if ∠M and ∠N are angles in a linear pair and the m∠M is 30°? *.
Given:
[tex]\angle M=30\degree[/tex]And angle M and N are angles in a linear pair.
Required:
To find the angle N.
Explanation:
The sum of angles of a linear pair is always equal to 180°.
Therefore,
[tex]\begin{gathered} \angle M+\angle N=180\degree \\ \\ 30\degree+\angle N=180\degree \\ \\ \angle N=180\degree-30\degree \\ \\ \angle N=150\degree \end{gathered}[/tex]Final Answer:
[tex]\angle N=150\degree[/tex]-1010The graph of the equation y - 272. 2 is shown. Which equation will shift the graph up 3 units?A)ya 2x²y=2x-1y=2x²-3D)y = 2(x+3)²
f(x) + 3, translates f(x) 3 units up
In this case, the function is y = 2x² - 2.
Applying the above rule, we get:
y = 2x² - 2 + 3
y = 2x² + 1
Find an angle with θ with 0∘ < θ < 360∘ that has the same :
Sine as 220∘ : θ = _______ degrees
Cosine as 220∘ : θ = _______ degrees
The complete trigonometry ratios are sin(220) = -sin(40) and cos(220) = cos(140) and the angles are 40 and 220 degrees
How to determine the measure of the angles?Angle 1
The trigonometry ratio of the angle is given as
sin(220)
Expand the above expression
sin(220) = sin(180 + 40)
Apply the sine rule
sin(220) = sin(180)cos(40) + cos(180)sin(40)
Evaluate the ratios
sin(220) = 0 x cos(40) - sin(40)
So, we have
sin(220) = - sin(40)
So, the measure of the angle is 40 degrees
Angle 2
The trigonometry ratio of the angle is given as
cos(220)
Expand the above expression
cos(220) = cos(360 - 140)
Apply the cosine rule
cos(220) = cos(360)cos(140) + sin(140)sin(360)
Evaluate the ratios
cos(220) = 1 x cos(140) + sin(140) x 0
So, we have
cos(220) = cos(140)
So, the measure of the angle is 140 degrees
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A grocery store sells sliced cheddar cheese by weight. The relationship between the amount of cheddar cheese in pounds, and the time in dollars of cheddar cheese in pounds, x, and the total cost in dollars of the sliced cheddra cheese, y, is represented by a graph drawn in the xy-planeIf the point (8, 44) lies on the graph, what does the point (8, 44) indicate?
Remember that the pair of coordinates
[tex](x,y)[/tex]of a point that lies on the graph of the function tells us the x-value and the
y-value related to that value.
Therefore, the point
[tex](8,44)[/tex]Represents that 8 pounds of cheddar cheese cost $44 in total (y represents the total cost, not the cost per pound)
(Correct answer is option B)
which of these is a formula that can be used to determine the nth term of the arithmetic sequence 15,27,39,51,....?
For an arithmetric progression, we need to find the common difference in the sequence
common difference = d = 2nd term - 1st term = 3rd term - 2nd term = 4th term - 3rd term
2nd term - 1st term = 27 -15 = 12
3rd term - 2nd term = 39-27 = 12
The result are the same.
Hence, d = 12
The first trm = 15
The formula for arithmetric sequence:
The nth term = 1st term + d(n - 1)
Replacing with the values we got above:
The nth term = 15 + 12(n - 1)
Since none of the options have the above, we would expand the parenthesis.
The nth term = 15 + 12×n - 12×1
The nth term = 15 + 12n - 12
= 15 -12 + 12n
The nth term = 3 + 12n = 12n + 3
From the options:
The nth term = 12n + 3 (option B)
[tex]a_n=\text{ }12n+3\text{ (}optionB)[/tex]
help meeeee pleaseeeee!!!
thank you
The value of x is -2.
We are given a graph of a function f(x).
We have to find the value of x when the value of f(x) is -3.
We know that x- axis represents x and the y-axis shows f(x).
Hence, the x and y coordinates of a point on the line will be (x, f(x)).
To find the value of x , I will check the coordinates of the point (x, -3) because it is given that f(x) is -3.
Using the graph, we found the coordinates of that point to be (-2,-3).
Hence, we can say that,
x = -2
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Claim: The mean pulse rate (in beats per minute) of adult males is equal to bpm. For a random sample of adult males, the mean pulse rate is bpm and the standard deviation is bpm. Find the value of the test statistic.
For solving this question, you should apply the equation:
The question gives
Next step - replace the values in the equation
[tex]z_T=\frac{70.4-69}{\frac{10.8}{\sqrt[]{129}}}=\frac{1.4}{\frac{10.8}{\sqrt{129}}}=1.47[/tex]Daisy is buying a video game in the shop. The price before tax is $21, and after sales tax is $24.74. What is the sales tax plied to the video game? Round to the nearest hundredth
Recall that:
[tex]\text{salesprice}=\text{originalprice+taxes.}[/tex]Therefore Daisy pays:
[tex]24.74-21=3.74\text{ dollars}[/tex]in taxes for the videogame.
Now, recall that to determine the percentage that a represents from b we use the following expression:
[tex]\frac{a}{b}\cdot100.[/tex]Therefore, the sales tax applied to the videogame is:
[tex]\frac{3.74\text{dollars}}{21\text{dollars}}\cdot100\approx17.81[/tex]percent.
Answer: The tax applied to the videogame is 17.81%, in this case, the sales tax is 3.74 dollars.
What fraction of $36,000 is $27,000?
We need to keep in mind that
36000 is 1
In order to know the fraction we need to divide 27000 between 36000, and then simplify the fraction
[tex]\frac{27000}{36000}=\frac{27}{36}=\frac{3}{4}[/tex]the fraction of 36000 that is 27000 is 3/4
I'm needing help with graphing equation
what is the equation?
a) y = 2x
x y
1 2(1) = 2
2 2(2) = 4
3 2(3) = 6
4 2(4) = 8
5 2(5) = 10
b) y = x - 2
x y
2 2 - 2 = 0
3 3 - 2 = 1
4 4 - 2 = 2
5 5 - 2 = 3
6 6 - 2 = 4
a) line a
line b
c)
y = 3x + 2
x y
1 3(1) + 2 = 5
2 3(2) +2 = 8
3 3(3) + 2 = 11
4 3(4) + 2 = 14
5 3(5) + 2 = 17
line d
y = 5x - 3
x y
0 5(0) - 3 = -3
2 5(2) - 3 = 7
4 5(4) - 3 = 17
6 5(6) - 3 = 27
What are the possible values for the missing term of the geometric sequence? .004, _____, .4.04.04, -.04.0004.0004, -.0004
By definition, in a Geometric sequence the terms are found by multiplying the previous one by a constant. This constant is called "Common ratio".
In this case, you know these values of the set:
[tex]\begin{gathered} .004 \\ .4 \end{gathered}[/tex]Notice that you can set up this set with the value given in the first option:
[tex].004,.04,.4[/tex]Now you can check it there is a Common ratio:
[tex]\begin{gathered} \frac{0.04}{0.004}=10 \\ \\ \frac{.4}{0.04}=10 \end{gathered}[/tex]The Common ratio is:
[tex]r=10[/tex]Therefore, it is a Geometric sequence.
Apply the same procedure with each option given in the exercise:
- Using
[tex].004,.04,-.04,.4[/tex]You can notice that it is not a Geometric sequence, because:
[tex]\begin{gathered} \frac{-.04}{.04}=-1 \\ \\ \frac{.4}{-.04}=-10 \end{gathered}[/tex]- Using
[tex].004,.0004,.4[/tex][tex]\begin{gathered} \frac{.0004}{.004}=0.1 \\ \\ \frac{4}{.0004}=1,000 \end{gathered}[/tex]Since there is no Common ratio, if you use the value given in the third option, you don't get a Geometric sequence.
- Using this set with the values given in the last option:
[tex].004,.0004,-.0004,.4[/tex]You get:
[tex]\begin{gathered} \frac{.0004}{.004}=0.1 \\ \\ \frac{-.0004}{.0004}=-1 \end{gathered}[/tex]It is not a Geometric sequence.
The answer is: First option.
Larry Mitchell invested part of his $17000 advance at 2% annual simple interest and the rest at 5% annual simple interest. If his total yearly interest from both accounts was $610, find the amount invested at each rate
The simple interest is given by:
[tex]SI=Prt[/tex]where P is the principal (the amount we invest in the account), r is the interest rate and t is the time of investment.
Let P be the interest Larry made in the 2% account, the simple interest in this case is given by:
[tex]0.02P[/tex]Now for the second account we would have an envestment of (17000-P), then the simple interest have to be:
[tex]0.05(17000-P)[/tex]and we know that both investments have to be equal to 610, then we have:
[tex]\begin{gathered} 0.02P+0.05(17000-P)=610 \\ 0.02P+850-0.05P=610 \\ -0.03P=610-850 \\ -0.03P=-240 \\ P=\frac{-240}{-0.03} \\ P=8000 \end{gathered}[/tex]Therefore Larry invested $8000 in the 2% account and $9000 in the 5% account.