The answer is A) 10,000,000 seven-digit numbers; B) The number is 20,000 ; C) 5,314,410 identification numbers are possible if no two adjacent digits are the same.
Seven-digit identification number:
A.) The number of possible identifying numbers
Possible digits are 0 up to 9.
Total number of digits: 10
Any of the 10 digits may be used for each;
Hence,
10×10×10×10×10×10×10 equals 10,000,000 potential outcomes.
B.) For it to start begin with either 023 and 003.
- the first digit must be 0 (1 possible value)
- 2nd digit must be 2 or 0 (2 possible values)
- 3rd digit must be 3 (1 possible value)
- 4th and 5th can be filled with any digit (10 × 10 possible values)
Which gives
1×2×1×10×10×10×10 = 20,000
3.) no two adjacent digits are the same that is no two digits that follows each other are the same.
In this case only one digit have 10 possible values.
The other four digits have 9 possible values each.
Which gives:
10×9×9×9×9×9×9 = 10× [tex]9^{6}[/tex] = 5,314,410
The full question:
A certain identification number is a sequence of seven digits. (a) How many identification numbers are possible? (b) How many of them begin with either 023 or 003? (c) How many identification numbers are possible if no two adjacent digits are the same? (For example, 123-4-567 is permitted, but not 123-3-456.).
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A random sample of teenagers were surveyed about
their favorite sport. The bar graph below displays their
responses.
Frequency
(0
Basketball
Favorite Sports
Football
Lacrosse
Soccer
Favorite Sport
Volleyball
Which of the following statements is correct?
O The bar for lacrosse is one-third the height of the
bar for football.
O More teenagers in the sample chose lacrosse over
volleyball as their favorite sport.
OTwice as many teenagers in the sample chose
soccer over basketball as their favorite sport.
Twice as many teenagers in the sample chose
football over basketball as their favorite sport.
Answer:
it is C i just got a 100 on the unit test review
Step-by-step explanation:
cylinder is cut in thirds, find surface area of the small cylinders. Radius is 0.25, height is 1.2, surface area is 2.28 and volume is 0.2356
The surface area of each small cylinder is 2.28 square units
How to find the surface area of the cylinderThe surface area of each small cylinder is:
Surface area = 2πr(h + r)
Where
r is the radius (0.25) and
h is the height (1.2).
Plugging in the values, we get:
Surface area = 2 * π * 0.25 * (1.2 + 0.25)
Surface area = 2 * π * 0.25 * 1.45
Surface area = 2.28
Each small cylinder has a surface area of 2.28 square units.
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Round 2 , 236.8 to the nearest ten
suppose a random sample of size 5 from a uniform(0, theta) distribution yielded the measurements 1.52, 7.81, 1.28, 6.90, 1.17. what is the method of moments estimate of theta?
The exact values of trigonometric functions cosine and tangent are 4 / 5 and 3 / 4, respectively.
How to determine the exact value of a trigonometric function
In this question we must determine the exact value of two trigonometric functions on the basis a given value of another trigonometric function, whose quadrant is also known. According to the statement, sine is in the first quadrant, then both cosine and tangent are also positive. The value of cosine can be found by means of following trigonometric formula:
cos θ = √(1 - sin² θ)
cos θ = √[1 - (3 / 5)²]
cos θ = 4 / 5
And the exact value of tangent can be found by this formula:
tan θ = sin θ / cos θ
tan θ = (3 / 5) / (4 / 5)
tan θ = 3 / 4
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HELP !!!!!!! Select all the solutions to the inequality 3(2x-1)>5(x+1)
A.-2
B.0
C.2
D.8
E.11
F.15
Answer:
E. and F. (11 and 15). D. is not correct since the equation says > 8, not >= to 8.
Step-by-step explanation:
3(2x-1)>5(x+1)
6x-3>5x+5
x>8
A bakery is selling breakfast platters. a platter of 12 bagels costs $10.20. additionally, it costs $4.65 for a gallon of coffee. what is the slope of this situation? a. 10.20 b. 4.65 c. 0.85 d. 0.12
The slope of the situation is 10.20. Answer (a) is correct.
How to determine the slope?The cost of the breakfast platter of 12 bagels is $10.20 and the cost of a gallon of coffee is $4.65.
The slope represents the rate of change between two variables, typically represented as y and x. In this case, it's not clear which variables we should use to calculate the slope. If we use the number of bagels as x and the cost as y, then the slope would represent the rate of change in cost per bagel.
Alternatively, if we use the gallons of coffee as x and the total cost as y, then we can calculate the slope. The total cost would be the sum of the cost of bagels and the cost of coffee, which is $10.20 + $4.65 = $14.85.
Using the formula for slope, which is (change in y) / (change in x), we can calculate the slope as follows:
slope = (change in cost) / (change in gallons of coffee)
= ($14.85 - $4.65) / (1 - 0)
= $10.20 / 1
= 10.20
Therefore, the slope of the situation is 10.20. Answer (a) is correct.
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PLEEEEASSE HELP
Consider the function, where C is the total cost, in dollars, for a sports uniform company to manufacture two different uniform pieces, x and y.
C=3x+2y
The given inequalities represent the constraints for a customer’s order.
x+y≥10
x−y≤10
x−y≥0
x≤20
What is the minimum total cost, C, for the company if all of the order constraints are fulfilled?
The minimum total cost for the company if all of the order constraints are fulfilled is given as follows:
$25.
How to obtain the minimum total cost?The cost function is given as follows:
C = 3x + 2y.
Meaning that:
Each item x costs $3.Each item y costs $2.The relevant restrictions to minimize the costs are given as follows:
x+y≥10: at least 10 items.x−y≥0: x equals or greater than y.Since an item y costs less than an item x, considering the second bullet point above, the cost is minimized with an equal amount of x and y.
From the first restriction, they must have at least 10 amounts, hence the cost is minimized with:
x = 5 and y = 5.
And the cost is of:
C = 3 x 5 + 2 x 5
C = $25.
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k/2.9+ 80.2=23.1 what is k?
Answer: -165.59
Step-by-step explanation: Search math w ay on the internet :)
you want to make a graph to display the distribution of the salaries of the 1,700 professors at a large university. the best choice is a
Histogram. is a best choice to display the data.
A histogram is a type of graph that is used to represent the distribution of continuous or discrete data by dividing the data into intervals (bins) and counting the number of data points in each bin.
In a histogram, the bins are represented by bars, and the height of each bar represents the frequency or density of the data within the corresponding interval.
In the case of the salaries of professors, a histogram would be a good choice for displaying the distribution of the salaries because it provides a visual representation of the frequency of different salary ranges and helps to identify any patterns or anomalies in the data.
By dividing the salaries into appropriate intervals, the histogram allows you to see how many professors have salaries within a particular range, and to compare the frequency of different salary ranges.
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HELP ASAP! A biologist measured the length and weight of several bluegills, which is a species of fish. Use linear regression to estimate the weight of a bluegill that has a length of 9.5 inches. Round your answer to the nearest tenth of an ounce.
Answer:
The weight is 95.53 ounces of bluegill which has a length of 9.5 inches using linear regression.
Step-by-step explanation:
good luck to you
you have two six-sided dice that you roll at the same time. how would you calculate the probability of rolling a 1 with the first die and a 5 with the second die?
The probability of rolling a 1 with the first die and a 5 with the second die is P(A ∩ B) = (1/6) x (1/6) = 1/36.
The probability of rolling a 1 with the first die and a 5 with the second die can be calculated using the joint probability formula. The joint probability formula is P(A ∩ B) = P(A) x P(B|A). In this case, A is rolling a 1 with the first die and B is rolling a 5 with the second die. P(A) is the probability of rolling a 1 with the first die, which is 1/6. P(B|A) is the probability of rolling a 5 with the second die given that a 1 was rolled with the first die, which is also 1/6. Therefore, the probability of rolling a 1 with the first die and a 5 with the second die is P(A ∩ B) = (1/6) x (1/6) = 1/36.
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Write 5 2/11 as a decimal rounded to the nearest tenth.
Answer:
5.18181818182
5.2 (nearest 10th)
Step-by-step explanation:
PROBLEM #2
Three stores are having a sale on apples. Which store has the
BETTER deal?
FRUIT MARKET 5 apples for 2.25 FRUITZ: 8 apples for 4.20
VITAMIN C:$6.62 from 12 apples
0.45 is the smallest cost per apple, the best deal can be found at Fruit Market.
What do you mean by cost?Cost refers to the amount of money, time, or resources that are required to obtain, produce, or achieve something. It can refer to the expense involved in purchasing a product or service, or the investment required to start a new business, undertake a project, or undertake some other endeavor. In general, cost can be thought of as the sacrifice made in order to gain something of value.
To compare the deals, we need to find the cost per apple for each store.
For Fruit Market: 5 apples cost 2.25, so the cost per apple is 2.25 / 5 = 0.45.
For Fruitz: 8 apples cost 4.20, so the cost per apple is 4.20 / 8 = 0.525.
For Vitamin C: 12 apples cost 6.62, so the cost per apple is 6.62 / 12 = 0.55.
Since 0.45 is the smallest cost per apple, the best deal can be found at Fruit Market.
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J.D. Power and Associates surveys new automobile owners to learn about the quality of recently purchased vehicles. The following questions were asked in the J.D. Power Initial Quality Survey, May 2012.
a. Did you purchase or lease the vehicle?
b. What price did you pay?
c. What is the overall attractiveness of your vehicle’s exterior? (Unacceptable, Average, Outstanding, or Truly Exceptional)
d. What is your average miles-per-gallon?
e. What is your overall rating of your new vehicle? (1- to 10-point scale with 1 unacceptable and 10 truly exceptional)
A plurality of magnitude can represent the property of number or amount, which exhibits both discontinuity and continuity and in the given situation, we would pay a quantitative amount to the seller.
What is Quantitative?A property called quantity or amount can take the form of a plurality of magnitude, which shows both discontinuity and continuity.
Comparing quantities can be done by using phrases like "greater," "less," or "equal," as well as by assigning a numerical value that is a multiple of the unit of measurement.
Among the well-known examples of quantitative qualities are mass, time, distance, heat, and angle.
Along with quality, substance, change, and relationship, quantity is one of the fundamental categories of things.
Some quantities serve as states (properties, dimensions, qualities) of things like heavy and light, long and short, broad and narrow, little and large, or much and little, while others are such by their very nature (as numbers).
Therefore, in the given situation, we would pay a quantitative amount to the seller.
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Correct question:
J.D. Power and Associates surveys new automobile owners to learn about the quality of recently purchased vehicles. The following questions were asked in the J.D. Power Initial Quality Survey, May 2012.
What Price did you pay?
Can someone tell me how to do this step by step please
Step-by-step explanation:
Pythagoras
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Plugging in numbers
[tex] {4}^{2} + {8}^{2} = {c}^{2} [/tex]
If we do the math given
[tex]16 + 64 = {c}^{2} - - - 80 = {c}^{2} [/tex]
Last but not least, we root both sides
[tex] \sqrt{80} = c[/tex]
Which means C = 8.9
Decide if each statement about the expressions is true or false for each statement.
a. 6(-b+8) and 2(-3b + 4) are equivalent
expressions.
b. -8h-3.5 and -0.5(16h - 7) are equivalent
expressions.
c. -9(k-5+ 2k - 8) and -27k + 117 are
equivalent expressions.
d. (36m +12) and 12m + 4 are equivalent
expressions.
True False
O
Il cholves bold hitems
a. False . 6(-b+8) and 2(-3b + 4) are non equivalent expressions.
b. False . -8h-3.5 and -0.5(16h - 7) are non equivalent expressions.
c. True . -9(k-5+ 2k - 8) and -27k + 117 are equivalent expressions.
d. False .(36m +12) and 12m + 4 are equivalent non expressions.
What are equivalent expressions ?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
What are non equivalent expressions ?
If "x" is the same for both equations, then they are equivalent. If "x" is different (i.e., the equations have different roots), then the equations are not equivalent.
Hence ,
a. False . 6(-b+8) and 2(-3b + 4) are not equivalent expressions.
b. False . -8h-3.5 and -0.5(16h - 7) are not equivalent expressions.
c. True . -9(k-5+ 2k - 8) and -27k + 117 are equivalent expressions.
d. False .(36m +12) and 12m + 4 are equivalent not expressions.
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help, does anyone know the answer to this?
The figure with the least surface area is the cube.
How to find the surface area of a figure?The surface area of a 3 dimensional figure or solid figure is the sum of the area of the whole surface.
Therefore,
surface area of the cube = 6a²
where
a = side lengthsurface area of the cube = 6 × 6²
surface area of the cube = 6 × 36
surface area of the cube = 216 units²
surface area of the second rectangular prism = 2(lh + lw + hw)
where
l = lengthw = widthh = heightTherefore,
surface area of the second rectangular prism = 2(54 + 54 + 16)
surface area of the second rectangular prism = 2(124)
surface area of the second rectangular prism = 248 units²
Therefore,
surface area of the third rectangular prism = 2(13.5 + 216 + 16)
surface area of the third rectangular prism = 2(245.5)
surface area of the third rectangular prism = 491 units²
Therefore, the least surface area is the cube.
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OAB is a sector of a circle.
Calculate the radius of the circle to 2 d.p.
B.
131°
cm
192 cm
Not drawn accurately
The radius of the circle is 83.91 cm
How to determine the radius of the circleFrom the question, we have the following parameters that can be used in our computation:
Angle = 131 degrees
LEngth of arc = 192 cm
The length of arc is calcuulated as
Length = Angle/360 * 2pi r
Substitute the known values in the above equation, so, we have the following representation
131/360 * 2 * 22/7 * r = 192
So, we have
r = (192 * 7 * 360)/(131 * 2 * 22)
Evaluate
r = 83.91
Hence, the radius is 83.91 cm
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20 PNTS!! WILL MARK BRAINLIEST QUICK! fill this out
Answer:
2. 3 and 5
3. 3 and 4
4. 3 and 2
5. 3 and 6
Simplify the expression:
[tex]\frac{\frac{a+b}{2a^2} }{\frac{a-b}{4a} }[/tex]
The simplification of the given expression gives the value 2(a + b) / a(a - b).
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is,
[(a + b) / 2a²] ÷ [(a - b) / 4a]
The fractional term in the denominator of the main expression can be written as the multiplication of it's reciprocal.
[tex]\frac{a}{b}[/tex] ÷ [tex]\frac{c}{d}[/tex] = [tex]\frac{a}{b}[/tex] × [tex]\frac{d}{c}[/tex]
So the expression becomes,
[tex]\frac{a+b}{2a^2}[/tex] × [tex]\frac{4a}{a-b}[/tex]
= 2(a + b) / a(a - b)
Hence the simplified form of the given expression is 2(a + b) / a(a - b).
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A cylinder has a height of 19 feet and a radius of 12 feet. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
8595.4
Step-by-step explanation:
The formula for volume of cylinder is: V = [tex]\pi[/tex][tex]r^{2} h[/tex]
[tex]\pi[/tex] = 3.14
radius = 12
height = 19
plug in the numbers which would give us = 3.14(12)^2(19)
which gives us 8595.4
What is the definition of data
Answer:
A collection of facts, such as numbers, words, measurements, observations.
Step-by-step explanation:
Which number is one hundredth less than 7.3?
I’m not sure how to do it I’ve done a similar question but I don’t get this one
The standard deviation for the given data is 5
What is Standard Deviation ?
The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
Given that,
the data,
X Xₙ - X₀ (Xₙ - X₀)²
18 -7 49
21 -4 16
24 -1 1
24 -1 1
25 0 0
31 6 36
32 7 49
175 152
X₀ = 175/7 = 25
Variance = (Xₙ - X₀)²/(n-1)
= 152/(7-1)
= 25.33
Standard deviation = √Variance
= √25.33
= 5.03
Hence, the standard deviation is 5
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3(2x + 1) + 2(x + 4)
Answer: 8x + 11
Step-by-step explanation:
1. Distribute the 3 on both variables. SO 3 times 2x plus 3 times 1 is (6x+3).
2. Do the same for the 2. You get (2x +8)
3.(6x+3) + (2x+8).
4. Rid the parenthesis.
5. 6x + 3 +2x + 8.
6. Combine like terms.
7. 8x + 11 is your solution.
recall that in problem 3 of the reading questions for section 2.1, you found that if , then . use this to find a formula for the tangent line to at .
The tangent line is y=x-1 and differentiation of ln(x) is 1/x
What does differentiation in mathematics mean?
Differentiation is a technique for determining a function's derivative. In mathematics, the technique of differentiation is used to determine the instantaneous rate of change in a function dependent on one of its variables.
The most prevalent example is velocity, which is the rate at which a distance changes in relation to time.
The ratio of the vertical to the horizontal distance between any two points on it is called slope of ray or line or line segment in analytical geometry.
y-y1 = m(x-x1)
If the function passes through (1,0) and the slope equals to 1 is:
y-0 = 1(x-1)
y=x-1
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The complete question is -
Recall that in Problem 3 of the reading questions for Section 2.1, you found that if f(x) = ln(x), then f'(2) = 1/2. Use this to find a formula for the tangent line to f(x) = ln(x) at x = 2.
the time in hours taken to travel from city a to city b is what type of variable? multiple choice distraction discrete numerical categorical continuous numerical
The time in hours taken to travel from city A to city B is a continuous numerical variable.
A continuous numerical variable is a type of variable that can take on any value within a given range. It is numerical in nature, meaning it can be represented as a number, and it is continuous, meaning it can take on values at any point within a given range, not just specific, discrete values.
In the case of the time taken to travel from city A to city B, it can take on any value within a certain range of time, for example, from 0 hours to 24 hours.
This value can be any number, including a fraction of an hour, such as 3.5 hours or 4.75 hours, which are continuous values within the given range. This makes the time taken to travel a continuous numerical variable.
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A cylindrical vase has height 15 in. and radius 3in. Find the exact surface area of the vase in terms of . Suppose a second vase has double the radius, but the same surface area. What is the height of this vase?
Answer: pi*3^2= 9pi
pi*6=6pi
6pi*17= 102pi
102pi+9pi= 111pi in. squared
pi*6^2=36pi
pi*12=12pi
36pi+12pi*x=111pi
12pi*x=75pi
x=6.25pi
x=Height btw
what is the potential energy of the water in a lake of surface area 10 square miles, average depth 40 ft, and elevation above the electrical generator of 600 ft?
The potential energy of the water in a lake is 57 trillion N × m, which is 57 trillion joules (J).
Gravitational potential energy applies in this situation. G P E = m g h is the formula for gravitational potential energy, where: mg stands for weight or mass times gravity (w). The height to which an object can fall before kinetic energy replaces potential energy is denoted by the symbol h. In the example of the lake, we first determine the amount of water using the equation for the volume of a typical cylinder in order to determine the weight of the cylinder: V cy l = π r²L , The weight density of the water per cubic foot, which is about 62 lb, can then be multiplied by this volume: W(water) = (Volume) (Density)
W (water) = (28,000,000 ft² ⋅ 40ft) ( 62 lb ÷ ft³ )
W (water) = 69,440,000,000 lb
To calculate the potential energy, multiply this weight by the height. GPE=mgh
GPE=Wh=(69,440,000,000lb)(600ft)
GPE=41,644,000,000,000ft⋅lb
matching the level of precision by rounding the response to two significant digits. 4.2X10¹³ft⋅lb , or 42 trillion ft-lb.
Because joules are measured in N × m units, multiply the result by fractional equivalencies. 42trillionft × lb × (4.45N ÷ lb) × (m ÷ 3.28ft)
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Make a scatter plot of the data below.
Speed (mph)
Stopping distance (ft)
10
12.5
20
36.0
30
69.5
40
114.0
50
169.5
60
249.0
70
325.5
Using the quadratic regression equation
y = 0.06 x squared + 0.31 x + 4
predict what your stopping distance would be if you were going 80 miles per hour.
a.
363.2 ft
b.
412.8 ft
c.
355.2 ft
d.
33.6 ft
By using the quadratic regression feature of a graphing calculator a quadratic model would be;
⇒ y = 0.06x² + 0.31 x + 4
And, Your stopping distance would be if you were going 80 miles per hour is, 412.8 ft.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Speed (mph) Stopping distance (ft)
10 12.5
20 36.0
30 69.5
40 114.0
50 169.5
60 249.0
70 325.5
Now, Use the quadratic regression feature of a graphing calculator to find a quadratic model.
Hence, From the above data, we get;
⇒ y = 0.06x² + 0.31 x + 4
Hence, Your stopping distance would be if you were going 80 miles per hour is,
⇒ y = 0.06x² + 0.31 x + 4
⇒ y = 0.06(80)² + 0.31 (80) + 4
⇒ y = 384 + 24.8 + 4
⇒ y = 412.8 ft
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