The three consecutive odd integers are 47, 49, and 51. The third number is 51, so the answer is (d) 51.
Let's represent the first odd integer as x. Then, the next two consecutive odd integers would be x + 2 and x + 4.
According to the problem, the sum of these three consecutive odd integers is 147:
x + (x + 2) + (x + 4) = 147
We simplify and solve for x, which gives us the value of the first integer.
Simplifying and solving for x, we get:
3x + 6 = 147
3x = 141
x = 47
So the three consecutive odd integers are 47, 49, and 51. The third number is 51, so the answer is (d) 51.
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What is the light collecting area (aperture), in [m2], of a telescope with the primary mirror diameter: 50 [cm]?
The area of the aperture storing light is 0.196 [tex]m^{2}[/tex].
What are shapes?Mathematical figures which have a set of pre defined properties are known as shapes. For example, Square shape is a mathematical figure who has four sides and all of them are equal in length and all the four corner of square have an angle of 90 degree. Similarly if there a figure who has been formed by the help of four lines of equal length but the corners are not 90 degrees then it will be Rhombus and not Square.
Now for the given question:
Diameter of the mirror=50 cm
we convert dia. unit in meter as area is asked in meter.
Dia.= [tex]\frac{50}{100}[/tex]
= [tex]\frac{1}{2}[/tex]
Area of a circle=π× [tex](\frac{dia}{2} )^{2}[/tex]
=π×[tex](\frac{1}{4} )^{2}[/tex]
Area= π/16
π=3.14
Area=[tex]\frac{3.14}{16}[/tex]
= 0.196 [tex]m^{2}[/tex]
Hence area of the aperture is 0.196 [tex]m^{2}[/tex].
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how to find the average value of a function on an interval?
To find the average value of a function on an interval dividing the definite integral [tex]\int\limits^a_b f{(x)} \, dx[/tex] by the length of the interval.
The definition of average value of a function is -"The average value of a function is the height of the rectangle that has an area that is equivalent to the area under the curve of the function."
When there's a need to find the average value of a function, rather than adding up numbers we can just integrate, and instead of dividing by the number of values we can just divide by the length of the interval.
Adding values → Integration
Number of values → Length of the interval
When we use the length of the interval it makes more sense as we all know intervals have an infinite number of values, so it is more appropriate to use the length of the interval instead.
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I need help
I'm confused
According to the information, the number sequences would go as follows: arithmetic: 1, 9, 17, 25, 33...; 83, 84, 85, 86, 87... Geometric: 6, 24, 96, 384, 1536...; 1, 6, 36, 216, 1296...; 7, 14, 28, 56, 112...; neither: 4, 9, 16, 25, 36...; 1, 1, 2, 3, 5, 8, 13,...
How to identify the sequences that belong to each category?To identify the sequences that belong to each category, we must take into account the difference between a geometric sequence and an arithmetic sequence. In the case of geometric sequences, they are those sequences made up of numbers that are the result of multiplying the first number by a common factor.
On the other hand, arithmetic sequences are those that are made up of numbers that differ from the previous and the following number by a fixed amount. According to the above, the values would be classified as follows:
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Julissa wants to join her local gym. A gym membership is $27 a month with a one–time initiation fee of $117. Which equation represents the amount of money, y, she will spend on her gym membership for x months?
y=117x+27
y=27x+117
x=117y+27
x=27y+117
The equation to represent the amount of money, y, Julissa will spend on her gym membership for x months is y=117x+27, which means that for each month Julissa has a membership, she will pay $117 for the initiation fee plus $27 for the monthly fee.
If Julissa has a gym membership for 3 months:
y = 117x + 27
y = 117(3) + 27
y = 360 + 27
y = 387
The equation y=117x+27 is used to represent the amount of money, y, that Julissa will spend on her gym membership for x months. This equation states that for each month of membership, Julissa will pay $117 for the initiation fee plus $27 for the monthly fee. This can be calculated for any number of months by substituting the value of x into the equation. For example, if Julissa has a gym membership for 3 months, y = 117x + 27 can be rearranged as y = 117(3) + 27, which equals y = 360 + 27. This is a total of 387 dollars, which is the amount Julissa will spend for 3 months of gym membership.
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Plot the z intercepts y-intercept, vertex and axis of symmetry of the function h(x)=(x+1)^2-4
The axis of symmetry of the function is x=-1.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is h(x)=(x+1)²-4.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (-1,-4)
Focus: (-1,-15/4)
Axis of Symmetry: x=-1
Directrix: y= -17/4
Plot the points (-3, 0), (-2, -3), (-1, -4), (0, -3) and (1, 0)
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (1,0),(-3,0)
y-intercept(s): (0,-3)
Therefore, the axis of symmetry of the function is x=-1.
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Pls show your work thank you will mark the Brainliest
Answer:
12.3
Step-by-step explanation:
take x=0 because intercept means cutting the y axis when x=o
Answer:
Step-by-step explanation:
7
. a school has 100 business majors, 60 math majors, and 40 psych majors. every student at the school belongs to one and only one of these majors. three different students are chosen to be interviewed for a focus group. how many ways are there to choose this focus group where all three students do not all come from the same major?
Number of ways are there to choose this focus group where all three students do not all come from the same major is 240,000
It is given that a school have three majors i.ie, business, math and psych
Number of students in business majors is 100
Number of students in math majors is 60
Number of students in psych majors is 40
Total number of students (100+60+40) = 200 students
Three different students are chosen to be interviewed for a focus group.
Therefore, number of student in focus group = 3
Now, number of ways are there to choose this focus group where all three students do not all come from the same major
= [tex]^{100}C_{1} \times ^{60}C_{1}\times^{40}C_{1}[/tex]
= 100×60×40
= 240,000 ways
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QUESTION FOR FOR LIH04
Joe and Martha shared 56 books joe had 2 more books than Martha how many did Martha have
Answer:
26
Step-by-step explanation:
56/2 -2
Solve the right triangle table
The measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
We shall first evaluate for the angle m∠B as follows:
m∠A + m∠B + m∠C = 180° {sum of interior angles of a triangle}
49° + B + 90° = 180°
B + 139° = 180°
B = 180° - 139° {subtract 139° from both sides}
m∠B = 41°
12.7/sin90° = a/sin41
a = (12.7 × sin49)/sin90° {cross multiplication}
a = 9.5848
12.7/sin90° = b/sin49
b = (12.7 × sin49)/sin90 {cross multiplication}
b = 8.3319
Therefore, the measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.
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the density of zinc is 7.13 g/cm3. calculate the probability that a density measurement of the post-1982 pennies made using the caliper method is within 5% of the density of zinc. use the caliper data for the entire lab session to perform your calculation, and assume that the data fits a normal distribution.
As per the density the probability that a density measurement of the post-1982 pennies is 0.3565 g/cm3.
Density is an important physical property that can help identify materials. In this case, we are interested in the density of zinc and how it relates to the post-1982 pennies.
To calculate the probability of a density measurement within 5% of the density of zinc, we need to first determine the range of densities that fall within 5% of the zinc density.
The 5% range of the zinc density is calculated by multiplying the zinc density (7.13 g/cm3) by 5% (0.05), which gives us 0.3565 g/cm3.
The upper and lower limits of this range are then calculated by adding and subtracting this value from the zinc density, respectively.
The upper limit is 7.4865 g/cm3 (7.13 + 0.3565),
while the lower limit is 6.7735 g/cm3 (7.13 - 0.3565).
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If Jimmy drove 300 miles at a rate of 50 miles per hour, find the number of hours Jimmy traveled.
Answer:
He drove 6 hours.
Step-by-step explanation:
distance = rate times time
300 = 50t Divide both sides by 50
t = 6
Help with geometry pls?
The following are the area of the sectors:
6a). π square inches
6b). 24π square centimeters
7a). 9 square centimeters
7b). 16.7 square inches
How to evaluate for the area of the sectors.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
For question 6:
a). (40/360) × π × 3 in × 3 in = π in²
b). (135/360) × π × 8 cm × 8 cm = 24π cm²
For question 7:
a). (90/360) × π × 6 cm × 6 cm = 9 cm²
b). (60/360) × π × 10 in × 10 in = 16.7π in²
Therefore, the following are the area of the sectors:
6a). π square inches
6b). 24π square centimeters
7a). 9 square centimeters
7b). 16.7 square inches
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A cable company charges an installation fee to install cable at a residence. There is also a monthly fee for the cable service. The total cost for months 2, 4, 6 and 8 are $145, $255, $365, and $475, respectively. How much is the installation fee? Assume that the relationship between the two quantities is linear
$13,000 and $15,000.
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I need help, Find the volume of this object. Use 3 for Pi.
The volume of the given 3 - D figure is 156.36 cubic inches.
What is volume?A volume is a collection of a three dimensional coordinate points enclosed by a two dimensional coordinate points.
Given is the 3 - D figure as shown in the image.
We can write the volume as -
V = πr²h/3 + lbh
V = (3.14 x 3 x 3 x 8)/3 + (9 x 9 x 1)
V = 156.36 cubic inches
Therefore, the volume of the given 3 - D figure is 156.36 cubic inches.
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HELP ME PLEASEEEE
Round each fraction to help you estimate the solution for the following equation
nine-tenths minus four-tenths equals.
Options
1. 0
2. 1/2
3. 1
4. 1 1/2
In 2004, $6,000 was invested in a mutual fund that earned 9% interest per year.
a) Tell whether the model represents an exponential growth or decay and create a function that models it
b) How much was in the account in 2012?
a) The function would be A(t) = 6000(1 + 0.09)ᵗ
b) The amount in the account in 2012 was approximately $11,737.51.
What is the function model?
In mathematics, a function model is a mathematical equation or expression that represents a relationship between two or more variables. It is a way of describing the behavior or pattern of a particular phenomenon or system.
a) The model represents exponential growth since the amount in the account is increasing with time. The function that models the growth of the investment over time is given by:
A(t) = 6000(1 + 0.09)ᵗ
where A(t) is the amount in the account after t years.
b) To find the amount in the account in 2012, we need to find the value of A(2012 - 2004) = A(8). Substituting t = 8 into the function above, we get:
A(8) = 6000(1 + 0.09)⁸
= 6000(1.09)⁸
≈ $11,737.51
Therefore, the amount in the account in 2012 was approximately $11,737.51.
Hence,
a) The function would be A(t) = 6000(1 + 0.09)ᵗ
b) The amount in the account in 2012 was approximately $11,737.51.
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Aldo debe escoger una camisa y un par de pantalones para su atuendo de hoy. Puede escoger entre 2 camisas y 3 pares
de pantalones. ¿Cuántos diferentes atuendos puede crear?
The number of different outfits that Aldo can create from the shirts and the pairs of pants are 6 outfits.
How to find the number of outfits ?In this case, Aldo has 2 options for his shirt and 3 options for his pants. To find the total number of outfits, we can multiply these numbers together:
= Number of shirts x Number of pairs of pants
= 2 x 3
= 6 outfits
Therefore, Aldo can create 6 different outfits by choosing a shirt and a pair of pants from the available options.
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Factor 80+60. Write your answer in the form a(b+c) where a is the GCF of 80 and 60.
Answer:
20(4+3)
Step-by-step explanation:
GCF of 80 and 60 = 20
20*4=80
20*3=60
20(4+3)
hope this helps! :)
write the fraction in simplest form.
25/50
Answer:
25/50
will equal to 1/2
2) Jane wants to buy some compost. Both Suttons Shop and Greens Garden Shop sell compost. Suttons Shop Bags of compost 20 litres £2.25 each bag £3.25 for 2 bags Jane needs 140 litres of compost. She wants to buy all the compost from the same shop. She wants to buy the compost as cheaply as possible. Which shop should Jane buy the compost from? You must show all your working. Greens Garden Shop Bags of compost 70 litres £4.99 each bag
The cheapest option for Jane is to buy from Suttons Shop, as the total cost is £12, whereas, at Greens Garden Shop, the total cost is £9.98.
To determine the cheapest option, we need to calculate the cost of purchasing 140 liters of compost from each shop.
First, we'll calculate the cost at Suttons Shop:
Jane needs 140 liters of compost, so she needs 140 / 20 = 7 bags of compost.
If she buys 1 bag of compost, it will cost her £2.25.
If she buys 2 bags of compost, it will cost her £3.25.
Since she needs 7 bags of compost, she can buy 3 sets of 2 bags (6 bags) and 1 bag.
So the cost of 6 bags will be 3.25 x 3 = £9.75, and the cost of 1 bag will be 2.25.
The total cost of 7 bags at Suttons Shop will be 9.75 + 2.25 = £12.
Next, we'll calculate the cost at Greens Garden Shop:
Jane needs 140 liters of compost, so she needs 140 / 70 = 2 bags of compost.
Each bag at Greens Garden Shop costs £4.99.
So the total cost of 2 bags at Greens Garden Shop will be 4.99 x 2 = £9.98.
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when running Chao has a stride length of 70cm,correct to the nearet 5cm.
Chao runs a distance of 11.2 km, correct to the nearest 0.1km
work out the minumum number of stride that Chao could take to complete this distance
The minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
To calculate the minimum number of strides that Chao could take to complete a distance of 11.2 km, we need to first convert the distance to meters since the stride length is given in centimeters.
11.2 km = 11,200 meters (1 km = 1000 meters)
Stride length in meters = 70 cm / 100 cm/m = 0.7 m
Now, we can calculate the minimum number of strides as follows,
Minimum number of strides = (Distance covered in meters) / (Stride length in meters)
Minimum number of strides = 11,200 m / 0.7 m ≈ 16,000
Therefore, the minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.
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Can anybody answer the question I attached?
Answer:
36 bottles
Step-by-step explanation:
You want to know the number of bottles that must be painted and sold in order to make a profit of $120, given that 3 bottles can be purchased for $11, and each bottle can be sold for $7.
ProfitThe profit on each bottle is the difference between its cost and what it is sold for. The cost of 1 bottle is 1/3 of the cost of 3 bottles.
profit = selling price - purchase price
profit = $7/bottle - ($11/(3 bottles)) = $(21/3 -11/3)/bottle = $(10/3)/bottle
BottlesTo make a profit of $120, you need n bottles such that ...
(10/3)n = 120
n = 36 . . . . . . . . . multiply by 3/10
The club needs to buy, paint, and sell 36 bottles to raise $120.
PLEASE HELP!
Mrs. Harris is in the 20% income tax bracket. Last year, her taxable income was $75,400. How much did she need to pay in taxes?
A. $1,508
B. $15,080
C. $60,320
D. $73,892
Answer: B: 15,080
Step-by-step explanation:
Alright, let's convert 20% into a decimal: 0.20
Then multiply 0.20 x 75,400 which gets you to 15080
So she needed to pay $15,080 in taxes
Fill in the missing term and select the
missing description. Simplify any fractions.
6(a + 2)
a + 2 =3
a =
Subtract 2 from both side
The value of a in the equation a + 2 = 3 is 1.
How to calculate the valueAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
a + 2 = 3
Subtract 2 from both sides
a + 2 - 2 = 3 - 2
a = 1
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data with 860 observations are drawn from a bell-shaped distribution with a mean of 76 and a standard deviation of 18. approximately how many observations are more than 112? (round your answer to the nearest whole number.)
In the given case where 860 observations are drawn from a bell-shaped distribution, there are 2 observations of more than 112.
Total number of observations = 860
Mean of the observations = 76
Standard deviation = 18
The amount of standard deviations by which the value of a raw score differs from or differs above the mean value of what is observed or measured is known as the z score or standard score in the z test. The z-score calculates how far an X-score deviates from the mean by standard deviations. Calculating the observations utilizing the Z- score -
Z = X - u/a
Calculating the observations -
Where X = 112 u = 76 and a = 18
Z = 112 - 76/18
= 36/18
= 2
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The second smallest number that has 1,2,3,4 and 5 in them
12354 is the second smallest number that contains the digits 1, 2, 3, 4 and 5 in that order. It can be used in a variety of ways, such as counting, addition, subtraction, multiplication and division, as well as to represent dates and times.
The second smallest number that has 1,2,3,4 and 5 in them is 12354. This number is made up of the digits 1, 2, 3, 4, and 5 in that order. It is the second smallest number because the smallest number that contains these digits is 12345.
To form this number, we start by arranging the digits in descending order, from the largest to the smallest, 5, 4, 3, 2 and 1. We then combine the digits together to form 12354.
12354 is the second smallest number because it contains all the digits 1, 2, 3, 4 and 5 in that order. This number can be used in different ways, such as counting, addition, subtraction, multiplication and division. For example, 12354 divided by 4 equals 3088.75.
The number 12354 can also be used in other ways, such as to represent a date or time. For example, the number 12354 can represent the date 12/3/54, which is December 3, 1954.
In conclusion, 12354 is the second smallest number that contains the digits 1, 2, 3, 4 and 5 in that order. It can be used in a variety of ways, such as counting, addition, subtraction, multiplication and division, as well as to represent dates and times.
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for each pair of number, determine by what percent the second number is greater than the first. also determined by what percent the first number is less than the second 5 and 10
To get by what percent the second number (10) is greater than the first number (5), we can use the following formula:
percent increase = ((new value - old value) / old value) x 100%
So, for the pair of numbers 5 and 10:
percent increase = ((10 - 5) / 5) x 100% = 100%
This means that 10 is 100% greater than 5.
To determine by what percent the first number (5) is less than the second number (10), we can use the following formula:
percent decrease = ((old value - new value) / old value) x 100%
So, for the pair of numbers 5 and 10:
percent decrease = ((10 - 5) / 10) x 100% = 50%
This means that 5 is 50% less than 10.
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4 less than the product of 7 and a number.
Answer:
7n - 4
Step-by-step explanation:
question 13
help me asap
Answer:
AC = 16 cm
Step-by-step explanation:
given a tangent and a secant from an external point to the circle, then
the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant, that is
AB × AC = AD²
4x = 8² = 64 ( divide both sides by 4 )
x = AC = 16 cm
Answer:
16 cm
Step-by-step explanation:
tan/sec Theorem
a² = b(b+c)
8² = 4(4+c)
64 = 16 + 4c
48 = 4c
12 = c
12 + 4 = 16 cm
