Answer: 5 cm
Step-by-step explanation:
B = [tex]\sqrt{13^{2} -12^{2} } = 5[/tex]
Answer:
OPTION C, 5
Step-by-step explanation:
Using the formula, substitute the hypotenuse and the other leg of the right triangle.
13²=12²+b²
Rearrange appropriately.
13²-12²=c²
Convert.
13²=169
12²=144
Apply and work out.
169-144= 25
c²=25
c=√25
c=5
OPTION C is therefore the answer.
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how 4-digit positive integers have four differennt digits, where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largets digt
Answer:
There are 9 possible thousands digits, because 0 cannot be the leading digit.
There are 2 possible ones digits, 0 and 5.
If the ones digit is 5:
There are 5 possible thousands digits: 1, 2, 3, and 4.For each possible thousands digit, there are 5 possible hundreds digits. (We used one of the digits above to be the thousands digit, but 0 is a possible hundreds digit.)For each possible pair of thousands-and-hundreds digits, there are 4 possible tens digits.
So there are 5 x 5 x 4 = 100 possible 4-digit numbers that end in 5 with no repeated digit and no digit larger than 5.
If the ones digit is 0:
There are 5 possible thousands digits.For each possible thousands digit, there are 4 possible hundreds digits.For each possible pair of thousands-and-hundreds digits, there are 6 possible tens digits.
So there are 5 x 4 x 6 = 120 possible 4-digit numbers that end in 0 with no repeated digit and no digit larger than 5.
100+120=220
Answer: 220 possible numbers.
A function is shown: f(x) = 36x² - 1.
Choose the equivalent function that best shows the x-intercepts on the graph
Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)
What are equivalent functions?Equivalent functions are different functions that have equal values when evaluated and compared
How to determin the equivalent function that best shows the x-intercepts on the graph?
The function is given as:
f(x) = 36x^2 - 1
Express 1 as 1^2
f(x) = 36x^2 - 1^2
Express 36x^2 as (6x)^2
f(x) = (6x)^2 - 1^2
Apply the difference of two squares.
This is represented as:
(a + b)(a - b) = a^2 - b^2
So, we have the following equation
f(x) = (6x - 1)(6x + 1)
Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)
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A triangle has side lengths of (2b + 5c) centimeters, (10b + 7d) centimeters, and
(4d-3c) centimeters. Which expression represents the perimeter, in centimeters,
of the triangle?
The perimeter of the triangle can be express as follows:
12b + 11d + 2c
How to find perimeter of a triangle?The perimeter of a figure is the sum of the whole sides of the figure.
A triangle has three sides. Therefore, the perimeter of a triangle is the sum of the three sides.
Therefore, the sides of the triangle are of lengths (2b + 5c) centimetres, (10b + 7d) centimetres, and (4d-3c) centimetres.
Hence, the perimeter of the triangle can be represented as follows:
Perimeter of the triangle = 2b + 5c + 10b + 7d + 4d - 3c
Perimeter of the triangle = 2b + 10b + 7d + 4d + 5c - 3c
Perimeter of the triangle = 12b + 11d + 2c
Therefore, the perimeter of the triangle can be express as follows:
12b + 11d + 2c
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Evaluate the following expression. "5 less than 15"
A. -10
B. 8
C. 20
D. 10
Answer: 10
Step-by-step explanation: 5 less than 15 is 10 because 15 - 5 is 10. If it was 15 less from 5, only then it would be -10.
Answer:
5 less than 15 is Option D, 10. This is because using mathematical symbols, it says 15-5 which equals to 10.
Can someone help ???????
Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
The volume of the cone is 84.9 km³
How to find the volume of a cone?Volume of a cone = 1 / 3 πr²h
where
h = heightr = radiusTherefore,
radius = 3 km
height = √9.5² - 3²
height = √81.25
height = 9.01387818866
height = 9.014 km
Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014
volume of the cone = 254.732197612 / 3
volume of the cone = 84.9107325372
volume of the cone = 84.9 km³
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Which geometry or geometries are common for complexes with a coordination number of 4?.
Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.
What is geometry?Geometry is a subfield of mathematics that examines the measurement and relationships of surfaces, solids, solid surfaces, angles, and points.Ge and metria, two Greek terms that signify "measuring," are the origin of the word geometry. The foundation of geometry has been the method of geometry devised by the Ancient Greeks for more than 2000 years.The calculation of a triangle's angles is a geometry example.Plane geometry, solid geometry, and spherical geometry are the three most popular types of geometry.Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.
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Use what you know about reflections of functions
to match the graph to the function rule.
The answers are :
y = 3ˣ ⇒ b
y = 3⁻ˣ ⇒ a
y = -3ˣ ⇒ c
For y = 3ˣ, we will get a graph that will increase exponentially in the direction of positive y-axis.
For y = 3⁻ˣ, we will get a graph that will decrease exponentially in the direction of positive x-axis.
For y = -3ˣ, we will get a graph that will decrease exponentially in the direction of negative y-axis.
Write two different integers x, y, and z, and meet the following conditions. they do not all have the same sign and x-y-z=0
Two different integers are the same numbers, which have different signs.
What is integers?An integer is a number that includes negative and positive numbers, including zero. It does not include any decimal or fractional part. A few examples of integers are: -5, 0, 1, 5, 8, 97.
Given that,
x, y, and z are three integers. They follow the one condition: x-y-z = 0.
Any number in the number system that has only two signs, either + or -, So we consider that the third integer is 0 because 0 is a whole number that has neither a positive nor a negative sign.
The remaining two integers are the same numbers, but they have different signs to follow the given condition.
x-y-z = 0
x = y+z
Let y,z are the same numbers, They have different signs and x = 0.
Note: The value of x is always negative and y's value is always positive.
Example:
x = 0, y = +6, z = -6
x-y-z = 0
x = y+z
0 = +6-6
0 = 0
Hence, two different integers are the same numbers, which have different signs.
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Consider the word pencil. if all of the letters are used, and the first letter can’t be n or l, how many ways can the letters be arranged?
480 Ways can the letters be arranged.
What is the meaning of probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.First letter can't be n or l
= 4! × [tex]5P_{3}[/tex]
= 24 × 5! /3!
= 24 × 5 × 4
= 480
Therefore, 480 ways can the letters be arranged.
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Answer: 480 ways
Step-by-step explanation:
Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.
10%
30%
50%
90%
Question 2(Multiple Choice Worth 2 points)
(Sample Spaces LC)
List the sample space for rolling a fair seven-sided die.
S = {1, 2, 3, 4, 5, 7}
S = {1, 2, 3, 4, 5, 6, 7, 8}
S = {1}
S = {7}
Question 3(Multiple Choice Worth 2 points)
(Sample Spaces LC)
Which event will have a sample space of S = {h, t}?
Flipping a fair, two-sided coin
Rolling a six-sided die
Spinning a spinner with three sections
Choosing a tile from a pair of tiles, one with the letter A and one with the letter B
Question 4(Multiple Choice Worth 2 points)
(Theoretical Probability MC)
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
Question 5(Multiple Choice Worth 2 points)
(Likelihood MC)
A spinner is given.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
Question 6(Multiple Choice Worth 2 points)
(Experimental Probability MC)
Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Question 7(Multiple Choice Worth 2 points)
(Experimental Probability MC)
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials..
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Compare the theoretical probability and experimental probability of pulling a brown marble from the bag.
The theoretical probability, P(brown), is 50%, and the experimental probability is 25%.
The theoretical probability, P(brown), is 50%, and the experimental probability is 22.5%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 13.0%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
Question 8(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a spade.
0.15
0.25
0.35
0.50
The probability of not choosing red when choosing one marble from the bag is 90%.
S = {1, 2, 3, 4, 5, 7}
Flipping a fair, two-sided coin.
probability that a student studied for exactly 1 hour is 0.23.
The probability of landing on yellow is less than the probability of landing on blue.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
The experimental probability of drawing a spade is 0.15.
How to compute the probability?The probability of not choosing red when choosing one marble from the bag will be:
= (3 + 15 + 9)/30
= 27/30
= 90%
The sample space for rolling a fair seven-sided die will be S = {1, 2, 3, 4, 5, 7}.
The event that will have a sample space of S = {h, t} will be flipping a fair, two-sided coin.
The probability that a student studied for exactly 1 hour will be:
= 8/(1+8+2+5+9+7+3)
= 8/35
= 0.23
The true statement is that the probability of landing on yellow is less than the probability of landing on blue.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%. This was 13/40 = 32.5%.
The experimental probability of drawing a spade will be:
= 3/(7+3+6+4)
= 3/20
= 0.15.
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Answer: the sample space of the experiment from simultaneously flipping a coin and rolling a die consisted of: 2 × 6 = 12 possible outcomes.
Step-by-step explanation:
The sample space of 52 cards is all 52 possible outcomes, which is {Ace of Hearts, two of hearts, three of hearts...etc}.
The length and breadth of a rectangular park 25m and 12m. find the distance covered by a boy who takes 4 rounds of the garderean. also find its a
Answer:296 m
I’m assuming “breadth” is width and garderean is just the park.
(25+25+12+12) times 4.
A is never defined
What is 11% of 15?
1.65
1.56
2.5
Translate the sentence into an equation.
15 less than Taryn's age is 20
use the variable a to represent Taryn's age.
answer choices:
a. 20-a = 15
b. 15-a = 20
c. a-15= 20
d. 20-15 = a
Answer: c. a-15= 20
Step-by-step explanation:
The answer is c because a represents her age and 15 less than that would mean that you have to subtract 15 from her age which is represented by a, and then 15 less than a would equal 20, so a-15=20
Find the circumference of a circle with radius of 4.2in.
Answer: 26.39
Step-by-step explanation:
2xπxr
A scientist uses a submarine to study ocean life. She begins 88 feet below sea level. • After traveling down for 6 seconds, she's 182 feet below sea level. Find the rate of change in the submarine's elevation in feet per second. Round your answer to the nearest tenth.
Answer:
original ft below sea level =88 feet
In six seconds goes to 182 feet
Amount of feet covered in 6 seconds=182-88=94 ft
Step-by-step explanation:
rate in feet per second = 94/6=15.66
rounding to nearest tenth=15.7ft/s
Suppose you set up a function to show how many hot dogs you will purchase for a dinner when you have already bought two packages but must buy more, . What is the domain of this function?
The domain of the function is:
h > 0, only integers.
Then the correct option is the first one.
What is the domain of the given function?For a function f(x), we define the domain as the set of the possible values of x that we can use as inputs in the given function.
Here the function is:
f(h) = 6*h + 12
Where h is the number of packages that you buy.
Then h can be only integers larger than zero (as you can't buy half a package or something like that).
Then we conclude that the correct option is the first option.
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g(a) = 4a + 5
f(a) = a² + 2a
Find: g(f(a))
Step-by-step explanation:
g(f(a))=4(a²+2a) + 5
= 4a²+8a+5
Lou received requests for 150 tickets for their art show. The number of requests was 120% of the number of tickets they had. How many tickets do they have?
Answer:
180
Step-by-step explanation:
If she received requests for 150 tickets, and that is 120% of what they have, you would find 20% of 150. You would do this because 100% of 150 is 150, now you need to add the other 20%, so you have to find 20% of 150. Which is 30. You would then add that to 150 sine it is 120% of what they have. So, they have 180 tickets
Consider the exponential function g(x) = 1,296 x .
Find the output values for x-values x = –1.75, –1, –0.25, 0, 0.25, 0.50, 0.75, and 1.
The values associated to the exponential function are listed below:
g(- 1.75) = 3.572 × 10⁻⁶g(- 1) = 7.716 × 10⁻⁴g(- 0.25) = 0.167g(0) = 1g(0.25) = 6g(0.50) = 36g(0.75) = 216g(1) = 1 296How to evaluate an exponential function
Herein we have the exponential function [tex]g(x) = 1\,296^{x}[/tex], which has to be evaluated, that is, replacing the variable x by constants and make use of algebra properties until result is found.
g(- 1.75) = 3.572 × 10⁻⁶
g(- 1) = 7.716 × 10⁻⁴
g(- 0.25) = 0.167
g(0) = 1
g(0.25) = 6
g(0.50) = 36
g(0.75) = 216
g(1) = 1 296
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Determine what type of model best fits the given situation: A. none of these B. exponential C. linear D. quadratic
The option c is correct. Linear model suits best to this graphical representation out of the exponential and quadratic model.
According to the statement
We have given that a model in the graphical representation and we have to tell that which type of model used in this representation.
So,
According to this representation,
A linear representation is a representation on a category of vector spaces or similar.
The other meaning is that when the growth increases linearly or at the constant speed.
In this graphical representation, linear representation is used because it increases or decreases linearly not suddenly.
linear representation explain this graph perfectly.
So, Linear model suits best to this graphical representation.
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Scalcet8 4. 2. 26. suppose that 2 ≤ f '(x) ≤ 4 for all values of x. what are the minimum and maximum possible values of f(4) − f(1)? ≤ f(4) − f(1) ≤ show my work (optional)
The minimum value of f(4) - f(1) is 6.
The maximum value of f(4) - f(1) is 12.
In the question, we are given that, 2 ≤ f'(x) ≤ 4 for all values of x.
Taking the given inequality as (i).
We are asked to find the minimum and maximum possible values of f(4) - f(1).
We multiply (i) by dx throughout, to get:
4dx ≤ f'(x)dx ≤ 5dx.
To find this, we integrate (i) in the definite interval [4, 1] with respect to dx, to get:
[tex]\int_{1}^{4}2dx \leq \int_{1}^{4}f'(x)dx \leq \int_{1}^{4}4dx\\\Rightarrow [2x]_{1}^{4} \leq [f(x)]_{1}^{4} \leq [4x]_{1}^{4}\\\Rightarrow 2*4 - 2*1 \leq f(4)-f(1) \leq 4*4 - 4*1\\\Rightarrow 6 \leq f(4) -f(1) \leq 12[/tex]
Thus, the minimum value of f(4) - f(1) is 6.
The maximum value of f(4) - f(1) is 12.
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Cory saw 27 animals in the woods. two-thirds of them were insects. one-third of the insects were ants. the rest of the insects were flies. cory saw two times as many squirrels as rabbits. cory also saw a family of deer: a buck, a fawn, and a doe. how many of each animal did cory see?
Number of ants = 6
Number of flies = 12
Number of buck = 1
Number of fawn = 1
Number of doe = 1
Number of squirrels = 3
Number of rabbit = 6
What is the number system?
A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.
A system for representing numbers is called a number system. It also defines a set of numbers to represent a quantity and is referred to as the system of numeration.
Given,
Total number of animals Cory saw = 27
Number of insects = [tex]27 \times \frac{2}{3}[/tex]
[tex]= 18[/tex]
Remaining number of animals = [tex]27-18[/tex]
= [tex]9[/tex]
From the insects-
Number of ants = [tex]18 \times \frac{1}{3}[/tex]
[tex]=6[/tex]
Number of flies = [tex]18-6[/tex]
= [tex]12[/tex]
Number of buck = 1
Number of fawn = 1
Number of doe = 1
Let the number of squirrels be [tex]x[/tex]
Then, the number of rabbits = [tex]2x[/tex]
Remaining animals = [tex]2x+x[/tex]
⇒ [tex]9=3x[/tex]
⇒ [tex]x= 3[/tex]
Therefore,
Number of squirrels = 3
Number of rabbits = [tex]2x[/tex]
= 6
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Select the correct answer.
Which expression is equivalent to 3/2?
Answer:
Here is the full list of equivalent fractions to 32. 3/2, 6/4, 96, 12/8, 15/10, 18/12, 21/14, 24/16, 27/18, 30/20, 33/22, 36/24, 39/26, 42/28, 45/30, 48/32, 51/34, 54/36, 57/38, 60/40
Step-by-step explanation:
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Find the surface area of the composite figure.
5 cm
6 cm
20 cm
4 cm
5 cm 4 cm
SA =
12 cm
-6 cm
[?] cm²
Step-by-step explanation:
we have 2 blocks, as the graphic shows.
the surface areas of both blocks are the sum of their 6 sides each.
the special thing about seeing them as "composite figure" is that 2 sides (one for each block) are partly or even completely blocking each other off from being seen, so these parts and whole side are not part of the combined surface area.
let's start with the large block :
it is 5cm × 6cm × 20cm.
its surface area is the sum of
top and bottom 5×6
front and back 20×5
left 20×6
visible right (20 - 12)×6 = 8×6
it is (20-12)cm long, because the short block
is 12cm high.
so, we have
2 times 5×6 =2×30 = 60 cm²
2 times 20×5 = 2×100 = 200 cm²
20×6 = 120 cm²
8×6 = 48 cm²
in total : 428 cm²
now the small block :
it is 4cm × 6cm × 12cm.
its surface area is the sum of
top and bottom 4×6
front and back 4×12
no left (completely covered by the large block)
right 6×12
so, we have
2 times 4×6 = 2×24 = 48 cm²
2 times 4×12 = 2×48 = 96 cm²
6×12 = 72 cm²
in total : 216 cm²
the complete surface area of the composite figure is
428 + 216 = 644 cm²
The data in the table can be entered into a calculator to determine a linear equation of best fit where x represents the number of years with a company and y represents an employee’s salary in dollars.
What conclusion can be drawn from the correlation coefficient associated with this linear equation?
Based on the given table which shows the number of years with a company in relation to the employee salary, the conclusion that can be drawn is There is a weak positive correlation between the variables.
What is the correlation between the values?When two variables are said to be positively correlated, then it means that when one variable increases, the other variable would increase as well.
If the correlation between them is strong, then the increase between the variables would be more uniform i.e. we can tell with higher accuracy, how the increase in one variable would affect the other.
In the table, we see that with every increase in the number of years with the company, there is an increase in the salary. This means that there is a positive correlation.
The increase is not uniform however. Sometimes it increases by $1,000, and other times by $7,000. As the increase is not uniform, it means that the correlation is weak.
In conclusion, there is a weak positive correlation between number of years and salary.
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Create one symmetrical (normal) and one asymmetrical set of data, and explain why each fit the definition.
- Knowing the type of distribution and the skewness of the data, is it possible to draw conclusions about the mean and the median?
- Why would it be best to use particular measures of center and spread if the data is symmetrical or asymmetrical?
- What measures would you use in each case?
If the data is symmetrical, then the mean is the best measure of central tendency to use, and the standard deviation is the best spread to use.
If the data is asymmetrical, the median is the best measure of central tendency to use, and the inter-quarterly range is the best spread to use.
What are symmetrical and asymmetrical data?A histogram for symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of the central tendency to use is the mean. The standard deviation shows how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency in this case, the standard deviation should be used as the spread.
A histogram for a an asymmetric data set will give an asymmetric shape, and the mean is not always equal to the median. Therefore, the best measure of central tendency to use is the median. The inter-quarterly range shows the range of the middle 50% of a certain data, which is considered from the median value. Since the median is used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.
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Of the following, which reads the same forwards, backwards, and upside down (when viewed on a calculator screen)?
(A) 6889
(B)1991
(C)1961
(D) 1881
Answer: D 1881
Step-by-step explanation: 6889 and 1961 don't read the same forwards and backward. 1991 upside down is 1661. So, only 1881 works
For the following pair of lines, identify the system by type.
consistent
inconsistent
equivalent
Considering that the two lines intersect at only one point, the system of equations described by them is consistent.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
According to the number of solutions, the system is classified as follows:
Consistent: One solution.Equivalent: Infinite solutions.Inconsistent: No solutions.In this graph, each equation is described by a line, and they intersect once, meaning that there is one solution and the system is consistent.
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(6.04)the equation of the line of best fit of a scatter plot is y = −5x − 2. what is the slope of the equation? −5 −2 2 5
Answer:
slope = - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 5x - 2 ← is in slope- intercept form
with slope m = - 5