Answer:
[tex]|x - y| > 10[/tex] ---- Nita wins
[tex]|x - y| < 10[/tex] --- Eric wins
Step-by-step explanation:
The complete instruction is to determine the range at which Erik or Nita wins.
To start with, let
[tex]x \to[/tex] Erik's score
[tex]y \to[/tex] Nita's score
If the difference is greater than 10, the Nita wins.
This implies that:
[tex]|x - y| > 10[/tex] ---- Nita
If less than 10, then Eric wins
This implies that:
[tex]|x - y| < 10[/tex] --- Eric wins
Now, assume that Nita chose 5.
For Nita to win, we have:
[tex]|x - y| > 10[/tex]
[tex]|x - 5| > 10[/tex]
Remove the absolute symbol
[tex]-10 > x - 5 > 10[/tex]
Split
[tex]-10 > x - 5\ or\ x - 5 > 10[/tex]
Solve for x
[tex]5 -10 > x \ or\ x > 10 + 5[/tex]
[tex]-5> x \ or\ x > 15[/tex]
Rewrite as:
[tex]x< -5 \ or\ x > 15[/tex]
x cannot be negative.
So:
[tex]x > 15[/tex]
x cannot exceed 20.
So:
[tex]15 < x \le 20[/tex]
Math! Help Marking brainliest if it's correct and Explain
Answer:
Option C : Step 3After harvesting, she weighs each pumpkin on a scale and records its height
On Tuesday, 14 students handed in a permission slip for a field trip. On Thursday, twice as many students handed in their permission slip than on Tuesday. On Friday, an additional 7 students turned in their permission slip. What expression could be used to find the total number of permission slips handed in?
14 x 2 + 7
14 + (2 x 14) + 7
14 + (2 x 7)
14 ÷ (2 x 7) + 14
Sheldon spins the two spinners below one time what are the chance he will spin 3 or c ?
Answer:
[tex]P(3\ or\ c) = 0.45[/tex]
Step-by-step explanation:
Given
See attachment for spinner
Required
[tex]P(3\ or\ c)[/tex]
From the first spinner, we have:
[tex]S = \{1,2,3,4,5\}[/tex] --- Sample Space
[tex]n(S)=5[/tex]
So, P(3) is:
[tex]P(3) = \frac{n(3)}{n(S)}[/tex]
[tex]P(3) = \frac{1}{5}[/tex]
[tex]P(3) = 0.20[/tex]
From the second spinner, we have:
[tex]S = \{a,b,c,d\}[/tex]
[tex]n(S) = 4[/tex]
So, P(c) is:
[tex]P(c) = \frac{n(c)}{n(S)}[/tex]
[tex]P(c) = \frac{1}{4}[/tex]
[tex]P(c) = 0.25[/tex]
The required probability is then calculated as:
[tex]P(3\ or\ c) = P(3) + P(c)[/tex]
[tex]P(3\ or\ c) = 0.20 + 0.25[/tex]
[tex]P(3\ or\ c) = 0.45[/tex]
what is (20)+(475)? I need it now
3 x 1/2 in fraction form
Answer:
3*1/2= 3/2
Step-by-step explanation:
[tex]\frac{3}{1}[/tex]*[tex]\frac{1}{2}[/tex] = 3/2
3*1/2= 3/2
3 is equal to 3/1
we then directly multiply
equation: (3/1)(1/2)
(3/1)(1/2)
3*1 = 3
1*2= 2
3/2 or 1 1/2.
How do you write in fraction form?
Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenth place, so we place 6 over 10 to create the equivalent fraction, 6/10.
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A certain type of automobile battery is known to last an average of 1,150 days with a standard deviation of 40 days. If 100 of these batteries are selected, find the following probabilities for the average length of life of the selected batteries. (Round your answers to four decimal places.) A button hyperlink to the SALT program that reads: Use SALT. (a) The average is between 1,142 and 1,150. (b) The average is greater than 1,158. (c) The average is less than 950.
Answer:
a) 0.4772 = 47.72% probability that the average is between 1,142 and 1,150.
b) 0.0228 = 2.28% probability that the average is greater than 1,158.
c) 0 = 0% probability that the average is less than 950.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
A certain type of automobile battery is known to last an average of 1,150 days with a standard deviation of 40 days.
This means that [tex]\mu = 1150, \sigma = 40[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{40}{\sqrt{100}} = 4[/tex]
(a) The average is between 1,142 and 1,150.
This is the pvalue of Z when X = 1150 subtracted by the pvalue of Z when X = 1142. So
X = 1150
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1150 - 1150}{4}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
X = 1142
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1142 - 1150}{4}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.5 - 0.0228 = 0.4772
0.4772 = 47.72% probability that the average is between 1,142 and 1,150.
(b) The average is greater than 1,158.
This is 1 subtracted by the pvalue of Z when X = 1158. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1158 - 1150}{4}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
1 - 0.9772 = 0.0228
0.0228 = 2.28% probability that the average is greater than 1,158.
(c) The average is less than 950.
This is the pvalue of Z when X = 950. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{950 - 1150}{4}[/tex]
[tex]Z = -50[/tex]
[tex]Z = -50[/tex] has a pvalue of 0
0 = 0% probability that the average is less than 950.
C u m s t e r g o i n t r e b a r e de pe b r a i n l y?
Answer:rf JAMES CHARLE's?!?
Step-by-step explanation:
6 members of the Benton family are going to their school's Community Day. They have a coupon for $4.50 off their total. If they pay $40.50 for all their tickets, how much does one ticket cost without the coupon?
Answer:
$7.50
Step-by-step explanation:
you add 40.50 + 4.50 which then equals 45 and you divide that by 6 and you get 7.50
One ticket costs $7.50 without the coupon this we obtained by dividing total cost before discount by Number of tickets
Let us find the total cost of the tickets before the coupon is applied. We can do this by adding the discount amount ($4.50) to the final cost ($40.50):
Total cost before discount = Final cost + Discount amount
Total cost before discount = $40.50 + $4.50
Total cost before discount = $45.00
Now we can divide the total cost before discount by the number of tickets
(6) to find the cost of one ticket:
Cost of one ticket = Total cost before discount / Number of tickets
Cost of one ticket = $45.00 / 6
Cost of one ticket = $7.50
Therefore, one ticket costs $7.50 without the coupon.
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Bonus Is the point (-3, -5) inside, outside, or on the circle whose equation is (x + 7)² + (y − 2)² = 62? (SOMEONE PLEASE EXPLAIN!!)
Answer:
Outside, as the distance between the point and the center of the circle is more than the radius.
Step-by-step explanation:
Equation of a circle:
The equation of a circle has the following format:
[tex](x-x_0)^2 + (y-y_0)^2 = r^2[/tex]
In which [tex](x_0,y_0)[/tex] is the center and r is the radius.
Testing if a point is inside the circle:
Point (x,y), we replace in the equation. If it is less than the radius squared(in this case, 62), it is in.
In this question:
Point (-3,-5). So
[tex](-3+7)^2 + (-5-2)^2 = 4^2 + (-7)^2 = 16 + 49 = 65[/tex]
The square distance of the point to the center is of 65, which is more than the square of the radius, meaning that the point is outside the circle.
Answer:
Outside
Step-by-step explanation:
Given a circle with a circumference of 30pi inches, solve for the exact area of a sector in terms of pi, whose central angle is one-fifth of the measure of the
circle.
LE
11. The diagram shows two night-angled triangles, joined together along a common side
AB = 10-8 cm, BC = 14 4 om and CD = 24 cm.
24 am
10-8 cm
B
14-4 cm
Diagram noi drawn to scale
Calculate the area of triangle ACD.
You must show all your working.
Answer:
216 cm²
Step-by-step explanation:
Area of ∆ACD = ½*CD*CA
CD = 24 cm
CA = ?
Use pythagorean theorem to find CA.
Thus:
CA² = AB² + BC²
Substitute
CA² = 10.8² + 14.4² = 324
CA = √324
CA = 18 cm
Area of ∆ACD = ½*CD*CA
Substitute
Area = ½*24*18
= 216 cm²
Ebony discovered she had $8 in quarters how many quarters are there in $8 choose the division expression you would use to find the number of quarters and $8
1. $8 ÷4
2. $8 ÷ 1/4
3. $8 ÷ 1/2
Approximate the value of 5(pi)
A)Slightly more than 20
B)Slightly less than 15
C)Slightly more than 15
D)Slightly less than 20
Answer: C
Step-by-step explanation: 5pi converts to 15.70796
Answer:
slightly less than 15 of b.
The 7 times the sum of a
number and 6 IS 63
Answer:
Missing number = 3
Step-by-step explanation:
Let [tex]x[/tex] be the missing number. We have the following:
[tex]7\cdot (6+x)=63,\\6+x=9,\\x=\boxed{3}[/tex]
A. 1/3
B. 1
C. 2
D. 3/1
E. 1/2
F. 2/3
Answer:
B
Step-by-step explanation:
the graph is completely proportional so the answer would be 1
if n is an integer,what is the sum of the next three consecutive even integers greater than 2n?
Answer:
6n + 12
Step-by-step explanation:
Given an integer n, the 3 consecutive even integers greater than 2n are 2n+2, 2n+4 and 2n+6
Taking their sum;
Sum = (2n+2)+(2n+4)+(2n+6)
Sum = 2n+2n+2n+2+4+6
Sum = 6n + 12
Hence the sum of the 3 consecutive even integers greater than 2n is 6n+12
You are walking along a path y= 2x + 12 and your
best friend is walking along 4x + y = 6. At what point will
you cross paths?
Answer:
(-1,10)
Step-by-step explanation:
At the point when the paths cross, the respective x and y values of each equation will be equal.
Your path is y=2x+12, and your friends path is 4x+y=6. Sub 2x+12 in for y (from your path's equation) into your friends equation to find the value of x:
4x+2x+12=6
6x=-6
x=-1
y=2x+12
y=2(-1)+12=10
So you will cross paths at (-1,10)
5c + 2d^2 if c = 6 and d = 3
Answer:
48
Step-by-step explanation:
Substitute c=6 and d=3 in your formulas
[tex]5*6 + 2*3^{2}\\ 30 + 18\\48[/tex]
In the paper airplane shown , ABCD=EFGH, m
Answer:
i would think it would be the same as angle bcd so 90
Step-by-step explanation:
Si en un examen 27 preguntas son correctas el 90%, cuántas preguntas son en total?
Respuesta:
30
Explicación paso a paso:
Número total de preguntas = 100%
Número de preguntas correctas = 27
Porcentaje de aciertos = 90%
Por eso,
Si 90% = 27
Luego ; 100% = x
Multiplicar en cruz:
0,9 veces = 27
x = 27 / 0,9
x = 30
Número de preguntas = 30
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. What value of x satisfies this equation? 1.5(4)^2x=12 Round your answer to the nearest hundredth. The value of x is .
Answer:
O.75
Step-by-step explanation:
The value of x in the equation 1.5(4)^2x is equal to 12 is 3/4 after equation the power of same base.
What is integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
We have an equation:
[tex]\rm 1.5(4)^2^x=12[/tex]
[tex]\rm (4)^2^x=8[/tex]
[tex]\rm (2^2)^{2x}= 2^3[/tex]
[tex]\rm 2^{4x}=2^3[/tex]
4x = 3 (equating powers of same base)
x = 3/4
Thus, the value of x in the equation 1.5(4)^2x is equal to 12 is 3/4 after equation the power of same base.
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1 mark question please answer me
Given:
The polynomial is:
[tex]P(x)=ax+b[/tex]
To find:
Whether [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial or not.
Solution:
We have,
[tex]P(x)=ax+b[/tex]
Putting [tex]x=-\dfrac{b}{a}[/tex], we get
[tex]P(-\dfrac{b}{a})=a(-\dfrac{b}{a})+b[/tex]
[tex]P(-\dfrac{b}{a})=-b+b[/tex]
[tex]P(-\dfrac{b}{a})=0[/tex]
Since the value of the given polynomial is 0 at [tex]x=-\dfrac{b}{a}[/tex], therefore [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial.
HELP I NEED TO DO THIS NOW
Answer: The answer is 1:2, i hope it helps.
find the slope intercept form (y=mx+b)
Answer:
5/9??? I think thats the answer
CAN SOMEONE HELP ME PLEASE ASAP
Answer:for the permieter dont you just add both sides?
Step-by-step explanation:
Use two unit multipliers to convert 4000 square inches to square feet.
Answer:
(4000 in^2) * (1 ft/12 in)^2 = 27 7/9 ft^2
Step-by-step explanation:
4,000 Square Inches =
27.777778 Square Feet
Martha Stewart needs a total of 520 napkins for her restaurant. She currently has 234 napkins. If each package of napkins has 20 napkins, what is the minimum number of packets of napkins she should buy? Write an algebraic equation, solve, and conclude.
Answer:
520=20x+234
15 packages
Step-by-step explanation:
520-234
286
286/20
14.3, so she needs 15 packages
HELPP ASAP DONT SEND A FILE PLS WHATS THE RULE FOR THIS TRANSFORMATION FOR ROATIONS QUESTION 5 ? I ONLY A FEW MINUTES PLZ HELP
Answer:
90-degree clockwise rotation: (x,y)⇒(y,-x)
Step-by-step explanation:
For D⇒D', (0,-3)⇒(-3,0)
For E⇒E', (2,-1)⇒(-1,-2)
For F⇒F', (5,-3)⇒(-3,5)
We can see that the pattern here is (x,y)⇒(y,-x), which is the rule for a 90-degree clockwise rotation.
simplify 1/3 : 2.5 : 3 3/4
Answer:
1/3x3 3/4 /2.5 = 0.3
Given
f(x) = 2x - 1 and g(x) = 4x + 6,
which operation completes the statement?
f(x) ___ g(x) = 8x^2 + 8x - 6
i need to determine what math sign i have to use on the ____ the options are *,+,-, and the divide symbol
this is operations on functions!!!
f(x) times g(x) = 8x^2+8x-6
(2x-1) times (4x+6) = 8x^2+8x-6
====================================================
Explanation:
The functions f(x) and g(x) are linear functions. The result of f(x) ___ g(x) is some quadratic function.
It's very likely that the answer is a multiplication sign because of the general template of
(linear)*(linear) = (quadratic)
For example, x*3x = 3x^2.
Let's see if the two functions multiply out to 8x^2+8x-6 or not.
-----------------------
f(x) * g(x) = ( f(x) ) * ( g(x) )
f(x) * g(x) = ( 2x-1 ) * ( 4x+6 )
f(x) * g(x) = y * ( 4x+6 ) ......... let y = 2x-1
f(x) * g(x) = 4xy + 6y ......... distribute
f(x) * g(x) = 4x( y ) + 6( y )
f(x) * g(x) = 4x( 2x-1 ) + 6( 2x-1 ) .... replace y with 2x-1
f(x) * g(x) = 8x^2-4x + 12x-6 .... distribute twice more
f(x) * g(x) = 8x^2+8x-6
We end up getting the correct result. So this confirms that a multiplication sign is needed to fill in the blank.