Answer:
A. Rectangle
Step-by-step explanation:
Find the area of the shaded circles. Leave your answer in terms of pi or round to the nearest 10th
step 1
Find out the area of the complete circle
[tex]A=\pi\cdot r^2[/tex]we have
r=10 units
substitute
[tex]\begin{gathered} A=\pi\cdot10^2 \\ A=100\pi\text{ unit2} \end{gathered}[/tex]Remember that the area of the complete circle subtends a central angle of 360 degrees
so
Applying proportion
Find out the area of the circle with a central angle of 330 degrees
100pi/360=x/330
solve for x
x=(100pi/360)*330
x=91.67pi unit2Reginald wants to buy a new collar for each of his 3 cats. The collars come in a choice of 6 different colors. How many selections of collarsfor each of the 3 cats are possible if color repetitions are allowed
We will have the following:
Assuming that color repetitions can be made, then total number of selections for collars for the 3 cats will be:
[tex]6\ast6\ast6=216[/tex]So, there will be a total of 216 possible permutations of choices.
Amelia used 6 liters of gasoline to drive 48 kilometers.How many kilometers did Amelia drive per liter?kilometers =At that rate, how many liters does it take to drive 1 kilometer?liters =
Answer:
8km /hr
1/ 8 of a litre.
Explanation:
We are told that Amelia drives 48 kilometres in 6 hours, this means the number of kilometres she drives per litre is
[tex]48\operatorname{km}\div6\text{litres}[/tex][tex]\frac{8\operatorname{km}}{\text{litre}}[/tex]Hence, Amelia drives 8 kilometres per litre.
The next question can be rephrased as, given that Amelia drives 8 km per litre, how many litres will it take to drive one kilometre?
To answer this question, we make use of the equation
[tex]\operatorname{km}\text{ travelled = 8km/litre }\cdot\text{ litres}[/tex]Now, we want
km travelled = 1 km
and the above equation gives
[tex]\begin{gathered} 1=\frac{8\operatorname{km}}{\text{litre}}\cdot\text{litres} \\ 1=8\cdot\text{litres} \end{gathered}[/tex]Dividing both sides by 8 gives
[tex]\text{litres}=\frac{1}{8}[/tex]Hence, it takes 1/8 of a litre to drive 1 kilometre.
Consider the functions below.Represent the interval where both functions are increasing on the number line provided.
The function f(x) is increasing for the intervals:
[tex]\begin{gathered} x\in(-\infty,-2\rbrack \\ x\in\lbrack2,\infty) \end{gathered}[/tex]If you have a 40% decrease, what percentage of the original amount do you have?
A 40% decrease represents subtraction.
[tex]100-40=60[/tex]So, the initial percentage is 100%, if it decreases by 40%, we get 60% as result.
Hence, we would have 60% of the original amount.If A=(-7,8,1) and B(8,7,7), find ||AB||. Round to 3 decimal places
Given,
A= (-7, 8, 1).
B= (8, 7, 7)
The value of ||AB|| is,
[tex]\begin{gathered} \mleft\Vert AB\text{ }\mleft\Vert\text{ = }A.B\mright?\mright? \\ \end{gathered}[/tex]The value of A.B is ,
[tex]\begin{gathered} A\mathrm{}B=(-7.8+8.7+1.7) \\ AB=(-56+56+7) \\ AB=7 \end{gathered}[/tex]Hence, the value is 7.
Lemons are sold in bag of six lemons for four dollars If you bought 24 how much would you spend
Lemons cost $4 for a bag of six, so using the unitary method, which states, "The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of units," $16 will be spent for 24 lemons.
What is Unitary method?The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel.
Here,
Let x be the cost of 24 lemons.
6 lemons for $4
24 lemons for $x
by unitary method,
cost of 1 lemon=$4/6
cost of 24 lemons,
=24*(4/6)
=$16
Using the unitary method, which states that "The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of units," $16 will be spent for 24 lemons since a bag of six costs $4.
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Find the midpoint of the coordinates (3. -18) and (-5, -10) WHAT IS THE XVALUE?
Given the points (3, -18) and (-5, -10)
Let the midpoint of the given coordinates is (x , y)
[tex]x=\frac{3+(-5)}{2}=\frac{-2}{2}=-1[/tex][tex]y=\frac{(-18)+(-10)}{2}=\frac{-28}{2}=-14[/tex]So, the coordinates of the midpoint is (-1 , -14)
Ashley can text 60 words in 45 seconds. At this rate, how many words can she text in 60 seconds?
Let Ashley can text x words in 60 minutes. Then equation for x is,
[tex]\begin{gathered} \frac{60}{45}=\frac{x}{60} \\ x=\frac{60\cdot60}{45} \\ =80 \end{gathered}[/tex]Thus, Ashley text 80 words in 60 seconds.
True or false? Based only on the given information, it is guaranteed thatAD EBDADGiven: ADI ACDBICBAC = BCBCDO A. TrueB. FalseSUBMIT
According to the information given, we can assure:
For both triangles, two interior angles and the side between them have the same measure and length, respectively. This is consistent with the ALA triangle congruence criterion.
ANSWER:
True.
If 1 centimeter equals 3 ft what is the actual length of the 5cm side of the yard?
this is
[tex]\begin{gathered} \frac{1}{3}=\frac{5}{x} \\ 1\times x=3\times5 \\ x=15 \end{gathered}[/tex]answer: 15 ft
Translate this phrase into an algebraic expression.72 decreased by twice a numberUse the variable n to represent the unknown number.
When the questions uses the word "decreased" this means that a value was subtracted by another value. The word "twice" symbolizes that a number was doubled or multiplied by 2. With this understanding, we can create the expression:
[tex]72-2n[/tex]Remmy establishes a loan for an $8000 vacation package to Transylvania. The vacation company charges 5.5% simple interest rate. Remy plans to pay back the loan over 1.5 years.How much interest will Remmy pay?
Remmy will pay $660 interest.
Step - by - Step Explanation
What to find? The amount of interest to be paid.
Given Parameters:
• Principal (P) = $8000
,• Rate of interest(R) = 5.5
,• Time(t in years) = 1.5
The formula for calculating simple interest is given below:
[tex]S.I=\frac{P\times R\times T}{100}[/tex]Where P is the principal.
R represents the rate.
T is the time given in years.
S.I is the simple interest.
Substitute the values into the formula and simplify.
[tex]S.I=\frac{8000\times5.5\times1.5}{100}[/tex][tex]S.I=\frac{80\cancel{00}\times5.5\times1.5}{1\cancel{00}}[/tex][tex]=80\times5.5\times1.5[/tex]= 660
Hen
how do I do domin and range on a graph
Consider that the domain are the set of x values with a point on the curve.
In this case, based on the grap, you can notice that the domain is:
domain = (-8,2)
domain = {-8,-7,-6,-5,-4,-3,-2,-1,0,1,2}
In this case you can observe that the circle has a left limit given by x = -8 (this can be notices by the subdivisions of the coordinate system) and a right limit given by x = 2. That's the reason why it is the interval of the domain.
The range are the set of y values with a point on the curve.
range = (-3,7)
range = {-3,-2,-1,0,1,2,3,4,5,6,7}
In this case, you observe the down and up limits of the circle.
14 POINTS!!!!! BRAINLY!!!!A lamp produced a shadow of a man standing in the middle of a stage.How long is the shadow.A 9.60B 11.38C 20.98D 22.51
Given the graph:
The length of the shadow = y - x.
• To find x:
[tex]\begin{gathered} tan21\text{\degree}=\frac{opposite}{adjacent} \\ \\ tan21\text{\degree}=\frac{x}{25} \\ \\ x=25\times tan21\text{\degree = 9.6m} \end{gathered}[/tex]• To find y:
[tex]\begin{gathered} tan40\text{\degree}=\frac{y}{25} \\ \\ y=25\times tan40\text{\degree}=21m \end{gathered}[/tex]Length of the shadow:
[tex]\begin{gathered} length=21-9.6 \\ \text{ }=\text{ 11.4 m} \end{gathered}[/tex]ANSWER
Length of the shadow = 11.4 m
Rewrite the following equation in slope-intercept form.
y + 8 = –3(x + 7)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer: y = -3x - 21
Step-by-step explanation:
Slope intercept form: y = mx + b
m is the slope, and b is the y-intercept.
y + 8 = -3(x + 7)
Start by distributing -3 into the parenthesis.
y + 8 = -3x - 21
subtract 8 from both sides to get the final answer.
y = -3x - 29
Answer:
Slope-intercept form,
y = -3x - 29Step-by-step explanation:
Now we have to,
→ Rewrite the given equation in the slope-intercept form.
The slope-intercept form is,
→ y = mx + b
The equation is,
→ y + 8 = -3(x + 7)
Then the value of y will be,
→ y + 8 = -3(x + 7)
→ y + 8 = -3x - 21
→ y = -3x - 21 - 8
→ [ y = -3x - 29 ]
Hence, answer is y = -3x - 29.
If the formula x=1/n, is used to find the mean of the following sample, what is the value of n? 2, 63, 88, 10, 72, 99, 38, 19
Given:
The formula is:
[tex]x=\frac{1}{n}\sum_{i=1}^nx_i[/tex]Series is:
[tex]2,63,88,10,72,99,38,19[/tex]Find-:
The value of "n"
Explanation-:
In the given formula "n" represent the number of member in a series.
Given series is:
[tex]2,63,88,10,72,99,38,19[/tex]The number of members is:
The members are 8.
So the value of "n" is:
[tex]n=8[/tex]The value of "n" is 8.
Answer: The answer to this problem is 6
Step-by-step explanation: i took the quiz, this is the correct answer.
Hello hope all is well can you tell me what am doing wrong for number 6
We have the next data
70,89,75,36,80
First we will calculate the mean
(70+89+75+36+80)/5=70
mean=70
Then we will calculate the Median
36,70,75,80,89
median =75
Then we will calculate the mode because any value is repeated all the values given are the mode
mode:70,89,75,36,80
Range
89-36=53
Range =53
Segment AC has a midpoint B. If AB = 2x - x - 42 andBCI_x+11x +21, find the length of Ac.
The equation for the segment AB is;
[tex]2x^2-x-42[/tex]The equation for the segment BC is ;
[tex]x^2+11x+21[/tex]If segment AC has midpoint at B , this means ;
AC = AB + BC
To get AC we add the equation for AB and BC
Performing addition as;
[tex]2x^2-x-42+x^2+11x+21[/tex]Collect like terms as;
[tex]2x^2+x^2+11x-x-42+21=AC[/tex][tex]3x^2+10x-21=AC[/tex]Answer
[tex]AC=3x^2+10x-21[/tex]
Let h(t)=tan(4x + 8). Then h'(3) is
and h''(3) is
The most appropriate choice for differentiation will be given by
h'(3) = 24.02
h''(3) = [tex]210.48[/tex]
What is differentiation?
Differentiation is the process in which instantaneous rate of change of function can be calculated based on one of its variables.
Here,
h(x) = tan(4x + 8)
h'(x) = [tex]\frac{d}{dx} (tan(4x + 8))[/tex]
= [tex]sec^2(4x + 8)\frac{d}{dx}(4x + 8)[/tex]
= [tex]4sec^2(4x + 8)[/tex]
h'(3) =
[tex]4sec^2(4\times 3 + 8 )\\4sec^220\\24.02[/tex]
h''(x) =
[tex]\frac{d}{dx}(4sec^2(4x + 8))\\4\times 2sec(4x + 8)\times \frac{d}{dx}(sec(4x + 8))\\8sec(4x + 8)sec(4x+8)cosec(4x+8)\times\frac{d}{dx}(4x + 8)\\32sec^2(4x + 8)cosec(4x +8)[/tex]
h''(3) =
[tex]32sec^2(4\times 3+8)cosec(4\times 3+8)\\32sec^220cosec20[/tex]
[tex]210.48[/tex]
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Find a polynomial function of lowest degree with rational coefficients that has the
given numbers as some of its zeros.
√3,51
The polynomial function in expanded form is f(x) =
Answer: [tex]f(x)=x^3 -51x^2 -3x+153[/tex]
Step-by-step explanation:
By the conjugate root theorem, the roots are [tex]\sqrt{3}, -\sqrt{3}, 51[/tex].
Letting the leading coefficient be 1,
[tex]f(x)=(x-\sqrt{3})(x+\sqrt{3})(x-51)\\\\=(x^2 -3)(x-51)\\\\=x^3 -51x^2 -3x+153[/tex]
if 5 is added eighteen times to a number the result is 174 what is the number
Answer
The number is 84.
Step-by-step Explanation
The question wants us to find a number that gives 174 when 5 is added to it eighteen times.
Let that number we are looking for be x.
Interpreting the question into a mathematical equation, we have
x + (5 × 18) = 174
x + 90 = 174
Subtract 90 from both sides
x + 90 - 90 = 174 - 90
x = 84
Hence, the number we are looking for, is 84.
Hope this Helps!!!
Need help Instructions: Find the measure of each angle Calculate the length of each side Round to the nearest tenth
Given,
The length of the perpendicular is 4.
The measure of the hypotenuse is 14.
Required:
The measure of each angle of the triangle.
As it is a right angle triangle,
The measure of angle C is 90 degree.
By using the trigonometric ratios,
[tex]\begin{gathered} cosA=\frac{AC}{AB} \\ cosA=\frac{4}{14} \\ A=cos^{-1}(\frac{4}{14}) \\ A=73.4^{\circ} \end{gathered}[/tex]By using the trigonometric ratios,
[tex]\begin{gathered} sinB=\frac{AC}{AB} \\ sinB=\frac{4}{14} \\ B=sin^{-1}(\frac{4}{14}) \\ B=16.6^{\circ} \end{gathered}[/tex]Hence, the measure of angle A is 73.4 degree, angle B is 16.6 degree and angle C is 90 degree.
Graph the parabola. I have a picture of the problem
Let's begin by listing out the given information
[tex]\begin{gathered} y=(x-3)^2+4 \\ y=(x-3)(x-3)+4 \\ y=x(x-3)-3(x-3)+4 \\ y=x^2-3x-3x+9+4 \\ y=x^2-6x+13 \\ \\ a=1,b=-6,c=13 \end{gathered}[/tex]The vertex of the function is calculated using the formula:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ x=-\frac{-6}{2(1)}=\frac{6}{2}=3 \\ x=3 \\ \\ y=(x-3)^2+4 \\ y=(3-3)^2+4=0^2+4=0+4 \\ y=4 \\ \\ (x,y)=(h,k)=(3,4) \end{gathered}[/tex]For the function, we assume values for x to solve. We have:
[tex]\begin{gathered} y=(x-3)^2+4 \\ x=1 \\ y=(1-3)^2+4=-2^2+4=4+4 \\ y=8 \\ x=2 \\ y=(2-3)^2+4=-1^2+4=1+4 \\ y=5 \\ x=3 \\ y=(3-3)^2+4=0^2+4=0+4 \\ y=4 \\ x=4 \\ y=(4-3)^2+4=1^2+4=1+4 \\ y=5 \\ x=5 \\ y=(5-3)^2+4=2^2+4=4+4 \\ y=8 \\ \\ (x,y)=(1,8),(2,5),(3,4),(4,5),(5,8) \end{gathered}[/tex]We then plot the graph of the function:
1(c). What is a better deal? Explain. Deal 1: 2 mediums 14'' (round) pizza for $14 total Deal 2: 1 large 20'' (round) pizza for $13 total
To get the better deal of the two, we need to find the cost per area of pizza for each deal and compare.
Deal 1: 2 medium 14'' (round) pizza for $14 total
The area of a circle is calculated as
[tex]A=\pi r^2[/tex]where r is the radius.
The area of the pizza is calculated to be:
[tex]\begin{gathered} r=14 \\ \therefore \\ A_1=\pi\times14^2=196\pi \end{gathered}[/tex]Hence, the total area for the two pizzas will be:
[tex]\Rightarrow196\pi\times2=392\pi[/tex]The cost per square inch of pizza is, therefore, calculated to be:
[tex]\Rightarrow\frac{14}{392\pi}=0.011[/tex]The pizza costs $0.011 per square inch.
Deal 2: 1 large 20'' (round) pizza for $13 total
The area of the pizza is calculated to be:
[tex]\begin{gathered} r=20 \\ \therefore \\ A_2=\pi\times20^2=400\pi \end{gathered}[/tex]Hence, the cost per square inch of pizza is calculated to be:
[tex]\Rightarrow\frac{13}{400\pi}=0.010[/tex]The pizza costs $0.010 per square inch.
CONCLUSION:
The better deal will be the deal with the lesser cost per square inch. As can be seen from the calculation, both deals are about the same price per square inch if approximated. However, without approximation, Deal 2 has a slightly lesser cost per square inch.
Therefore, DEAL 2 IS THE BETTER DEAL.
How do I solve this I do understand how to
Solve for the unknown variable using a pythagoras theorem:
Hypotenuse = 32+x
Opposite = 56
Adjacent = x
[tex]\begin{gathered} \text{Hyp}^2=\text{opp}^2+\text{adj}^2 \\ (32+x)^2=56^2+x^2 \\ (32+x)(32+x)=3136+x^2 \\ 1024+64x+x^2=3136+x^2 \\ \text{collect like terms} \\ 64x+x^2-x^2=3136-1024 \\ 64x=2112 \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} \frac{64x}{64}=\frac{2112}{64} \\ x=33 \end{gathered}[/tex]Therefore the correct value of x = 33
Penelope graphed the function below using the domain { 0,1,2,3,4 } .X + y = 4 Which graph did Penelope make ?
Given data:
The given equation x+y=4.
Substitute 0 for x in the given equation.
0+y=4
y=4.
Substitute 0 for y in the given equation.
x+0=4
x=4
So, the graph of the equation must pass from (0,4) and (4,0).
Thus, the option (a) is correct.
Omaha Beef Company purchased a delivery truck for $66,000. The residual value at the end of an estimated eight-year service life is expected to be $12,000. The company uses straight-line depreciation for the first six years. In the seventh year, the company now believes the truck will be useful for a total of 10 years (four more years), and the residual value will remain at $12,000. Calculate depreciation expense for the seventh year.
Given:
Company purchased = $66000
Find-:
Depreciation expense for the seventh year
Sol:
First, depreciate for 6 years using the regular method:
[tex]\begin{gathered} =\frac{\text{ Cost - salvage value}}{\text{ initial useful life}} \\ \\ =\frac{66000-12000}{8} \\ \\ =6750 \end{gathered}[/tex]The annual depreciation is 6750.
For 6 years
[tex]\begin{gathered} =6750\times6 \\ \\ =40500 \end{gathered}[/tex]So
[tex]\begin{gathered} \text{ Remaining useful life = 10-6} \\ =4 \\ \\ =\frac{66000-40500-12000}{4} \\ \\ =\frac{13500}{4} \\ \\ =3375 \end{gathered}[/tex]For seventh-year depreciation expense is $3375
Determine if the situation below are biased or unbiased and explain why. Two people from each 8th period class are askedwhat they think the theme of the next dance shouldbe.
Answer
The situation is not biased because it takes a random sample from each group.
Lana draws ALMN on the coordinate plane. What is the perimeter of ALMN? Round to the nearest unit
We are asked to determine the perimeter of triangle LMN. To do that we will use the fact that the perimeter is the sum of the length of the sides of the triangle. Therefore, we have:
[tex]P=LM+MN+LN[/tex]To determine the value of the length of "LM" we will use the formula for the euclidian distance:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where:
[tex]\begin{gathered} (x_1,y_1)_;\left(x_2,y_2\right) \\ \end{gathered}[/tex]Are the endpoints of the segment. For LM we have that the coordinates of the endpoints are:
[tex]L=\lparen-3,2)[/tex][tex]M=(3,5)[/tex]Substituting we get:
[tex]d_{LM}=\sqrt{(3-(-3))^2+(5-2)^2}[/tex]Solving the operations:
[tex]d_{LM}=\sqrt{6^2+3^2}[/tex]Solving the operations:
[tex]d_{LM}=\sqrt{45}[/tex]Now, we use the endpoints of MN:
[tex]M=(3,5)[/tex][tex]N=(9,2)[/tex]Substituting we get:
[tex]d_{MN}=\sqrt{(9-3)^2+(2-5)^2}[/tex]Solving the operations we get:
[tex]\begin{gathered} d_{MN}=\sqrt{6^2+\left(-3\right)^2} \\ \\ d_{MN}=\sqrt{45} \end{gathered}[/tex]Now, we apply the equation for segment LN:
[tex]d_{LN}=\sqrt{}(9-(-3))^2+(2-2)^2[/tex]Solving the operations:
[tex]d_{LN}=12[/tex]Now, we substitute in the formula for the perimeter:
[tex]P=\sqrt{45}+\sqrt{45}+12[/tex]Adding like terms:
[tex]P=2\sqrt{45}+12[/tex]In decimal form rounded to the nearest unit this is:
[tex]P=25[/tex]Therefore, the perimeter of the figure is 25.