In a village the cases of a particular infectious disease have been exponentially decreasing at a rate of 95% per year since the pople started receving the vaccine. If there were 200 cases in the village to start with, predict the number of cases after 2 years. First complete the equation:
Remaining amount=
The number of cases after two years is 221.
What is the number of cases after two years?As a result of the disease, the population of the village would decrease by 95% per year. The number of cases at the village is function of the rate of infection, the number of years and the beginning number of cases.
The exponential function that can be used to represent this situation is:
FV = P( 1 + r)^t
FV = Future value P =beginning number of casesR = rate of increase in the number of cases : 100% - 95% = 5%t = timeFV = 200 (1.05)^2 = 221
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Prove that :-
(sinA + secA)² + (cosA + cosecA)² = 1 + secAcosecA
May this answers be helps you to solve
Sims waist is 30 inches. He wants to put on more weight and is hoping to gain enough weight to increase his waist size by 8%. How many inches does he want his waist to be?
Sim wants to increase his waist size to 32.4 inches.
How many inches does Sim want his waist to be?Sim wants the increase to be 8% of 30 inches.
The amount of increase Sim wants in his waist size exists
8% × 30 inches.
= 0.08 × 30 inches.
= 2.4 inches.
Adding the wanted increase to his present size would create Sim's waist size to be
30 in + 2.4 in = 32.4 inches.
Sim wants to increase his waist size to 32.4 inches.
Therefore, the correct answer is 32.4 inches.
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Find the distance between each pair of points. Round your answer to the nearest tenth if necessary
(IMAGE)
find the slope of the line that passes through each pair of points a. (-4, 5), (1, 1)
1. Graph the linear function f(x) = -2x + 1
Answer: The slope is -2 and the y-intercept is (0,1)
Step-by-step explanation:
what fraction of four weeks is 8 days
Answer:
For weeks are 28 days, so the fraction is 28/8= 3,5 and the fraction is 7/2
three varieties of coffee -coffee A coffee B and coffee C are combined and roasted yield a 54 lb batch of coffee beans. twice as many pounds of coffee C which is retails for $10.39 per pound are needed as coffee a which sells for $15.21 per pound coffee b retails for $13.21 per pound. how many pounds of each coffee should be used in a blend that sells for $12.61 per pound?
8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent coffee A, y represent coffee B and z represent coffee C, hence:
x + y + z = 54 (1)
Also:
2x = z (2)
And:
15.21x + 13.21y + 10.39z = 12.61(54) (3)
x = 8.9, y = 27.3 and z = 17.8
8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.]
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A coin is flipped, and a number cube is rolled. What is the probability of getting heads on the coin and a number less than 3 on the number cube?
a.one eighth
b. one sixth
c. one fourth
d. one half
=============================================================
Explanation:
The probability of getting heads is 1/2 because there's one side we want out of two sides total
The probability of getting less than 3 is 2/6 = 1/3 since we have two sides we want (rolling a "1" or a "2") out of six sides total.
Multiply the two mentioned fractions: 1/2 times 1/3 = 1/6
1/6 can be written as "one sixth", but I prefer the first format better since it's shorter.
---------------
If you are a visual learner, you can make a table with 2 rows and 6 columns, or vice versa (6 rows and 2 columns). The order doesn't matter.
The two rows represent the events Heads or Tails. The 6 columns show the different outcomes on the number cube. We have 6*2 = 12 different outcomes of rolling a die and flipping a coin.
Of those 12 outcomes, shade in 2 boxes to represent getting heads and either a "1" or "2". Refer to the diagram below.
We have 2 shaded rectangles out of 12 total to get 2/12 = 1/6
The visual representation of a table like this may help show why we multiplied the fractions 1/2 and 1/3 to get the answer. Hint: think of area = length*width.
The probability of getting heads on the coin and a number less than 3 on the number cube is 1/6, Option A is correct.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
A coin is flipped, and a number cube is rolled.
We need to find the probability of getting heads on the coin and a number less than 3 on the number cube.
The probability of getting heads when flipping a coin is 1/2
The probability of getting less than 3 is 2/6 = 1/3 since we have two sides
Now the probability of getting heads on the coin and a number less than 3 on the number cube
The product of 1/2 and 1/3
1/2×1/3
1/6
Hence, the probability of getting heads on the coin and a number less than 3 on the number cube is 1/6, Option A is correct.
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Solve for the following equation
9/4x + 1/3 = 5/2x
Answer:
3/4
Step-by-step explanation:
plug values in for x till you get it right
A poster is 15 inches wide by 24 inches tall. A smaller version of the same poster is created using a scale factor of 2/3. What is the area of the smaller poster
The area of the small poster is 160 inches square
How to determine the area
From the information given, we have the poster to take the form of a rectangle
The formula for area of a rectangle is;
Area = length × width
For the smaller poster created using a scale of factor 2/3
Length = 2/ 3 × 24
Length = 16 inches
Width = 2/ 3 × 15
Width = 10 inches
Substitute into the formula
Area = 16 × 10
Area = 160 inches square
Thus, the area of the small poster is 160 inches square
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Sarah is spending the day at a state fair. While at the fair, she can play games or ride rides. When Sarah arrives at the fair, she purchases 15 tickets and wants to use all of the tickets that she purchases. Playing a game at the fair requires three tickets, and riding a ride at the fair requires six tickets. To make her trip to the fair worthwhile, Sarah decides she must participate in seven activities at the fair.
Sarah requires the purchase of additional 12 tickets to ensure her participation in the seven activities at the fair.
How are the additional (missing) tickets determined?The additional tickets required by Sarah can be determined as follows:
Number of tickets purchased initially = 15
Number of tickets for playing a game = 3
Number of tickets for riding a ride = 6
Sarah can play five (5) games with 15 tickets (15/3).
Sarah can then purchase 12 additional tickets (6 x 2).
The later action enables Sarah to participate in 5 games and 2 rides, making it a total of 7 activities.
Thus, by purchasing additional 12 tickets, Sarah can participate in 5 games and 2 rides, making it a total of 7 activities.
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Question Completion:How many more tickets does Sarah require to ensure her participation in the seven activities at the fair?
Is
7 3
a proper, an improper, a mixed number, or a decimal fraction?
a proper fraction
an improper fraction
a mixed number
a decimal number
Answer: an improper fraction
Step-by-step explanation: An improper fraction is a fraction that is larger than 1 7/3 is larger than one because 7, the numerator is larger than the denominator so 7/3 is an improper fraction
Find the value of x.
Answer:
17
Step-by-step explanation:
i think its the right answer
On the grid draw y = 4x - 5 for values of c from -2 to 2
Step-by-step explanation:
shown above but I need words so
The ratio of Sadias age to her fathers age is 3:5. The sum of their ages is 96. What is Sadias age.
Answer:
36 years old
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
sum the parts of the ratio , 3 + 5 = 8
divide the sum of their ages by 8 to find the value of one part of the ratio
96 ÷ 8 = 12 ← value of 1 part of the ratio , then
3 parts = 3 × 12 = 36 ← Sadias age
Find the equation of the line parallel to y equals 1 half x plus 2 that passes through the point (4, 5) in slope-intercept form.
Answer: [tex]y=\frac{1}{2}x+3[/tex]
Step-by-step explanation:
We can solve this by using the point-slope form, which can help get the equation of a line given the slope of the line and a point on the line. Slope-intercept form is the form [tex]y=mx+b[/tex], and we can convert from point-slope form to this with simple algebra.
The point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope of the line, and [tex](x_1,y_1)[/tex] is the point.
We know that the line is parallel to [tex]y=\frac{1}{2}x+2[/tex], which means it will have the same slope. The slope of this line is [tex]\frac{1}{2}[/tex], so the slope of any line parallel to it will also be [tex]\frac{1}{2}[/tex].
[tex]y-5=\frac{1}{2}(x-4)\\y-5=\frac{1}{2}x-2\\y=\frac{1}{2}x+3[/tex]
What is the sum of ∞Σn=1 2(1/5)^n-1? s=1/5 s=2/5 s=5/3 s=5/2
The sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2
How to determine the sum of the notation?The sum notation is given as:
∞Σn=1 2(1/5)^n-1
The above notation is a geometric sequence with the following parameters
Initial value, a = 2Common ratio, r = 1/5The sum is then calculated as
S = a/(1 - r)
The equation becomes
S = 2/(1 - 1/5)
Evaluate the difference
S = 2/(4/5)
Express the equation as products
S = 2 * 5/4
Solve the expression
S= 5/2
Hence, the sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2
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Answer:
S = 5/2
Thank me later
Will give brainliest !!
Type the correct answer in the box.
Which trigonometric expression can be used to find value of x? Replace a and b with the correct values.
(trigonometry)
Answer:
x = 12cos(35)
Step-by-step explanation:
Well you have hyp and adj, meaning cosine. and u have the angle and need the adjacent, so side(cos(theta)).
12cos(35).
The human eye contains approximately 9.1 x 10^7 rod cells and 4.5 x 10^6 cone cells . Samuel subtracts 9.1-4.5 and says there are about 46,000,000 more rod cells than cone cells in the human eye . Use the drop - down menus to explain why Samuel is incorrect
Samuel is incorrect because he didn't subtract the power of the numbers.
How many more rod cells are there?The number of rod and cone cells in the human eye is written in scientific notation. Scientific notation is used in expressing large numbers in smaller numbers. To write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 1 x 10² is equivalent to 100
(9.1 x 10^7) - (4.5 x 10^6)
= (9.1 - 4.5) x 10^(7 - 6)
4.6 x 10 = 46
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Suppose the probability that the instructor asks Sam, one of your classmates, is 0.05 and the probability that she/he asks John, another student in your class, is 0.07. What is the probability that the instructor asks one of these two students
The probability that the instructor asks one of Sam and John whose probabilities of being asked are as indicated in the task content is; 0.12.
What is the probability that the instructor asks one of these two students?It follows from the task content that the probability that Sam is being asked is; 0.05 while that for John being asked is; 0.07.
Consequently, we may conclude that the probability of either of the two classmates being asked the question in discuss is; the sum of the probabilities and hence, we have;
P(Sam or John) = 0.05 + 0.07
= 0.12.
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Evaluate: 15 x 105 i need help
Answer:
1575
Step-by-step explanation:
105
× 15
525 ( First multiply 105 by 5 )
+1050 ( Then multiply 105 by 1. Remember to place a 0 below 5 )
( It is very important to write each and every number in a
straight line)
1575 ( Now add them )
∴ 105 × 15 = 1575
What is the equation of the circle that has its center at -26,120 and passed through the origin
well, first off let's check those two points, we know it's centerd at (-26 , 120) and we also know it passes through (0 , 0), so the distance between those two points is its radius
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{-26}~,~\stackrel{y_2}{120})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(~~-26 - 0~~)^2 + (~~120 - 0~~)^2} \implies r=\sqrt{(-26)^2 + (120 )^2} \\\\\\ r=\sqrt{( -26 )^2 + ( 120 )^2} \implies r=\sqrt{ 676 + 14400 } \implies r=\sqrt{ 15076 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-26}{h}~~,~~\underset{120}{k})}\qquad \stackrel{radius}{\underset{\sqrt{15076}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-26) ~~ )^2 ~~ + ~~ ( ~~ y-120 ~~ )^2~~ = ~~(\sqrt{15076})^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (x+26)^2+(y-120)^2 = 15076~\hfill[/tex]
Complete the equivalent fraction 3/5 = ?/10
Answer:
Step-by-step explanation:
3/5 = x/10
5x = 30
x = 6
6/10
Hey there!
Original equation:
3/5 = ?/10
Convert to:
3/5 = x/10
Cross multiply the numbers:
3 * 10 = 5 * x
Simplify it:
3 * 10 = 5 * x
30 = 5x
5x = 30
Divide 5 to both sides:
5x/5 = 30/5
Simplify it:
x = 30/5
x = 6
Therefore, your mystery number should be: 6
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
help please.
Malaysia police traffic department claims that 54% of fatal car accidents are caused by driver error. A researcher studies 30 randomly selected accidents and founds that 14 were caused by driver error. Using a = 0.05, is that Malaysia police traffic department's statement is true?
Answer:
The Malaysia police departments statement was true, because 14/30 is extremely close to 54% (roughly 15.5/30).
Type: Probability
Please rate this answer based on how helpful it was!Suppose that the sum of the three vectors u, v, and w shown in the figure is the zero vector. If w = 10 find u and v.
a. The value of v is 9.2
b. The value of u is 9.9
What are vectors?Vectors are physical quantities that have both magnitude and direction
How to find the value of vectors u and v?Since we have vectors
u at 70° to the x-axis v at 47° to the x-axis and w = 10 at 15° to the x-axis,We resolve them into component form
So, u = -(ucos70°)i - (usin70°)j
u = -(0.3420u)i - (0.9397u)j
v = -(vcos47°)i + (vsin47°)j
v = -(0.6820v)i - (0.7314v)j
w = (wcos15°)i + (wsin15°)j
w = (0.9659w)i + (0.2588w)j
w = (9.659)i + (2.588)j
Since the sum of the three vectors is zero, we have that
u + v + w = 0
u + v = -w
So,
-(0.3420u)i - (0.9397u)j + [-(0.6820v)i - (0.7314v)j] = -[(9.659)i + (2.588)j]
-(0.3420u)i - (0.9397u)j -(0.6820v)i - (0.7314v)j = -(9.659)i - (2.588)j]
-(0.3420u)i -(0.6820v)i - (0.9397u)j - (0.7314v)j = -(9.659)i - (2.588)j]
-[0.3420u + 0.6820v]i - [0.9397u + 0.7314v]j = -(9.659)i - (2.588)j
Equating i components, we have
-[0.3420u + 0.6820v]i = -9.659i
0.3420u + 0.6820v = 9.659
Dividing through by 0.3420. we have
u + 1.994v = 28.242 (1) and
Also, equating j components, we have
- [0.9397u + 0.7314v]j = -2.588j
0.9397u + 0.7314v = 2.588
Dividing through by 0.9397 we have
u + 0.778v = 2.754 (2)
a. The value of v
Subracring equation (2) from(1),we have
u + 1.994v = 28.242 (1)
-
u + 0.778v = 2.754 (2)
2.772v = 25.488
v = 25.488/2.772
v = 9.19
v ≅ 9.2
The value of v is 9.2
b. The value of uSubstituting v into (1), we have
u + 1.994v = 28.242 (1)
u + 1.994(9.19) = 28.242
u + 18.325 = 28.242
u = 28.242 - 18.325
u = 9.917
u ≅ 9.9
The value of u is 9.2
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Use the number line to find each measure
1. 2. 3. 4. 5. 6.
Essentially just count the tick marks between the two letters.
JL= 5
JK= 3
KP= 9
NP= 2
JP= 12
LN= 5
The asked lengths are from the number line:
JK = 3, JL = 5, KP = 9, NP = 2, JP = 12 and LN = 5.
Given that is a number line we need to find the asked values,
1. JK =
K = -4 and J = -7
So, JK = -4-(-7)
JK = -4+7
JK = 3
2. JL =
J = -7 and L = -2
So, JL = -2-(-7)
JL = -2+7
JL = 5
3. KP =
K = -4 and P = 5
So, KP = 5-(-4)
KP = 9
4. NP =
N = 3 and P = 5
So, NP = 5-3
NP = 2
5. JP =
J = -7 and P = 5
So, JP = 5-(-7)
JP = 12
6. LN =
L = -2 and N = 3
So, LN = 3-(-2)
LN = 5
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5
1
The measure of Z1 =
O 55
O62.5
110
5
Answer: 55
Step-by-step explanation:
Congruent angles intercept congruent chords, so since the circumference of a circle is 360 degrees, the arc angle 1 is inscribed in measures 110 degrees.
So, by the inscribed angle theorem, angle 1 measures 55 degrees.
Congruent angles intercept congruent chords, so since the circumference of a circle exists 360 degrees, arc angle 1 exists inscribed in measures 110 degrees.
So, by the inscribed angle theorem, angle 1 measures 55 degrees.
What are congruent angles?Congruent angles exist as two or more angles that exist identical to each other. Therefore, the measure of these angles exists equivalent to each other. The kind of angles does not create any distinction in the congruence of angles, which implies they can be acute, obtuse, exterior, or interior angles.
The Inscribed Angle Theorem states that the measure of an inscribed angle exists half the measure of its intercepted arc. Inscribed angles that intercept the exact arc exist congruent. This exists named the Congruent Inscribed Angles Theorem and exists shown below.
∠ A D B and ∠ A C B intercept, so m ∠ A D B = m ∠ A C B.
Congruent angles intercept congruent chords, so since the circumference of a circle exists 360 degrees, arc angle 1 exists inscribed in measures 110 degrees.
So, by the inscribed angle theorem, angle 1 measures 55 degrees.
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Val’s whole-house central air conditioner uses 2,500 watts when running. Val runs the AC 7 hours per summer day. Electricity costs (18 cents)/(1 kilowatt-hour). How much does Val’s AC costs to run for a summer month of 30 days?
The total cost to run Val’s AC costs for a summer month of 30 days is $94.5.
Cost of electricityQuantity of electricity used in kilowatts
1000 watts = 1 kilowatts
2,500 watts = 2.5 kilowatts
Number of hours Val runs AC per day = 7 hoursNumber of days = 30 daysCost of electricity = $0.18 kilowatts per hourCost of Val’s AC to run for a summer month of 30 days = Quantity of electricity used × Number of hours Val runs AC per day × Number of days × Cost of electricity
= 2.5 × 7 × 30 × 0.18
= $94.5
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There is a set of 12 cards numbered 1 to 12. A card is chosen at random. Event A is choosing a number less
than 6. Event B is choosing a number divisible by 3. A diagram is given below.
(Can you help with #4 if you know it:)
The number of permutations of picking 4 pens from the box is 30.
There are six different unique colored pens in a box.
We have to select four pens from the different unique colored pens.
We have to find in how many different orders the four pens can be selected.
What is a permutation?A permutation is the number of different arrangements of a set of items in a particular definite order.
The formula used for permutation of n items for r selection is:
[tex]^nP_r = \frac{n!}{r!}[/tex]
Where n! = n(n-1)(n-2)(n-3)..........1 and r! = r(r-1)(r-2)(r-3)........1
We have,
Number of colored pens = 6
n = 6.
Number of pens to be selected = 4
r = 4
Applying the permutation formula.
We get,
= [tex]^6P_4[/tex]
= 6! / 4!
=(6x5x4x3x2x1 ) / ( 4x3x2x1)
= 6x5
=30
Thus the number of permutations of picking 4 pens from a total of 6 unique colored pens in the box is 30.
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