Answer:
2/8 < 7/8
Step-by-step explanation:
Since the denominators are the same, we compare the numerators
2<7 so
2/8 < 7/8
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 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
The probability that an egg on a production line is cracked is 0.01. Two eggs are selected at random from the production line. Find the probability that exactly one of the eggs is cracked. Write the entire decimal answer.
Answer:
Probability that exactly one of the eggs is cracked is 0.0198.
Step-by-step explanation:
We are given that the probability that an egg on a production line is cracked is 0.01.
Two eggs are selected at random from the production line.
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......[/tex]
where, n = number trials (samples) taken = 2 eggs
r = number of success = exactly one
p = probability of success which in our question is probability that
an egg on a production line is cracked i.e; p = 0.01
Let X = Number of eggs on a production line that is cracked
So, X ~ Binom(n = 2, p = 0.01)
Now, probability that exactly one of the eggs is cracked is given by = P(X = 1)
P(X = 1) = [tex]\binom{2}{1} \times 0.01^{1} \times (1-0.01)^{2-1}[/tex]
= [tex]2 \times 0.01 \times (0.99)^{1}[/tex]
= 0.0198
Therefore, the probability that exactly one of the eggs is cracked is 0.0198.
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 :)
Julius needs to determine how much information needs to be given about an isosceles triangle to be able to draw an isosceles triangle. He is looking at six different cases and is trying to determine if that amount of detail will allow him to construct just one isosceles triangle or if it allows for more than one isosceles triangle.
To uniquely construct an isosceles triangle, you would either need the lengths of two sides and the angle between them, two sides and the angle opposite to one of them, or two angles and any side.
Explanation:Julius is examining the principles of constructions in geometry. To construct a unique isosceles triangle, certain specific information is needed. An isosceles triangle is a triangle with two sides of equal length, and the angles opposite these sides are of equal measure too.
In general, there are three common cases in which the information given would be enough to construct only one unique isosceles triangle:
Two side lengths and the angle between them (SAS)Two sides and the angle opposite to one of them (SSA)Two angles and any side (AAS)If other information is given, it may or may not be possible to construct a unique isosceles triangle. For example, given only the lengths of two sides, multiple different isosceles triangles can be made, depending on the size of the included angle.
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the product of 4 and 1/6 is _
Answer:
2/3
Step-by-step explanation:
What are the soulutions to m^2-9=0
Answer:
m= 3, -3
Step-by-step explanation:
Hope this helps!
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
Examine the diagram.
Parallel lines a and b are crossed by transversal t to create 8 angles. Clockwise from top left, the angles are blank, 60.75 degrees, blank, blank; 2, 1, blank, blank.
What are the measures of angle 1 and angle 2?
The m Angle1 is degrees.
The m Angle2 is degrees
Answer:
[tex]m\angle 1 =60.75^\circ \\m\angle 2 =119.25^\circ[/tex]
Step-by-step explanation:
From the diagram:
[tex]m\angle 1 =60.75^\circ $(Corresponding Angles)\\[/tex]
Now Angle 1 and Angle 2 are on a straight line, therefore:
[tex]m\angle 1 +m\angle 2 =180^\circ $(Linear Postulate)\\Since m\angle 1=60.75^\circ\\60.75^\circ +m\angle 2 =180^\circ\\m\angle 2=180^\circ-60.75^\circ\\m\angle 2 =119.25^\circ[/tex]
Answer: 60.75
119.25
Step-by-step explanation:
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.
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.
(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
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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 ...
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.
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:
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:
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.
Is triangle ABC=DCB? Complete the table to prove or disprove this statement
Answer:
ABC ≅ DCB by SAS
Step-by-step explanation:
1. Segment DB ≅ segment AC because it was given
2. Angle C ≅ angle B because it was given
3. Segment CB ≅ segment CB because of Reflexive Property
4. Triangle ABC ≅ DCB because of SAS (side-angle-side postulate)
Hope I helped and please give me brainliest!
Saturn is 8.867 × 10^8 miles away from the Sun. Uranus is 1.787 × 10^9 miles away from the Sun. Approximately how many times farther is Uranus from the Sun than Saturn is?
Answer: 0.2 times
Step-by-step explanation:
Help me out please..
Answer:
[tex]g(x) = \frac{3}{4} {x}^{2} [/tex]
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:
HELP I WILL GIVE U A FREE HUG!!!!!!
Answer:
the screen it very tight( squished together)
Step-by-step explanation:
Answer:
Step-by-step explanation:
y=2x²-12x-32
=2(x²-6x+9-9)-32
=2(x-3)²-18-32
=2(x-3)²-50
so vertex is (3,-50)
again 2x²-12x-32=0
or x²-6x-16=0
or x²-8x+2x-16=0
or x(x-8)+2(x-8)=0
(x-8)(x+2)=0
x=8,-2
8>-2
d=8
e=-2
f=3
regina invests$12,600 in an account interest, 3,2% annual continuously .what is the value of the account after 12years ?
Answer: 4,838.40
Step-by-step explanation: 12,600* 3.2%*12
What is the y-intercept of y= -3x
Answer:
there is no y intercept. if there was it would be at the end of -3x
Will mark right answer brainlliest
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!
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.
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.
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
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.
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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