Answer:
range = 18 and SD = 6
Step-by-step explanation:
range = max - min
= 228 - 210
= 18
FOR STANDARD DEVIATION * USE A SCIENTIFIC CALCULATOR THEY WON'T PENALIZE YOU*
follow these steps:
1. press mode then STAT
2. then press 1-VAR
3. put all the numbers on the table in ascending order
4 after press AC
5. press shift then 1
6. you will see many things but we are only interested in standard deviation, press *Var*
7. then select the standard deviation sign and press the equal sign
Help! I need help with this math problem
Answer:
h(-1) is -1, h(-0.5) is 0 and h(1) is 1.
Step-by-step explanation:
functions :- an expression, rule or law that defines relationship between one variable and another variable. When a certain condition is fulfilled, then the result is corresponding to that condition.
h(-1)In the function it is given that when x∈(-2,-1] then we get -1. Now here x=-1 satisfies the given condition. So, the answer will be -1.
h(-0.5)In the function it is given that when x∈(-1,0] then we get 0. Now here x=-0.5 lies in the range (-1,0]. So, the answer is 0.
h(1)In the function it is given that when x∈(0,1] then we get 1. Clearly, x=1 satisfies this range of values. So, we get 1.
Hence, the Answer is h(-1) = -1, h(-0.5) = 0 and h(1) = 1.
know more about functions at brainly.com/question/15912209
#SPJ10
The Wilson family had 5 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had
at least 3 girls?
at most 3 girls?
The expression represents the probability of getting exactly 3 heads is,
[tex]C(n,r)(0.5)^3(0.5)^6[/tex]
We have given
Aron flips a penny 9 times.
We have to determine
Which expression represents the probability of getting exactly 3 heads
What is binomial distribution?The binomial distribution is determined as the probability of mass or discrete random variable which yields exactly some values.
The binomial probability formula shown has variables that represent:
[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]
Where n is the total number of trials (here, we flip penny 9 times, hence n = 9).
r is the number we want to find (here, we want the probability of 3 heads, so r = 3).
p is the probability of success (here, success means getting heads.
So, in a coin flip the probability of heads is always 1/2, so p = 1/2).
Therefore, The expression represents the probability of getting exactly 3 heads is;
[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]
[tex]=C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex]
Hence, the expression represents the probability of getting exactly 3 heads is [tex]C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex].
To learn more about Binomial Distribution visit:
brainly.com/question/7236644
#SPJ1
The probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given the probability of a child being girl is 0.5, therefore, the probability of a child being boy is 0.5. Now, the probability of at least 3 girls out of 5 is,
Probability (x≥3)
= ⁵C₃ (0.5)³(0.5)² + ⁵C₄ (0.5)⁴(0.5)¹ + ⁵C₅(0.5)⁵(0.5)⁰
= 0.5
Probability (x≤3)
= ⁵C₃ (0.5)³(0.5)² + ⁵C₂(0.5)²(0.5)³ + ⁵C₁(0.5)¹(0.5)⁴ + ⁵C₀(0.5)⁰(0.5)⁵
= 0.8125
Hence, the probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.
Learn more about Binomial Distribution:
https://brainly.com/question/14565246
#SPJ1
Prove triangle ABC is congruent to triangle DEC.
Triangle ABC and DEC are said to congruent since all their sides and angles are equal.
How to prove the statementThe angle for triangle ABC lies in angle B
The angle for triangle DEC lies in angle E
From the diagram, angles B and E are alternate angles and alternate angles are equal.
A corresponds to D
B corresponds to E
The measure of their angles are also equal
Note, congruent triangles are triangles with three corresponding sides and angles
Therefore, triangle ABC and DEC are said to congruent since all their sides and angles are equal.
Learn more about congruent triangles here:
https://brainly.com/question/1675117
#SPJ1
Determine the equation of the line that passes through the given points. (If you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.) (-5, 10) and (5, -10) a. y = 2x-10 b. C. d. y = 2x y = -2x+ 20 y=-2x A
Answer:
y = -2x
Step-by-step explanation:
It passes through -5, 10 and 5, -10
gradient = Δy/Δx
gradient = -10 - 10 / 5 -- 5
gradient = -20 / 10
gradient = -2
let's use -5, 10 for y = mx + b
10 = -2(-5) + b
10 = 10 + b
b = 10 - 10
b = 0.
the equation of the line is just y = -2x
What is −7.6 − 2(2.2)
Answer:
-12
Step-by-step explanation:
Order of operations:
PEMDAS
First, do parenthesis, 2 x 2.2 = 4.4 then do -7.6 - 4.4 = -12
1
0/1 point
A student wants to write an expression for, "all of the elements which are not in set A but are in set B".
The way to write this expression in mathematics is A'∩B
How to solve for the expressionIn order to get the right way to write this expression we have to break it down in two parts.
First we are told that some of the elements are not in A.
This is represented as A'.
Then we are told that they are in the set B. Hence we have it written as B.
Then the expression not in set A but are in set B would be written as
A'∩B.
Read more on sets here:
https://brainly.com/question/13458417
#SPJ1
For the first 8 months at his new job, James gets
an increase in pay. What is the rate at which
James receives a pay increase? Approximately
what was his starting pay? Write an equation to
model the relationship.
James receives a pay increase of 100% per month and has a starting salary of $500.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let b represent the rate of pay increase and a represent the initial pay.
Let us assume that he had received 128000 after the 8 months. hence:
128000 = ab⁸ (1)
Also in the 10th month, he had received 512000, hence:
512000 = ab¹⁰ (2)
From the both equations:
a = 500, b = 2
rate of increase = 200% - 100% = 100%
James receives a pay increase of 100% per month and has a starting salary of $500.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
How do you solve 32-34?
Answer:
32. {-4, 1, 2, 12}
33. {2, 6, 9, 31, 65}
34. No
Step-by-step explanation:
32. The domain of a relation is the set that contains all the x-coordinates of all the ordered pairs of the relation.
domain = {-4, 1, 2, 12}
33. The range of a relation is the set that contains all the y-coordinates of all the ordered pairs of the relation.
range = {2, 6, 9, 31, 65}
34. No since the same number, 2, appears twice as an x-coordinate. In a function, no two ordered pairs can have the same x-coordinate.
Consider the proof.
Given: In △ABC, BD ⊥ AC
Prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A)
Triangle A B C is shown. A perpendicular bisector is drawn from point B to point D on side A C. The length of B C is a, the length of D C is b minus x, the length of A D is x, the length of A B is c, and the length of B D is h.
Statement
Reason
1. In △ABC, BD ⊥ AC 1. given
2. In △ADB, c2 = x2 + h2 2. Pythagorean thm.
3. In △BDC, a2 = (b – x)2 + h2 3. Pythagorean thm.
4. a2 = b2 – 2bx + x2 + h2 4. prop. of multiplication
5. a2 = b2 – 2bx + c2 5. substitution
6. In △ADB, cos(A) = StartFraction x Over c EndFraction 6. def. cosine
7. ccos(A) = x 7. mult. prop. of equality
8. a2 = b2 – 2bccos(A) + c2 8. ?
9. a2 = b2 + c2 – 2bccos(A) 9. commutative property
What is the missing reason in Step 8?
Pythagorean theorem
definition of cosine
substitution
properties of multiplication
The missing reason in Step 8 is substitution
When a triangle is not a right triangle and when either the lengths of two sides and the measurement of the included angle are known (SAS) or the lengths of the three sides are known (SSS), the Law of Cosines is used to discover the remaining pieces of the triangle.
According to the law of cosine, if a, b, and c are any triangle's three sides, then a² = b² + c² - 2bcosa
The x in statement 5 of the preceding proof is changed to c cos A from statement 6 in statement 8 of the proof.
Option C, from the list of alternatives, is the one that best explains statement 8.
Hence missing reason in Step 8 is substitution
Learn more about substitution here:
https://brainly.com/question/190818
#SPJ10
Answer: OPTION C
Step-by-step explanation:
EDGE22
PLEASE HELP AND SHOW WORK PLEASE.
How is this a no solution answer? I came out with the answer x < -2 and x ≥ 5
5 - x > 7 and 2x + 3 ≥ 13
Inequalities help us to compare two unequal expressions. There exists no solution to the given set of inequalities.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given Inequalities can be solved as,
5 - x > 7
-x > 7 - 5
-x > 2
x < -2
2x + 3 ≥ 13
2x ≥ 10
x ≥ 5
As per the solution of the two inequalities, the value of x should be less than -2 but at the same time, it should be more than or equal to 5, which is impossible. Thus, there is no solution for the given inequalities.
This can be confirmed by graphing the two inequalities, as shown below. Since there is no area in common between the two inequalities, there exists no solution to the given set of inequalities.
Learn more about Inequality:
https://brainly.com/question/19491153
#SPJ1
There were 582 students enrolled in a freshman-level chemistry class. By the end of the semester, the number of students who passed was 5 times the number of students who failed.
Answer:
let the no. of students who failed the examination be X
therefore, no. of students passed = 5x
total no. of students = 582
5x + X = 582
6x = 582
x = 97
no. of students failed the examination = 97
no. of students passed = 97*5 = 485
Suppose that
f
(
x
,
y
)
=
x
+
5
y
f
(
x
,
y
)
=
x
+
5
y
at which
−
1
≤
x
≤
1
,
−
1
≤
y
≤
1
-
1
≤
x
≤
1
,
-
1
≤
y
≤
1
.
Absolute minimum of
f
(
x
,
y
)
f
(
x
,
y
)
is
Absolute maximum of
f
(
x
,
y
)
f
(
x
,
y
)
is
========================================================
Explanation:
The range of x values is [tex]-1 \le x \le 1[/tex] which means x = -1 is the smallest and x = 1 is the largest possible.
Similarly the smallest y value is y = -1 and the largest is y = 1.
----------
Plug in the smallest x and y value to get
f(x,y) = x+5y
f(-1,-1) = -1+5(-1)
f(-1,-1) = -6
Therefore, the absolute min is -6
----------
Now plug in the largest x and y values
f(x,y) = x+5y
f(1,1) = 1+5(1)
f(1,1) = 6
The absolute max is 6
Which number comes next in this series 1/64 1/32 1/16 1/8 1/4 1/2
Answer:
1/1
Step-by-step explanation:
As the question is halfing by 2
So
2 divide 2 equals 1
Answer:
1
Step-by-step explanation:
it's fractions of divided half. next one will be number 1
Select all the correct graphs.
Choose the graphs that indicate equations with no solution.
Answer:
First Graph: -2x - 1 = 3(^-x)
Last Graph: 2^(-x) + 2 = 5^-x + 3
Step-by-step explanation:
For a system of equations to have a solution set, the graphs that depict them must intersect at one point.
Both graphs #1 and #5 do not intersect, hence graphs #1 and #5 are the only graphs that do not have solutions while the other graphs do.
Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.5 cm tall. How many cotton swabs tall will your model be? If necessary, round your answer to the nearest whole number.
Answer:
6.3 *30= 189; so 4 cotton swabs
46. Machine A produces 500 springs a day. The number of defective springs produced by this machine each day is recorded for 60 days. Based on the distribution given below, what is the expected value of the number of defective springs produced by Machine A in any single day?
F. 0.00
G. 0.45
H. 0.70
J. 1.00
K. 1.50
Answer:
G. 0.45
Step-by-step explanation:
To find expected value, you simply multiply the value of each outcome (the numbers in the left column) by its probability
(the numbers in the right column) and then add them all together.
0(0.7) + 1(0.2) + 2(0.05) + 3(0.05)
0 + 0.2 + 0.1 + 0.15 = 0.3 + 0.15 = 0.45
The expected value is 0.45. Thus, the correct option is G.
What is the expected value?In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
The expected value is calculated as,
E(x) = 0 x 0.70 + 1 x 0.20 + 2 x 0.05 + 3 x 0.05
E(x) = 0 + 0.20 + 0.10 + 0.15
E(x) = 0.45
Thus, the correct option is G.
More about the expected value link is given below.
https://brainly.com/question/13945225
#SPJ2
Think about all of the ways in which a circle and a parabola can intersect.
Select all of the number of ways in which a circle and a parabola can intersect.
00
1
2
03
04
05
DONE
There will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have a circle and a parabola:
As we know the standard form of a circle:
[tex]\rm (x-h)^2 +(y-k)^2=r^2[/tex]
The standard form of the parabola:
[tex]\rm y = a(x-h)^2+k[/tex]
If we plug the value of y from the parabola equation in the circle equation, we get a quartic equation(4th order equation)
The solution of the quartic equation will be 4.
Thus, there will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
Learn more about circle here:
brainly.com/question/11833983
#SPJ1
A farmer has 250 ft of fencing and wants to enclose a rectangular area of 3750 ft². What dimensions should she use?
The length of the longer side of the fence is:
The length of the shorter side of the fence is:
Answer:
Longer side is 75 feet, shorter side is 50 feet.
Step-by-step explanation:
Let l be the length of the longer side and w be the length of the shorter side.
2l + 2w = 250, which simplifies to
l + w = 125. Solving for w, we have
w = 125 - l.
lw = l(125-l) = 3750
[tex] {l}^{2} - 125l - 3750 = 0[/tex]
[tex]( l - 50)(l - 75) = 0[/tex]
l = 75, w = 50
Which expression can be used to find the difference of the polynomials?
The expression that can be used to find the difference of the polynomials is (4m - 5) + ( -6m + 7 - 2n). D
How to find the difference
Given the expression:
(4m - 5) - (6m - 7 + 2n)
Note that - * - = +
+ * - = -
So in finding the difference, we have
(4m - 5) - ( 6m + 7 - 2n )
It could as be written as
(4m - 5) + ( -6m + 7 - 2n)
Therefore, the expression that can be used to find the difference of the polynomials is (4m - 5) + ( -6m + 7 - 2n) . D
Learn more about polynomials here:
https://brainly.com/question/4142886
#SPJ1
Please solve this equation, I don't understand...
show all work!
Answer:
x = - 5/2
Step-by-step explanation:
Using the law of indices
. a^-n = 1/a^n
. (a^4)^5 = a^5×4 = a^20
Note : When two base are equal , we equate the Exponents.
3^4x-5 = (1/27)^2x+10
= 3^4x-5 = (27^-1)^2x+10
= 3^4x-5 = (3^-3)^2x+10
= 3^4x-5 = 3^ -3(2x+10)
= 3^4x-5 = 3^ -6x-30
The two base are 3 so we equate the exponents.
= 4x - 5 = -6x - 30
= 4x + 6x = -30+5
= 10x = -25
= 10x/10 = -25/10
x = -25/10
x = - 5/2
X is -5/2
Given mCT=26 and m/CAT =124° find the length of CA, the radius in Circle A. Use
π = 3.14 in your calculation and round to the nearest tenth.
Answer:
[tex]\text{length of \textit{CA}} \ = \ 12.0 \ \ \ (\text{nearest tenth})[/tex]
Step-by-step explanation:
Radian measure is the ratio of the length of a circular arc to its radius.
A radian is the measurement of the central angle which subtends an arc whose length is equal to the length of the radius of the circle.
In the case of the unit circle, as shown in the figure below, one radian is the angle of the sector with a radius of 1 and circular arclength of 1.
Following this definition, the magnitude, in radians, of one complete revolution of a unit circle is the circumference of the unit circle divided by its radius, [tex]\displaystyle\frac{2\pi}{1}[/tex] or [tex]2\pi[/tex]. Thus, [tex]2\pi[/tex] radians is equal to [tex]360^{\circ}[/tex] degrees. Alternatively, one radian is equal to [tex]\displaystyle\frac{180^{\circ}}{\pi} \ \approx \ 57.296^{\circ} \ \ \ (3 \ d.p.)[/tex].
Since radian measure is defined as the ratio of the arc length of a sector to its radius, hence
[tex]\displaystyle\frac{s}{r} \ = \ \theta \\\\ s \ = \ r\theta[/tex]
where [tex]s[/tex] is the arclength, [tex]r[/tex] is the radius, and [tex]\theta[/tex] is the central angle, in radians.
Therefore, the length of CA is
[tex]\displaystyle\frac{s}{\theta} \ = \ r \\ \\ r \ = \ \displaystyle\frac{26}{124^{\circ} \ \times \ \displaystyle\frac{\pi}{180^{\circ}} \ \text{rad}} \\ \\ r = \displaystyle\frac{26 \ \times \ 45}{31 \ \times \ 3.14} \\ \\ r\ = \ 12.0 \ \ \ \ \left(\text{nearest tenth}\right)[/tex]
A car has a maximum speed of 355.7 feet/second. Convert this speed to miles/hour.
Answer:
242.5226626 mphStep-by-step explanation:
1 ft/s = 0.681818 mph
355.7 * 0.681818 = 242.5226626
355.7 ft/s = 242.5226626 mph
If 3x − 6 ≤ f(x) ≤ x2 − 3x + 3 for x ≥ 0, find lim x→3 f(x).
Answer:
Step-by-step explanation:
1) When the polynomial P(x) is divided by x+5, the remainder is 3. Which of the following is definitely true?
a) P(3) = 5
b) P(-5) = 3
c) P(5) = 3
d) P(-3) = 5
2) P is a degree 3 polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i. What is the other zero?
a) 4-3i
b) 4+3i
c) -5
d) 3-4i
1) The definitely true for the statement is b) P(-5) = 3.
2) The three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
What is the remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x)
Given;
1) When the polynomial P(x) is divided by x+5, the remainder is 3.
If a polynomial P(x) is divided by (x-a), then the remainder is P(a).
If the polynomial P(x) is divided by (x+5), then the remainder will be P(-5).
So, P(-5) = 3
Therefore, the definitely true for the statement is b) P(-5) = 3.
2) P is a 3 degree polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i.
The complex roots always exist in conjugate pairs so,
3 + 4i and 3 - 4i
Thus, the three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
Learn more about polynomial :
https://brainly.com/question/16399195
#SPJ1
solve the system of equations for one of the variables x+4y=5 x-4y=5
Answer:
x=5 y=0
Step-by-step explanation:
cancel out the 4y's and then add the x's together. also add the 5s together. 2x = 10, x = 5, and plug it in, and 5 cancels out, leaving y by itself.
Which expression is equivalent to (a²b¹c)²(6a³b)(2c³)³₂ 4ab¹2c3 ?
The expression (a²b¹c)² × (6a³b) × (2c³)³ × (4ab¹) × (2c³) is equivalent to the expression 384a⁸b⁴c¹⁴.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given below.
⇒ (a²b¹c)² × (6a³b) × (2c³)³ × (4ab¹) × (2c³)
By simplifying, we have
⇒ a⁴b²c² × 6a³b × 8c⁹ × 4ab¹ × 2c³
⇒ 384a⁸b⁴c¹⁴
More about the equivalent link is given below.
https://brainly.com/question/889935
#SPJ1
WILL GIVE THE BRAINLIEST!
If r and s are real numbers such that
r>s>0, then
(A) -s>-r> 0.
(B) 0>-r> -s.
(C) 0> -s> -r.
(D) -s>0> -r.
(E) -r> -s > 0.
Answer: Choice (C) 0> -s> -r
==========================================================
Explanation:
Let's consider an example. Pick any two positive numbers for r and s, where r is larger than s. I'll go with these:
r = 5s = 2We see that r > s is true since 5 > 2 is true
Also both are larger than 0 so we can say r > 0 and s > 0
This all combines into r > s > 0 being the case.
If we negate each number, then -r > -s would no longer be true. Use a number line to see that -5 is to the left of -2, so -5 > -2 is not true. Instead it would be -5 < -2
You can think of it like floors on a skyscraper. Positive numbers are above ground, while negative numbers are below ground in the basement levels. See the diagram below.
So -r > -s must be -r < -s instead. Both are smaller than 0
-r < 0 and -s < 0
This combines to -r < -s < 0
Flip everything and swap the outer sides to get 0 > -s > -r which leads us to choice C as the final answer
Simplify the expression -3z(1.8z-2.2).
-5.4z² + 6.6z
-5.4z²-6.6z
-1.2z²+5.2z
-1.2z²-5.2z
Mark this and return
Save and Exit
Next
Submit
Answer:
[tex] - 5.4z {}^{2} + 6.6z[/tex]
Step-by-step explanation:
Given:
[tex]-3z(1.8z-2.2)[/tex]
Solution:
Applying Distributive property,we obtain
[tex](−3z)(1.8z)+(−3z)(−2.2)[/tex]Simplifying using PEMDAS:
[tex] - 5.4z {}^{2} + 6.6z[/tex]Done!
Answer:A
Step-by-step explanation:
If f(x) = x + 8 and g(x) = –4x – 3, find (f + g)(x).
A. (f + g)(x) = 5x + 11
B. (f + g)(x) = –3x + 5
C. (f + g)(x) = –5x – 11
D. (f + g)(x) = 3x – 5
Answer:
B
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= x + 8 - 4x - 3 ← collect like terms
= - 3x + 5
Answer:
[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]
Step-by-step explanation:
Given functions:f(x) = x + 8g(x) = -4x - 3Solution:Add both functions
(f + g)(x) = x + 8 + (-4x - 3)
(f + g)(x) = x + 8 - 4x - 3
(f + g)(x) = x - 4x + 8 - 3
(f + g)(x) = -3x + 5
[tex]\rule[225]{225}{2}[/tex]
Find the slope of the line passing through the points (3,-9) and (2, -3).
Answer:
The slope of the line passing through is -6.