Answer:
It was that great mathematician Leonhard Euler who discovered the number e and calculated its value to 23 decimal places. It is often called Euler's number and, like pi, is a transcendental number (this means it is not the root of any algebraic equation with integer coefficients
the number of real solutions to the quadratic equ
5a² + 30a + 45 = 0
The answer is 1.
There is one unique real solution, which is x = -3.
Hello, please consider the following.
[tex]5a^2+30a+45 = 0\\\\<=> 5(a^2+6a+9)=0\\\\<=> a^2+6a+9=0\\\\<=> a^2+2*3*a+3^2=(a+3)^2=0\\\\<=>\boxed{a=-3}[/tex]
Thank you
Answer:
two equal, real solutions
Step-by-step explanation:
The quickest way to determine this is to find the discriminant b^2 - 4ac. If this determinant (D) is > 0, the quadratic has two different real roots; if + 0, the quadratic has two equal real roots, and if < 0, the quadratic has two imaginary or complex roots.
Here a = 5, b = 30 and c = 45. The discriminant is
30^2 - 4(5)(45) = 900 - 900 = 0
and so this quadratic has two equal, real solutions.
Could anyone help me with this?
Answer:
x = 17
KNM = 131
Step-by-step explanation:
(8x - 5) + (4x - 19) = 180
12x - 24 = 180
12x = 204
x = 17
Answer:
x = 17
Step-by-step explanation:
Opposite Angles must be the Same Value so In other words, 2(8x - 5) + 2(4x - 19) = 360.
2(8x - 5) + 2(4x - 19) = 360
24x - 48 = 360
24x = 408
x = 17
Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data.
5 1 2 4 0 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
3 4 2 1 3 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
8 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
(a) Determine frequencies and relative frequencies for the observed values of x = number of nonconforming transducers in a batch. (Enter relative frequencies to three decimal places.)
x Frequency Relati veFrequency
0
1
2
4
5
6
7
8
(b) What proportion of batches in the sample have at most six nonconforming transducers? (Enter your answer to three decimal places.)
What proportion have fewer than six? (Enter your answer to three decimal places.)
What proportion have at least six nonconforming units? (Enter your answer to three decimal places.)
(c) Draw a histogram of the data using relative frequency on the vertical scale, and comment on its features.
a) The center of the histogram is around 2 or 3 and it shows that there is some negative skewness in the data.
b) The center of the histogram is around 2 or 3 and it shows that the distribution is fairly symmetric.
c) The center of the histogram is around 4 or 5 and it shows that there is some positive skewness in the data.
d) The center of the histogram is around 2 or 3 and it shows that there is some positive skewness in the data.
e) The center of the histogram is around 4 or 5 and it shows that the distribution is fairly symmetric.
f) The center of the histogram is around 4 or 5 and it shows that there is some negative skewness in the data.
Answer:
The number of six non conforming transducers at most =54/60=0.9
The number of fewer than six non conforming transducers =51/60=0.85
The number of at least six non conforming transducers at most =30/60=0.5
d) The center of the histogram is around 2 or 3 and it shows that there is some positive skewness in the data
Step-by-step explanation:
Relative Frequency Frequency x
6/60=0.1 6 0
0.2 12 1
0.2 12 2
0.25 15 3
0.1 6 4
0.05 3 5
0.05 3 6
0.0167 1 7
0.033 2 8
∑ 60
The number of six non conforming transducers at most
= 6+12+12+15+6+3= 54
The number of six non conforming transducers at most =54/60=0.9
The number of fewer than five non conforming transducers
= 6+12+12+15+6 = 51
The number of fewer than six non conforming transducers =51/60=0.85
The number of at least six non conforming transducers
2+1+3+3+6+15= 30
The number of at least six non conforming transducers at most =30/60=0.5
We plot the histogram by placing the percentages (or relative frequency *100) on the y –axis and the X on the x-axis.
The center of the histogram is given by the mean of the distribution which in this case is = ∑fx/∑f= 161/60= 2.683
So option d is the best answer
d) The center of the histogram is around 2 or 3 and it shows that there is some positive skewness in the data
Because at the center (between 2 and 3) the curve is increasing
Suppose that X and Y are independent random variables from binomial experiments where n = 4 in both cases but the probability of success is p = 0.25 for X and p = 0.5 for Y . Calculate the probability of the events (a) {X = 1, Y = 2}, (b) {X + Y = 1}.
Answer:
(a) The value of P (X = 1, Y = 2) is 0.1583.
(b) The value of P (X + Y = 1) is 0.1055.
Step-by-step explanation:
It is provided that:
[tex]X\sim Bin(n=4,p=0.25)\\\\Y\sim Bin(n=4,p=0.50)[/tex]
The variables X and Y are independent random variables.
The probability mass function of a Binomial distribution is:
[tex]P(U=u)={n\choose u}(p)^{u}(1-p)^{n-u};\ u=0,1,2,3...[/tex]
(a)
Compute the value of P (X = 1, Y = 2) as follows:
[tex]P(X=1,Y=2)=[{n\choose x}(p_{x})^{x}(1-p_{x})^{n-x}]\times [{n\choose y}(p_{y})^{y}(1-p_{y})^{n-y}][/tex]; Independent
[tex]=[{4\choose 1}(0.25)^{1}(1-0.25)^{4-1}]\times [{4\choose 2}(0.50)^{2}(1-0.50)^{4-2}]\\\\=0.422\times 0.375\\\\=0.15825\\\\\approx 0.1583[/tex]
Thus, the value of P (X = 1, Y = 2) is 0.1583.
(b)
Compute the value of P (X + Y = 1) as follows:
[tex]P(X+Y=1)=P(X=0,Y=1)+P(X=1,Y=0)[/tex]
[tex]=\{[{4\choose 0}(0.25)^{0}(1-0.25)^{4-0}]\times [{4\choose 1}(0.50)^{1}(1-0.50)^{4-1}]\}\\+\{[{4\choose 1}(0.25)^{1}(1-0.25)^{4-1}]\times [{4\choose 0}(0.50)^{0}(1-0.50)^{4-0}]\}\\\\=(0.3164\times 0.25)+(0.422\times0.0625)\\\\=0.0791+0.0264\\\\=0.1055[/tex]
Thus, the value of P (X + Y = 1) is 0.1055.
what is the probability of spinning a multiple of 3 The Spinner is 1-8 numbered
Answer:
1/4
Step-by-step explanation:
There are 8 possible outcomes
Multiples of 3 are
3,6 = 2 outcomes
P ( multiple of 3) = number of multiples of 3/ total
= 2/8
= 1/4
The probability of spinning a multiple of 3 The Spinner is 1-8 numbered will be [tex]P= \dfrac{1}{4}[/tex]
What is probability?Probability is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.
There are 8 possible outcomes
Multiples of 3 are
3,6 = 2 outcomes
[tex]\rm P ( multiple \ of\ 3) =\dfrac{ number\ of\ \ multiples\ of\ 3 }{ total }[/tex] [tex]= \dfrac{2}{8}[/tex] [tex]= \dfrac{1}{4}[/tex]
Hence the probability of spinning a multiple of 3 The Spinner is 1-8 numbered will be [tex]P= \dfrac{1}{4}[/tex]
To know more about probability follow
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The presence of schizophrenia was measured in both monozygotic (MZ) and dizygotic (DZ) twins. The correlation between the MZ twins was .50 and the correlation between the DZ twins was .30. What is the heritability coefficient for schizophrenia?
Answer:
0.40
Step-by-step explanation:
Given the following :
Correlation between monozygotic twins (MZ) = 0.50
Correlation between dizygotic twins (DZ) = 0.30
Heritability Coefficient is obtained by multiplying by 2, the difference between the monozygotic correlation and dizygotic correlation.
Therefore, Heritability coefficient of schizophrenia :
2 × (monozygotic - dizygotic)
2 × (0.50 - 0.30)
2 × (0.20)
= 0.40
Solve the equation
34=7r-8
Answer:
r = 6
Step-by-step explanation:
34 = 7r - 8
+8 . +8
42 = 7r
__ . __
7 . 7
6 = r
Change 33 feet to yards
Answer: 11 yds
Step-by-step explanation: 1 yd=3 ft
Answer:
11 yards is the correct answer
Step-by-step explanation:
a yard = 3 feet
33/3 = 11 yards
Write a real word problem in which multiplies decimals
Each decimal word problem involves multiplication of a whole number with a decimal number. ... These decimal worksheets emphasize decimal multiplication and division. The perfect blend of word problems makes the grade 6 and grade 7 children stronger in performing the multiplication and division operation.
Estimate the mean of the age of the people in group A
Answer:
48
Step-by-step explanation:
The ages are 18,28,38,48,58,68,78 I don't use 88 bacause the graph don't show any data so there is 88 years old
now lets find the mean
18+28+38+48+58+68+78= 336= 48
7 7
so the mean of the age is 48
i hope u like it
When interest is compounded annually, the amount of money accumulated in one year is the same under either a simple or compound interest scenario.
a) true
b) false
Answer:
a) true
Step-by-step explanation:
In case when the interest is compounded on an annually so the amount of money that is accumulated in year 1 would remain the same if there is a simple interest or compound interest situation.
Therefore the given case should be true and hence, the same is to be considered
hence, the correct option is a. true
Chester, the dog, loves to eat treats. He has eaten twice as many today as yesterday. He has eaten a total of 15 dog treats in both days.
-write the equation-
Answer:
The equations are:
[tex]T = 2Y[/tex] and [tex]T + 2Y = 15[/tex]
Step-by-step explanation:
Given
Represent bones eaten Today with T and yesterday with Y
Required
Write the equation
In the first statement, we have that:
[tex]T = 2Y[/tex]
Reading further; In the second statement
[tex]T + 2Y = 15[/tex]
Hence, the equations are:
[tex]T = 2Y[/tex] and [tex]T + 2Y = 15[/tex]
Solving further:
Substitute 2Y for T in the second equation
[tex]2Y + 2Y = 15[/tex]
[tex]4Y = 15[/tex]
Divide both sides by 4
[tex]Y = \frac{15}{4}[/tex]
[tex]Y = 3.75[/tex]
Recall that
[tex]T = 2Y[/tex]
[tex]T= 2 * 3.75[/tex]
[tex]T= 7.5[/tex]
What is the probability that a randomly selected day of a leap year (with 366 possible days) is in February?
Answer:
0.0792
Step-by-step explanation:
Probability is the likelihood that an event is going to occur. The formula for probability is:
Probability = number of favorable outcomes / total number of outcomes.
Normally in a year there are 365 days and in the month of February there are 28 days but during a leap year there are 366 days in the year and 29 days in the month of February.
Probability that a selected day of a leap year is in February = 29 / 366 = 0.0792
The probability that a selected day of a leap year falls in February is 0.0792
Graph the solution to the inequality. −5√x-2<−10 Drag the symbol to the correct location on the number line to graph the solution.
Answer:
[tex]x>6[/tex]
Step-by-step explanation:
So we have the inequality:
[tex]-5\sqrt{x-2}<-10[/tex]
Divide both sides by -5. Since we're dividing by a negative, the sign changes:
[tex]\sqrt{x-2} >2[/tex]
Square both sides:
[tex]\sqrt{x-2}^2>2^2\\x-2>4[/tex]
Add two to both sides:
[tex](x-2)+2>4+2\\x>6[/tex]
Therefore, x>6.
However, the expression under the square root cannot be negative. Therefore, there is another inequality. Set the expression under the square root to greater than or equal to 0:
[tex]x-2\geq 0[/tex]
Add 2 to both sides:
[tex]x\geq 2[/tex]
However, previously, we determined that x must be greater than 6. That overrules this, so we will ignore it.
Thus, the answer is:
[tex]x>6[/tex]
So, drag the fourth option onto 6 on the line. This is an open circle and points to the right, so it includes all values greater than 6 not including 6.
Answer:
x > 6
Step-by-step explanation:
Drag the fourth option onto 6 on the line. This is an open circle and points to the right, so it includes all values greater than 6 not including 6.
write a sentence as a equation
h plus 240 is 18
Hey there! The sentence is h + 240 = 18
what is a + bc if a = 2, b=3, and c=4
Answer:
14
Step-by-step explanation:
So we have the expression:
[tex]a+bc[/tex]
Substitute 2 for a, 3 for b, and 4 for c:
[tex]=(2)+(3)(4)[/tex]
Multiply:
[tex]=2+12[/tex]
Add:
[tex]=14[/tex]
8 – 3x = 20
A.
x = 4
B.
x = 9.33
C.
x = –4
D.
x = –9.33
Please select the best answer from the choices provided
A
B
C
D
Answer:
The answer is option C.
Peter weighs 156 pounds, but he would like to wrestle in a lower weight
class. He loses 4 pounds one week, gains back 2 pounds the next, loses 5
pounds the third week and loses 3 pounds the fourth week. How much does
Peter weigh now?
Answer:
146 pounds
Step-by-step explanation:
He starts at 156 pounds.
1st week: He loses 4 pounds, indicating 156 - 4, or 152.
2nd week: He gains 2 pounds, indicating 152 + 2, or 154.
3rd week: He loses 5 pounds, indicating 154 - 5, or 149.
4th week: He loses 3 pounds, indicating 149 - 3, or 146.
Plz help
Question: Which expression is equivalent to
[tex] \frac{4}{9}(2n - 3)[/tex]
Answer:
[tex] \frac{8}{9}n - 1\frac{1}{3} [/tex]
Step-by-step explanation:
To find the expression that is equivalent to [tex] \frac{4}{9}(2n - 3) [/tex], let's simply as follows:
[tex] \frac{4}{9}(2n) - \frac{4}{9}(3) [/tex] (distributive property of multiplication)
[tex] \frac{4*2n}{9} - \frac{4*3}{9} [/tex]
[tex] \frac{4*2n}{9} - \frac{4*1}{3} [/tex]
[tex] \frac{8n}{9} - \frac{4}{3} [/tex]
[tex] = \frac{8}{9}n - 1\frac{1}{3} [/tex]
[tex] \frac{8}{9}n - 1\frac{1}{3} [/tex] is equivalent to [tex] \frac{4}{9}(2n - 3) [/tex].
1: During an electronics experiment in your laboratory, you measure the voltage at terminal A
on your newly designed circuit. You measure -12 volts. You check the same terminal after
making a small change to the circuit and this time you measure -18 volts. What was the voltage
difference between the two readings?
2: What is the change in temperature a customer in a grocery store experience when they walk from the chilled vegetable section at 4 c to the frozen fish section which is set to -18 c?
Answer:
1) - 6 volts (or 6 volts drop)
2) -22°C (or 22°C drop)
Step-by-step explanation:
1. ............................
Initial voltage = -12 volts
Later voltage = - 18 volts
The difference:
-18 - (-12) = -18 + 12 = - 6 volts2. ............................
Temperature in the chilled vegetable section = 4°C
Temperature in the frozen fish section = - 18°C
The difference:
-18°C - 4°C = -22°CWhat is the area of this figure? 15 yd 4 yd 7 yd 25 yd 21 yd 22 yd square yards Submit
3 - (4m + 1) > 5m - 25
Step-by-step explanation:
3 - (4m + 1) > 5m - 25
3 - 4m - 1> 5m - 25
3 - 1 +25 > 4m + 5m
27 > 9m
m> 27/9
m> 3
A triangle has sides with lengths of 5x - 7, 3x - 4, and 2x - 6. What is the perimeter of triangle?
Answer:
10x -17
Step-by-step explanation:
The perimeter is the sum of the side lengths:
P = (5x -7) +(3x -4) +(2x -6)
Grouping like terms can make simplification easier:
P = 5x +3x +2x -7 -4 -6
P = 10x -17
The two lines below are parallel. If the slope of the red line is 1/5 what is the slope of the green line?
Its 1/5.
Parallel lines have the same slope.
Hope this helps.
Answer:
The slope of the green line (and of the red one as well) is:
[tex]\frac{1}{5}[/tex]
Enter it as 1/5 as suggested
Step-by-step explanation:
Recall that parallel lines have the same slope. Therefore we can find the slope of either line and that will be the slope of the other line as well.
So if we use the two point given on the red line: (5,4) and (0,3)
We can find the slope of the segment joining them via the slope equation:
[tex]slope=\frac{4-3}{5-0} =\frac{1}{5}[/tex]
Simplify ((–3)^2)^3. A. (3)^6 B. (3)^5 C. (-3)^6 D. (-3)^5
Answer:
C
Step-by-step explanation:
So we have the expression:
[tex]((-3)^2)^3[/tex]
Use the power of a power property, where:
[tex](a^b)^c=a^{b\cdot c}[/tex]
So:
[tex]((-3)^2)^3=(-3)^{2\cdot 3}[/tex]
Simplify:
[tex]=(-3)^6[/tex]
Our answer is C
Answer:
(-3)⁶
Step-by-step explanation:
( (-3)² )³
= (-3)⁽²⁾⁽³⁾
= (-3)⁶
Need this urgently!! Please help me
Find the difference. Enter your answer in the box below as a fraction, using
the slash mark ( 1 ) for the fraction bar.
Answer:
2/17
Step-by-step explanation:
Given, [tex] \frac{16}{17} - \frac{14}{17} [/tex], to find the difference, first look for the common denominator of both fractions.
Common denominator of both fractions is 17.
Divide the common denominator by the denominator of each fraction, then multiply the result by its numerator and solve as follows:
[tex] \frac{1(16) - 1(14)}{17} [/tex]
[tex] \frac{16 - 14}{17} [/tex]
[tex] \frac{2}{17} [/tex]
The answer is 2/17
[tex] \frac{16}{17} - \frac{14}{17} [/tex] = 2/17
If m∠NLO = 41° and m∠NLM = 88°, what is m∠OLM?
Answer:
47°
Step-by-step explanation:
Given that m<NLO = 41°, and m<NLM = 88°, according to angle addition postulate, m<OLM + m<NLO = m<NLM
Therefore, subtracting m<NLO from both sides will give us:
m<OLM = m<NLM - m<NLO
m<OLM = 88° - 41°
m<OLM = 47°
Find the root(s) of the equation x2 = 169? A) x = ±13 B) x = ± 13 C) x = 13 D) x = 13
Answer:
We have this equation:
[tex]x^2 = 169[/tex]
What we do is a square root on both sides, so we get:
[tex]\sqrt{x^2}=\sqrt{169}[/tex]
[tex]x = \sqrt{169}[/tex]
And now, we calculate the square root, remember tehre are always two results when the root index is even:
[tex]\bold{x_1 = 13}[/tex]
[tex]\bold{x_2 = -13}[/tex]
As 13 * 13 = (-13)*(-13)
Answer:
I guess both A and B since they have the same exact answer: ±13
Step-by-step explanation:
The square root of any positive number is both the positive (+) version of the root and the negative (-) version of the root.
169 is a perfect square and its positive square root is 13, but you must also include its negative square root, -13, so the roots of this equation are ±13.
That means both answer choices A and B are correct, since they are exactly the same.
Which number is the smallest 2, -2, -4 or -5
PLEASE HELPPP
Answer:
-5
Step-by-step explanation:
think of it on a number line the number furthest to the left is always the smallest and the numbers to the right are bigger
Answer:
-5
Step-by-step explanation:
On a number line, there are negative and positive numbers.
The numbers -2, -4, and -5 are negative (see the little dash sign - ? that's negative).
2 is positive (you see no sign or a plus + before it).
The number line is a good way to learn negative and positive numbers.
go left, and the numbers go smaller
go right and they get bigger
-5 is the smallest since it is the most far left on the number line.