Answer:
2004 cm²
Step-by-step explanation:
To solve this problem, you just need to plug your values into the rectangular prism formula: A=2(wl+hl+hw)
Assuming that the length is 21 cm, the width is 18 cm, and the height is 16 cm, your problem would look like this:
A=2((18x21)+(16x21)+(16x18))=2(378+336+288)=2x1002=2004 cm²
John has a bag of different colored marbles. He has 6 red marbles, 3 blue marbles, 7 yellow marbles, and 5 green marbles. If John reaches into the bag and randomly pulls out a marble, what is the probability that the marble will be blue?
Answer:
3/21, 14.29%, or 14.29
Step-by-step explanation:
John has 21 total marbles, which includes 3 blue ones.
(That's 3 over 21)
Hope this helps!
The required probability of getting blue marble would be 1/7.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Given that bag contains 6 red marbles, 3 blue marbles, 7 yellow marbles, and 5 green marbles.
The total number of outcomes = 6 + 3 + 7 + 5 = 21
So n(S) = 21
Number of blue marbles = 3
Number of favorable outcomes, n(E) = 3
If John reaches into the bag and randomly pulls out a marble
So the probability of getting blue marble would be as:
⇒ P(E) = n(E)/n(S)
⇒ P(E) = 3/21
⇒ P(E) = 1/7
Therefore, the required probability of getting blue marble would be 1/7.
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Choose the correct x-intercepts for the following quadratic function. f(x)= x^2 + 5x – 14
A. x = 1, x = 3
B. X= 4, X = -3
C. x=2, x = -7
D. x = 2, x=-1
Answer:
x= -7 x = 2
Step-by-step explanation:
f(x)= x^2 + 5x – 14
To find the x intercepts, set the function equal to zero
0 = x^2 + 5x – 14
Factor
What two numbers multiply to -14 and add to 5
7*-2 = -14
7+-2 = 5
0= (x+7) (x-2)
Using the zero product property
x+7 =0 x-2 =0
x= -7 x = 2
Which set of lengths could be the side lengths of a right triangle? I need asap
A. 7 in., 7 in., 10 in.
B. 4.5 ft, 6 ft, 7.5 ft
C. 10 m, 11 m, 15 m
D. 8 cm, 10 cm, 13 cm
Plz plz plz plz plz plz plz plzplzplz help me plz thx thx plz plz help plz plz thx plz plz help
Answer:
97 pencils
Step-by-step explanation:
4074 (pencils) divided by 42 (sixth graders) is exactly 97 pencils.
Answer:
Each class received 97 pencils.
Step-by-step explanation:
4074 divided by 42 is equal to 97.
A colored chip is yellow on one side and red on the other. The chip was flipped 50 times and landed on red side up 22 times. What is the relative frequency of the chip landing with the red side facing up?
Answer:
44 %
Step-by-step explanation:
22 divided by 50 is 0.44 which is 44 percent
Answer:
40%
Step-by-step explanation:
A circle has the equation x2+12y+22x+y2−167=0.
What is the equation of the circle in standard form?
(x−11)2+(y−6)2=324
(x+11)2+(y+6)2=184
(x−11)2+(y−6)2=184
(x+11)2+(y+6)2=324
Answer:
[tex](x + 11)2 + (y + 6)2 = 184[/tex]
Answer: The answer would be (x+11)2+(y+6)2=324
Step-by-step explanation: I just got it right on my test :)
a right triangle with integer sides has area equal to 30. What is the length of its hypotenuse.
We have been given that a right triangle with integer sides has area equal to 30. We are asked to find the length of hypotenuse of right triangle.
We know that area of triangle is half the product of its base length and height.
Since our given triangle is a right triangle, so its base and height will be legs of right triangle.
[tex]\frac{1}{2}\cdot\text{Base}\times \text{Height}=\text{Area}[/tex]
[tex]\frac{1}{2}\cdot\text{Base}\times \text{Height}=30[/tex]
[tex]\frac{1}{2}\cdot 2\cdot\text{Base}\times \text{Height}=30\cdot 2[/tex]
[tex]\text{Base}\times \text{Height}=60[/tex]
This means that product of two bases is 60.
Now we need to find two multiples of 60 such that they are make a right triangle.
Multiples of 60:
1, 60
2, 30
3, 20
4, 15
5, 12
6, 10
We know that (5, 12 and 13) is a Pythagoras triplet.
[tex]5^2+12^2=13^2[/tex]
[tex]25+144=169[/tex]
[tex]169=169[/tex]
Therefore, the hypotenuse of right triangle is 13 units.
There are 1000 tickets. Of these, 75 are winning tickets. How likely are you to win the lottery if you take one ticket?
Answer:
7.5%
Step-by-step explanation:
75 is 7.5% of 1000
Hope this helps!
Write the word sentence as an inequality. Thank you!
13 less than a number M is at most 7
Answer:
13 < M = ≤7
Step-by-step explanation:
Which is the BEST estimate of the average rate of change for the function given in the table, over the interval 2 ≤ x ≤ 6?
a) 5
b) 10
c) 15
d) 20
The average rate of change for the function given in the table, over the interval 2 ≤ x ≤ 6 is: C) 15.
The average rate of a function over an interval can be calculated using the formula:
Average rate of change = change in y / change in x
When x = 2, y = 7
When x = 6, y = 67
Thus,
Average rate of change = 67 - 7 / 6 - 2
Average rate of change = 60 / 4
= 15
Option C is correct.
If f(x) = 3x - 1 and g(x) = x + 2, find (f - g)(x).
w
O A. 4x+1
O B. 2x-3
o c. 2x-1
O D. 3 - 2x
IR
SUBMI
Final answer:
To find (f - g)(x), subtract g(x) from f(x) which gives (f - g)(x) = (3x - 1) - (x + 2), resulting in 2x - 3 as the correct answer.
Explanation:
To find (f - g)(x), you need to subtract the function g(x) from the function f(x). The given functions are f(x) = 3x - 1 and g(x) = x + 2.
Subtraction of the functions is performed as follows:
(f - g)(x) = f(x) - g(x)
(f - g)(x) = (3x - 1) - (x + 2)
(f - g)(x) = 3x - 1 - x - 2
(f - g)(x) = 2x - 3
The correct answer for (f - g)(x) is 2x - 3, which corresponds to option B.
the sum of two numbers is 64. The smaller number is 6 less than the larger number. What are the numbers?
x + y = 64
x = y + 6
y + 6 + y = 64
2y + 6 = 64
2y = 58
y = 28x = y + 6
x = 28 + 6
x = 3434 + 28 = 64
34 - 28 = 6
Final answer:
The two numbers are 35 and 29, with the larger number being 35 and the smaller number being 29, which is 6 less than 35.
Explanation:
To find the two numbers whose sum is 64, with the smaller number being 6 less than the larger number, we can use a system of equations. Let the larger number be represented by x and the smaller number by y.
From the problem statement, we have two equations:
x + y = 64 (The sum of the two numbers)y = x - 6 (The smaller number is 6 less than the larger number)Substituting the second equation into the first gives us:
x + (x - 6) = 64
This simplifies to:
2x - 6 = 64
Adding 6 to both sides gives us:
2x = 70
Dividing both sides by 2 gives us:
x = 35
Since y = x - 6, we find that:
y = 35 - 6 = 29
Therefore, the larger number is 35 and the smaller number is 29.
(HELP WITH THIS )Suppose ages of cars driven by company employees are normally distributed with a mean of 8 years and a
standard deviation of 3.2 years. Approximately 75% of cars driven by company employees are older than
what age? Show your work and provide the exact answer.
Answer:
Let say 75% of cars older than age = Y years
than 25 % cars of age less than Y Years
Z score corresponding to 25 % = -0.674
Z score = (Value - Mean) /SD
Value = Y
Mean = 8
SD = 3.2
Z score = -0.674
-0.674 = (Y - 8)/3.2
=> Y =5.84 Years
=> Y ≈ 5.9 Years
Approximately 75% of cars driven by company employees are older than about 5.9 years
Learn More:
Assume that adults have iq scores that are normally distributed with ...
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Use technology or the z-distribution table on pages A-1 to A-2 in the ...
Matt and Taylor are taking a test. The test is designed to produce an overall mean score of 80, with a standard deviation of 6 for all test takers. Suppose Matt scored an 85 on the test and Taylor scored a 78 on the test. Given that the data is approximately normal, find the probability that another test taker, chosen at random, scored less than Matt and more than Taylor.
Answer:
P (r) = 1/3
Step-by-step explanation:
Matt 85 - 80 = +(5)
Taylor 80-78 = - (2)
+5-2 = 3 rise so deviation is the same.
Another test taker in 4 outcomes less than taylor more than taylor less than matt more than matt, would also be the same as AnB union.
So their are 3 outcomes = 1/3 = 0.333 rep.
What's the tenth term of a sequence with an explicit rule of ƒ(n) = 2 + (–3)(n – 1)?
Answer:
[tex]-25[/tex]
Step-by-step explanation:
Given: [tex]f(n)=2+(-3)(n-1)[/tex]
To find: tenth term of a sequence
Solution:
A sequence is a list of numbers in which order does matter and repetitions are allowed. A term is a number in the sequence.
For example in the sequence 1, 3, 5, 7, 9, ....,3 is the second term,9 is the fifth term.
To find the tenth term of a sequence, put n = 10 in [tex]f(n)=2+(-3)(n-1)[/tex]
[tex]f(n)=2+(-3)(n-1)\\=2+(-3)(10-1)\\=2+-3(9)\\=2-27\\=-25[/tex]
Answer:
-25
Step-by-step explanation:
The shed in Adam’s backyard is shown below. Which correctly describes the dimensions of the figures that make up the shed? a rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 8 feet
Step-by-step explanation:
The shed in Adam's backyard consists of two main figures: a rectangular prism and a triangular prism.
1. The rectangular prism has dimensions of: -Length = 5 feet
-Width = 6 feet
-Height = 8 feet
2. The triangular prism has dimensions of: -Base length = 3 feet
-Height of the triangle (perpendicular to the base) = 5 feet - Height of the prism = 8 feet
So, the shed consists of a rectangular prism with dimensions 5 fe by 6 feet by 8 feet and a triangular prism with base dimensions 3 by 5 feet and a height of 8 feet.
Match each logarithm to its value.
A log 3
Logarithm
N is equal to -3.
B. 1093, 27
Logarithm
is equal to z
c. log, 27
Logarithm
is equal to
log, 27
3
D.
Logarithmy
is equal to 3.
Answer:
Step-by-step explanation:
The picture helps a lot in understanding what the problem is. I could not understand what you typed.
OK, I can evaluate these log expressions.
A. log 3 (base 27) = (1/3) because 27^(1/3) = 3
B. log 27 (base 81) = (3/4) because 81^ (3/4) = 3^3 = 27
C. log 27 (base 9) = (3/2) because 9^(3/2) = 27
D. log 27 ( base 1/3) = -3 because (1/3)^-3 = 27
Answer:
D,C,B,A
Step-by-step explanation:
Number of Burgers
Number of Wing Servings
Sara is serving wings and burgers at her party. Wings cost $6.00 per serving and burgers are $3.00 each. Sara knows that at least 4 of
her friends want wings. Sara must spend less than $45.00. Sara graphs a system of inequalities to determine how many servings of
each kind of food she could serve to stay within her budget.
According to the dark blue area on the graph, how many burgers could Sara serve if she serves wings to 7 guests?
TII
Answer:
1 burger
Step-by-step explanation:Wings=$6.00
People, she is going to serve wings to=7
$6 times 7 is $42, $45 minus $42 is $3. Each burger is 3 dollars so she will only be able to serve one burger.
Math scores on the SAT exam are normally distributed with a mean of 514 and a standard deviation of 118. If a recent test-taker is selected at random, what is the probability the student scored between 455 and 573 on the exam?
Answer:
Probability that the student scored between 455 and 573 on the exam is 0.38292.
Step-by-step explanation:
We are given that Math scores on the SAT exam are normally distributed with a mean of 514 and a standard deviation of 118.
Let X = Math scores on the SAT exam
So, X ~ Normal([tex]\mu=514,\sigma^{2} =118^{2}[/tex])
The z score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean score = 514
[tex]\sigma[/tex] = standard deviation = 118
Now, the probability that the student scored between 455 and 573 on the exam is given by = P(455 < X < 573)
P(455 < X < 573) = P(X < 573) - P(X [tex]\leq[/tex] 455)
P(X < 573) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{573-514}{118}[/tex] ) = P(Z < 0.50) = 0.69146
P(X [tex]\leq[/tex] 2.9) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{455-514}{118}[/tex] ) = P(Z [tex]\leq[/tex] -0.50) = 1 - P(Z < 0.50)
= 1 - 0.69146 = 0.30854
The above probability is calculated by looking at the value of x = 0.50 in the z table which has an area of 0.69146.
Therefore, P(455 < X < 573) = 0.69146 - 0.30854 = 0.38292
Hence, probability that the student scored between 455 and 573 on the exam is 0.38292.
In a class of 25 students, 8 students have heights less than 65 inches and 10 students have heights of 69 inches or more. Find the probabilities described.
1. P(less than or equal to 65 inches and greater than or equal to 69 inches).
2. P(Greater than or equal to 65 inches.)
3. P(greater than or equal to 65 inches and less than or equal to 69 inches.)
Answer:
It should be 1.
Step-by-step explanation:
It stating that in a bunch of 25 students, only 8 are at least 65 inches or shorter, while the other ten, are at least 69 inches or taller, meaning there is nothing in between.
The probabilities described P(less than or equal to 65 inches and greater than or equal to 69 inches).
We have given that,
In a class of 25 students, 8 students have heights less than 65 inches and 10 students have heights of 69 inches or more.
What is the probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
It states that in a bunch of 25 students, only 8 are at least 65 inches or shorter, while the other ten, are at least 69 inches or taller, meaning there is nothing in between.
Therefore the probabilities described P(less than or equal to 65 inches and greater than or equal to 69 inches).
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Quadrilateral EFGH was dilated with the origin as the center of dilation to create
quadrilateral E' F'G'H'. The quadrilateral was dilated using a scale factor of 2.5.
The lengths of the sides of quadrilateral EFGH are given.
What is the length of side F'G'?
Answer:
The length of side F'G' is 17.5 units
Step-by-step explanation:
Given
Quadrilateral, EFGH.
EF = 2 units
EH = 6 units
GH = 5.5 units
FG = 7 units
Scale Factor = 2.5
Required
Length of F'G'
To dilate a shape means to increase or reduce the size of that shape using a given scale factor.
The length of the new shape is calculated by multiplying the scale factor by the length of the old shape.
The question requires that we calculate F'G'.
Here, F'G' is formed as a result of the dilation of side FG.
From the formula stated above.
F'G' = Scale Factor * FG
From the given diagram, FG = 7 units
And scale factor = 2.5
So, F'G' = 2.5 * 7 units
F'G' = 17.5 units
Hence, the length of side F'G' is 17.5 units
when 6x^2-4x+3 is subtracted from 3x^2-2x+3 The result is
Answer:
-3x^2 +2x
Step-by-step explanation:
3x^2 -2x +3 subtract 6x^2-4x+3
3x^2 -2x +3
-(6x^2 -4x +3)
--------------------------
Distribute the minus sign
3x^2 -2x +3
-6x^2 +4x -3
--------------------------
-3x^2 +2x
Devora tested two engines. As each engine's rotation got faster, its temperature increased at a constant rate.
The first engine's temperature (in degrees Celsius) as a function of its rotation speed (in cycles per second) is given by the following table of values:
The Table is for the first engine below
For the second engine, the graph is below
The temperature of which engine increased more for each increase of 1 cycles per second?
Choose 1 answer:
(Choice A)
A
The first engine
(Choice B)
B
The second engine
(Choice C)
C
The temperatures of both engines increased the same
Which engine was hotter when it rotated at 20 cycles per second?
Choose 1 answer:
(Choice A)
A
The first engine
(Choice B)
B
The second engine
(Choice C)
C
Both engines were equally hot
To compare the rates of temperature increase for the two engines, you can look at the slopes of their temperature vs. rotation speed graphs. To determine which engine was hotter at a rotation speed of 20 cycles per second, you can compare the corresponding temperature values on the graphs.
Explanation:The question asks which engine's temperature increases more for each increase of 1 cycle per second. To determine this, we need to compare the rates of change of temperature for both engines. The rate of change of temperature for the first engine can be determined by finding the slope of the temperature vs. rotation speed graph. From the graph, it can be seen that the slope of the line connecting two points on the graph represents the rate of change of temperature per unit increase in rotation speed. By comparing the slopes of the two graphs, we can determine which engine's temperature increases more for each increase of 1 cycle per second.
To determine which engine was hotter when it rotated at 20 cycles per second, we can look at the corresponding temperature values on the graph. By finding the temperature value for each engine when the rotation speed is 20 cycles per second, we can compare the two temperatures to determine which engine was hotter.
How many distinct triangles can be formed for which mZX = 51°, x = 5, and y = 2?
zero
one
two
Answer:
From the law of sines, we have:
,
where x and y are the sides opposite to angles X and Y, respectively.
Substituting the known values, we have:
, thus
.
Using a calculator, we can find that arcsin(0.31)=18 degrees, approximately.
We know that sine of (180-18)=162 degrees is also 0.31. But 162 and 51 degrees add up to more than 180 degrees.
Thus, there is only one triangle that can be formed under these conditions.
Hope this helps!
Answer:
From the law of sines, we have:
,
where x and y are the sides opposite to angles X and Y, respectively.
Substituting the known values, we have:
, thus
.
Using a calculator, we can find that arcsin(0.31)=18 degrees, approximately.
We know that sine of (180-18)=162 degrees is also 0.31. But 162 and 51 degrees add up to more than 180 degrees.
Thus, there is only one triangle that can be formed under these conditions.
Hope this helps!
Step-by-step explanation:
park rangers in yosemite estimared the number of racoons in one hiking area. the rangers tagged 15 racoons in the hiking area. the following week they captured 40 racoons. if the park rangers estimated there were 75 racoons in the area, how many of the captured racoons were tagged?
Answer:
8 racoons
Step-by-step explanation:
15/75=1/5 so 1/5 of the racoons are tagged. 1/5 of 40 is 8.
Will mark right answer brainlliest
Determine the line of reflection that maps the pre-image segment AB to the image segment A’B’.
x = 0
y = 0
y = x
It cannot be determined.
Answer:
B) y=0
Step-by-step explanation:
Option B is the correct answer.
We need to determine the line of reflection that maps the pre-image segment AB to the image segment A'B'.
What is the reflection transformation?In a reflection transformation, all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection.
In the given figure we can see that line segment AB is reflected on the y=0 and transformed into A'B'.
Therefore, option B is the correct answer.
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SHOW YOUR WORK.
Angle BAC is a right angle. Find
the measure of angle CAD.
Solution:
Answer:
26 I guess
Step-by-step explanation:
90 - 64 = 26
am I wrong?
What are the soulutions to m^2-9=0
Answer:
m= 3, -3
Step-by-step explanation:
Hope this helps!
numerical expression add 8 and 7 and then multiply by 2
Answer:
2(8+7)
Step-by-step explanation:
Answer:
(8+7)*2
(15)*2
30