If Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
Tₙ = a + (n-1)d
(for all positive integer values of n)
Given Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54. Therefore, the sequence can be written as,
4.54, 9.08, 13.62, 18.16, 22.7, 27.24, .........
Therefore,
The first term of the sequence is 4.54, To get the next term you need to add 4.54. This is an arithmetic sequence.Since 9 weeks (40.86/4.54 = 9) are already over, and there are 27 more weeks, therefore, the spending till 36 weeks will be,
a₃₆ = 4.54 + (36-1)4.54
a₃₆ = 163.44
Hence, if Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.
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The door prizes at a dance are gift certificates from local merchants. there are four $10 certificates, five $20 certificates, and three $50 certificates. the prize envelopes are mixed together in a bag and are drawn at random.
The probability that none of the prizes is a $10 gift certificate is; 7/99
The expected number of $20 gift certificates drawn is 2.083
How to find the Probability?This is a question of picking objects from a mixture without replacement. The modelling distribution is the hypergeometric distribution, given by the formula:
P(a) = C(A,a) * C(B,b)/C(A+B,a+b)
Where;
a = number of good objects picked
b = number of bad objects picked.
A = number of good objects in the given batch.
B = number of bad objects in the given batch.
a + b = total number of objects picked without replacement.
A + B = total number of objects in the batch.
A) In this question;
A = 4 ($10, good)
B = 3 + 5 = 8 ($20, $50, "bad")
a = 0, b = 5
a + b = 5
Thus;
P(a = 0) = C(4, 0) × C(8, 5)/C(12, 5)
P(a = 0) = 1 × 56/792
P(a = 0) = 7/99
B) $20 is the "good" prize.
Thus;
A = 5
B = 3 + 4 = 7
a + b = 5 (total number of prizes drawn)
Thus;
E[$20] = (5/(5 + 3 + 4)*5)
E[$20] = (5/12)*5
E[$20] = 25/12
E[$20] = 2.083
Complete Question is;
The door prizes at a dance are four $10 gift certificates, five $20 gift certificates, and three $50 gift certificates. The prize envelopes are mixed together in a bag, and five prizes are drawn at random.
What is the probability that none of the prizes is a $10 gift certificate?
What is the expected number of $20 gift certificates drawn?
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Beth says that the graph of g(x) = + 1 is a translation of 5 units to the left and 1 unit up of f(x) = . She continues to explain that the point (0, 0) on the square root function would be translated to the point (–5, 1) on the graph of g(x). Is Beth’s description of the transformation correct? Explain.
Beth's description of the transformation is incorrect
Complete questionBeth says that the graph of g(x)=x-5+1 is a translation of 5 units to the left and 1 unit up of f(x) = x. She continues to explain that the point (0,0) on the square root function would be translated to the point (-5,1) on the graph of g(x). Is Beth's description of the transformation correct? Explain
How to determine the true statement?The functions are given as:
g(x) = x - 5 + 1
f(x) = x
When the function f(x) is translated 5 units left, we have:
f(x + 5) = x + 5
When the above function is translated 1 unit up, we have:
f(x + 5) + 1 = x + 5 + 1
This means that the actual equation of g(x) should be
g(x) = x + 5 + 1
And not g(x) = x - 5 + 1
By comparison;
g(x) = x - 5 + 1 and g(x) = x + 5 + 1 are not the same
Hence, Beth's description of the transformation is incorrect
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How much greater is 8 x 10 to the power of 5 then 8 x 10 to the power of -1
Answer:
3.276.799.999,9875
Step-by-step explanation:
(8 × 10)^5 - (8 × 10)^-1 = 3.276.799.999,9875
Solve the equation using square roots. 4x^2-371=29
Answer:
x = 100
Step-by-step explanation:
[tex]4x^{2} -371=29\\[/tex]
+ 371 +371
[tex]4x^{2} =400[/tex]
[tex]\sqrt{4x^{2} } =\sqrt{400}[/tex]
[tex]4x=400[/tex]
Divide both sides by 4.
x = 100
Hope it helps!
IF G=(x)=x^2 find the value of g(2).g(3)
Answer: 36
Step-by-step explanation:
[tex]g(2)=2^{2}=4\\g(3)=3^{2}=9\\g(2) \cdot g(3)=4 \cdot 9=\boxed{36}[/tex]
Hello, can someone help with this problem?
The graph shows the probability distribution of a random variable.
What is the value of P(4≤X≤8)?
0.40
0.45
0.50
0.55
Answer:
P(5 ≤ X ≤ 8) = a rectangle with a width of 3 and height of .15 = 3(.15) = .45
P( 4 ≤ X ≤ 5) = a triangle with a base of 1 and a height of (0.15 -0.05) = .10
So....this area = (1/2)(1)(.10) = .05
And another rectangle with a width of 1 and height of .05 = (1) (.05) = .05
So
Adding these areas
P( 4 ≤ X ≤ 8 ) = .45 + .05 + .05 = .55
Step-by-step explanation:
Hoped this helped!
1.Isabel exercises no less than 45 minutes per day.
Use t to represent Isabel's amount of exercise (in minutes per day).
2. The vehicle's fuel is at least 45 miles per gallon.
Use f to represent the vehicle's fuel efficiency (in miles per gallon).
[1] t ≥ 45
Since Isabel exercises more ("no less") than 45 minutes a day, we will use greater than or equal to.
-> because being equal is not less, hence still "no less"
[2] f ≥ 45
Because the vehicle's fuel is "at least" that means it can also be equal too, hence the user of greater than or equal to.
Jason and yolanda both drew a simple random sample from a non-normally distributed population of 25,000. jason’s sample consisted of 0.24% of the population, while yolanda’s sample consisted of 0.32% of the population. whose sample can be used to make inferences about the population?
The correct answer is option D which is both Jason’s sample and Yolanda’s sample can be used to make inferences about the population
The complete question is given below:-
Jason and Yolanda both drew a simple random sample from a non-normally distributed population of 25,000. Jason’s sample consisted of 0.24% of the population, while Yolanda’s sample consisted of 0.32% of the population. Whose sample can be used to make inferences about the population?
neither Jason’s sample nor Yolanda’s sample
only Jason’s sample
only Yolanda’s sample
both Jason’s sample and Yolanda’s sample
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Since we have given that
Total number of population = 25000
Percent of a sample of Jason = 0.24%
Percent of a sample of Yolanda's = 0.32%
So, the number of the population according to Jason's sample is given by
= ( 0.24 / 100 ) x 25000
= 60
The number of the population according to Yolanda's sample is given by
= ( 0.32 / 100 ) x 25000
= 80
Both the sample can be used to make inferences about the population
Hence, the Last Option is correct.
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what is the absolute value of 2x + 3 = 11
A rectangular solid is dilated by a factor of 0.5
How many times larger is the volume of the resulting cube than the volume of the original cube
Enter your answer as a decimal and do NOT round
Answer:
0.125 times larger
Step-by-step explanation:
given the scale factor of 2 solids is k , then the volume factor = k³
here k = 0.5 , so
volume factor = (0.5)³ = 0.125
Please please help me 30 points if you can I need the answer I know how to do it I just suck with the fractions
Answer:
1
Step-by-step explanation:
[tex]\text{Given that,}~ (x_1,y_1) = (-2,4)~ \text{and}~ \text{slope,}~ m = -\dfrac 32\\ \\\text{Equation of line,}~\\\\~~~~~~~y -y_1 = m(x-x_1)\\\\\implies y -4 =-\dfrac 32(x+2)\\\\\implies y-4 =-\dfrac 32x - 3\\\\\implies y = -\dfrac 32x -3 +4\\\\\implies y = -\dfrac 32x +1[/tex]
The current equation of the perpendicular line;
⇒ is the slope-intercept form: [tex]y= mx + b[/tex]
m: is the coefficient in front of the x, which is also the slope's valueb: y-intercept of the functionNow for the point-slope form, we need a point on the line and the slope of the line:
⇒ we have
slope = -3/2point: (-2,4)Since this is the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex]
⇒ where the (x₁,y₁) is the point on the line and m is the slope
[tex]= > Equation: (y-4)=-\frac{3}{2}(x+2)[/tex]
To convert the equation to slope-intercept form:
⇒ must isolate 'y' to one side and everything to the other side
[tex]y= -\frac{3}{2}(x+2)+4\\ y=-\frac{3}{2} x-3+4\\y=-\frac{3}{2}x+1[/tex]
Answer: [tex]y = -\frac{3}{2}x+1[/tex]
Hope that helps!
Select the correct answer. in which career would you most likely apply concepts from geometry? a. food critic b. social worker c. radio dj d. computer game designer
Answer:
Computer game designer.
Step-by-step explanation:
If you want to design a game, you need to have some basic shapes and stuff in it. I'm not sure what else needs to be explained here lol
Find all angles, 0≤θ<360, that satisfy the equation below, to the nearest 10th of a degree.
4cos2θ+9=−14cosθ
Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees
Trigonometry identityTrigonometry identities are expressed as a function of cosine, sine and tangent.
Given the trigonometry expression shown
4cos2θ+9=−14cosθ
Equate to zero
4cos2θ+9 + 14cosθ = 0
According to trig identity
cos2θ = 2cos²θ - 1
Substitute to have:
4(2cos²θ - 1)+9 + 14cosθ = 0
Expand
8cos²θ - 4 + 9 + 14cosθ = 0
8cos²θ+ 14cosθ + 5 = 0
let P = cosθ to have;
8P² + 14P + 5 = 0
Factorize the result
8P² + 10P + 4P + 5 = 0
2P(4P+5)+1(4P+5)=0
(2P+1) = 0 and 4P+5 = 0
2P = -1 and P = -5/4
P = -1/2 and -5/4
Recall that P = cosθ
If P = -1/2
cosθ = -1/2
θ = -60
Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees
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Ms. Rudolph randomly selects one student from a group of students. 14 students are wearing a black shirt, 6 students are wearing a red shirt, and 9 students are wearing a blue shirt.
Show your work to determine the PROBABILITY that the selected student is wearing a BLACK shirt?
You may write your answer as a FRACTION or DECIMAL.
Answer:
14
29 as a fraction
Step-by-step explanation:
Based on the given conditions, formulate:
14=19+14+6）
2 Calculate
14
9+14+6
Calculate
14
23+6
Calculate the sum or difference
14
29
X
Calculate the sum or difference
14
29
Alternative forms
~ 0.482759, ~ 48.275862%,
4.827586 × 10
Hope it help :)
The population of center city is modeled by exponential function
The range of the exponential function will be y ≥ 250,0003. Then the correct option is B.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The Population Of Center City Is Modeled By Exponential Function F, Where X Is The Number Of Years After The Year 2015.
The graph is given below.
We know that the exponential function is given as
y = abˣ
For x = 0, y will be 250,000
250,000 = a
For x = 40, y will be 400,000
400,000 = 250,000b⁴⁰
b = 1.0118
Then we have
y = 250,000 (1.0118)ˣ
Then the range of the exponential function will be y ≥ 250,0003.
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Please help! Will mark big brain!
Answer:
The height of the ladder is 6.9 meter
Explanation:
Given:
angle: 60°opposite: 6 meterhypotenuse: height of ladderAs opposite and hypotenuse given, use sine rule:
[tex]\rightarrow \sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\rightarrow \sf sin(60) = \dfrac{6}{h}[/tex]
[tex]\rightarrow \sf h = \dfrac{6}{sin(60)} = 4\sqrt{3} = 6.928 \ meters \quad \approx \ 6.9 \ meters \ \ (one \ decimal \ place)[/tex]
Megan is one of the cheerleaders in her school. To prepare for the forthcoming Cheer Dance Competition, her coach is teaching them how to control their pom-poms when throwing them up into the air. One exercise is to toss the pom-poms twice as high as the previous toss from the top of their heads. If Megan is able to throw her pom-poms 2 feet above her head during her first toss, how high above her head should her fourth toss be? (problem solving)
Answer:
16 feet
Step-by-step explanation:
her first try is 2 and you multiply by 2 every time so her first would be 2 which we would multiply to get 4 which we would multiply again to get 8 which we would multiply AGAIN to get the final answer of 16
Each card in a standard deck of 52 playing cards is unique and belongs to 111 of 444 suits:
13 cards are clubs
13 cards are diamonds
13 cards are hearts
13 cards are spades
Suppose that Luisa randomly draws 4 cards without replacement.
What is the probability that Luisa gets 2 diamonds and 2 hearts (in any order)?
The probability that Luisa gets 2 diamonds and 2 hearts (in any order) is:
P = 0.022
How to get the probability?
The probability of getting a particular type of card, is given by the quotient between the number of cards of that type and the total number of cards.
Here, let's assume that the 4 draws are:
diamond-diamond-heart-heart.
In that order.
First, the probability of drawing a diamond card is equal to:
p₁ = 13/52
Because there are 13 diamond cards and 52 cards in total.
Bt after that draw, there will be 12 diamond cards and 51 cards in total, so the probability of getting the second diamond card is:
p₂ = 12/51.
Now, there are 13 heart cards and 50 cards in the deck, so the probability of getting the first heart card is:
p₃ = 13/50
And the probability of getting the second one is:
p₄ = 12/49.
The joint probability will be the product of the 4 individual probabilities, but we also need to take in account the possible permutations, these are:
(using D for diamond and H for heart).
D - D - H - H
D - H - D - H
D - H - H - D
H - D - D - H
H - D - H - D
H - H - D - D
So there are 6 permutations, this means that the probability is:
P = 6*p₁*p₂*p₃*p₄ = 6*(13/52)*(12/51)*(13/50)*(12/49) = 0.022
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anyone know the answer
Answer:
56
Step-by-step explanation:because 12345
a school spent 150$ on advertising for a breakfast fundraiser each plate of food was sold for 8.00$ but cost the school 2.00$ to prepare after all expenses were paid the school raised 2,400$ at the fundraiser . which equation can be used to find x the number of plates that were sold?
Answer:
375 plates were sold
Step-by-step explanation:
$2400 (profit) - $150 (advertising) = $6 (profit per plate $8 cost - $2 expense) times x
2400 - 150 = 6x
Simplify the left side: 2400 - 150 = 2250
2250 = 6x
Divide both sides by 6
2250/6 = 375
Pls Help, Will Give Brainlest
Answer:
19.1 ft³
Step-by-step explanation:
Hello!
Volume of a cylinder: [tex]V = \pi r^2h[/tex]
V = volumeπ = pi (3,14)r = radiush = heightWe can plug in the values and solve.
Solve[tex]V = \pi r^2 h[/tex][tex]V = (3.14)(1.5)^2(2.7)[/tex][tex]V = (3.14)(2.25)(2.7)[/tex][tex]V = 19.0755 \approx 19.1[/tex]The volume is approximately 19.1ft³
Step-by-step explanation:
[tex]\pink{\large{\underline{\underline{\sf Given:-}}}}[/tex]
[tex] \sf Radius_{\blue{cylinder}}=1.5 \: feet[/tex][tex] \sf Height_{\blue{cylinder}}=2.7 \: feet[/tex][tex]\pink{\large{\underline{\underline{\sf To\:find:-}}}}[/tex]
[tex] \sf Volume_{\blue{cylinder}}=?[/tex][tex]\pink{\large{\underline{\underline{\sf Solution:-}}}}[/tex]
We know that,
[tex]\underline{\boxed{\sf Volume_{cylinder}=πr^2h}}[/tex]
[tex]\longmapsto \sf 3.14×(1.5)^2×2.7[/tex]
[tex]\longmapsto \sf 3.14×2.25×2.7[/tex]
[tex]\longmapsto \sf 3.14×6.075[/tex]
[tex]\longmapsto \sf 19.0755≈19.1\: cubic\:feet[/tex]
helppppppppppppppppppppppppp
Answer:
reason 1.) This is the original expression
reason 2.) you subtract 4 from both sides
reason 3.) you divide both sides by 2 to get x=5
E im so confused-
( Please explain your answer! )
Answer:
B. 180° about the origin
Step-by-step explanation:
You are given a figure and its image, and asked to determine the angle of rotation. All of the answer choices indicate the center of rotation is the origin.
__
You have two clues that the rotation is 180° about the origin:
The original figure is in the 2nd quadrant, and the image is in the 4th quadrant, directly opposite the origin.Line ST is directed to the northeast; line S'T' is directed to the southwest, in exactly the opposite direction.__
To find the angle of rotation, you can look at the angle formed by a point, the center of rotation, and the image of the original point. Here, the angle UOU' is a straight angle, so the angle of rotation about O is 180°--the measure of that angle. (It can be convenient to use points close to the center of rotation, but any corresponding points on preimage and image will do.)
What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame? 16.7° 17.5° 72.5° 73.3°
The complete question is
"A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.
What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?
16.7°, 17.5°, 72.5°,73.3°"
The value of angle x would be 16.7 degrees.
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.
The angle of a right angle is always 90 degrees.
In order to find the value of x, a tan would be used.
This is because we have given the opposite and adjacent sides as 10 ft and 3 ft.
Tan Ф = opposite / adjacent
Tan Ф = (3/10)
= 16.7 degrees
The value of angle x would be 16.7 degrees.
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Answer: the answer is 16.7°.
Step-by-step explanation: it show below.
HELPP PLEASE 50 POINTS
Tucker bought some envelopes plain envelope cost twenty-five cents each decorative envelopes cost $0.45 each. he bought at least one plain envelope and at least one decorative envelope he spent exactly the same amount on Plain envelopes as on decorative envelopes.
before taxes added what was the least total amount he could have spent?
A. 1.40$
B. 2.30$
C. 3.10$
D4.50$
Answer:
D.
Step-by-step explanation:
0.45*5=2.25
0.25*9=2.25
2.25*2=4.50
Hope this helps!
If not, I am sorry.
Express Books advertised a college dictionary for $27.65 and a dictionary
software package for $29.80. The state tax is 5.5 percent and the city tax
is 1.5 percent. What is the total purchase price?
O $55.67
O $61.47
O $58.99
O $60.60
A
The total purchase price of the dictionary and the software package is $61.47.
What is the total purchase price?The total purchase price is the sum of the dictionary, software package and taxes.
Total cost of the dictionary and the software package = $27.65 + $29.80 = $57.45
Total cost after the taxes = ( 1 + 0.055 + 0.015) x $57.45 = $61.47
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1. suppose you purchased a new car for
$30,000 in 2015. if the value of the car
decreased by 8% each year, during what year
will the car be worth $10,000
Which is the range of the function f(x) = (9)×?
O all real numbers
O all real numbers less than 0
O all real numbers greater than 0
O all real numbers less than or equal to 0
Using it's concept, it is found that the range of the function [tex]f(x) = 9^x[/tex] is given by:
all real numbers greater than 0.
What is the range of a function?It is the set that contains all possible output values for the function.
In this problem, the function is:
[tex]f(x) = 9^x[/tex]
For exponential functions without vertical shifts, as is the case in this problem, the range is given by:
all real numbers greater than 0.
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Select the correct answer. if you pick a shirt at random from the given batch of 165 shirts, what is the probability that it is red and the size is medium? a. b. c. d. e.
The probability that a shirt picked at random is red and the size is medium is 48 / 165.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a shirt picked at random is red and the size is medium = number of red shirts that a medium size / total number of shirts
48 / 165.
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Answer:
The probability that a shirt picked at random is red and the size is medium is 48 / 165.
Step-by-step explanation:
because it is
i need help please thanks
Just give me the new coordinates
Answer: number 1 and number 2 and 4 and 5
Step-by-step explanation: