Answer:
Two solutions.
[tex]x = 8, -6[/tex]
Step-by-step explanation:
Given the equation:
[tex]\left|x-1\right|=7[/tex]
To find:
Number of solutions to the equation.
Solution:
First of all, let us learn about modulus function.
[tex]|x|=\left \{ {{x\ if\ x>0} \atop {-x\ if\ x<0}} \right.[/tex]
i.e. Modulus function changes to positive by adding a negative sign to the negative values.
It has a value equal to [tex]x[/tex] when [tex]x[/tex] is positive.
It has a value equal to -[tex]x[/tex] when [tex]x[/tex] is negative.
Here, the function is:
[tex]|x-1|=7[/tex]
So, two values are possible for the modulus function:
[tex]\pm(x-1)=7[/tex]
Solving one by one:
[tex]x-1 = 7\\\Rightarrow x =8[/tex]
[tex]-(x-1) = 7\\\Rightarrow -x+1=7\\\Rightarrow x = -6[/tex]
So, there are two solutions, [tex]x = 8, -6[/tex]
In a family with children, the probability that all the children are girls is appoximately . In a random sample of 1000 families with children, what is the approximate probability that or fewer will have girls? Approximate a binomial distribution with a normal distribution.
Answer:
The probability that 100 or fewer will have 3 girls is 0.00734.
Step-by-step explanation:
The complete question is:
In a family with 3 children, the probability that all the children are girls is approximately 0.125. In a random sample of 1000 families with 3 children, what is the approximate probability that 100 or fewer will have 3 girls? Approximate a binomial distribution with a normal distribution.
Solution:
Let X represent the number of families who has 3 girls.
The random variable X follows a Binomial distribution with parameters n = 1000 and p = 0.125.
But the sample selected is too large.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
1. np ≥ 10
2. n(1 - p) ≥ 10
Check the conditions as follows:
[tex]np=1000\times 0.125=125>10\\\\n(1-p)=1000\times (1-0.125)=875>10[/tex]
Thus, a Normal approximation to binomial can be applied.
So, [tex]X\sim N(\mu=np,\sigma^{2}=np(1-p))[/tex]
The mean and standard deviation are:
[tex]\mu=np=1000\times 0.125=125\\\\\sigma=\sqrt{np(1-p)}=\sqrt{1000\times 0.125\times (1-0.125)}=10.46[/tex]
Compute the probability that 100 or fewer will have 3 girls as follows:
Apply Continuity correction:
[tex]P(X\leq 100)=P(X<100-0.50)[/tex]
[tex]=P(X<99.50)\\\\=P(\frac{X-\mu}{\sigma}<\frac{99.5-125}{10.46})\\\\=P(Z<-2.44)\\\\=0.00734[/tex]
*Use a z-table.
Thus, the probability that 100 or fewer will have 3 girls is 0.00734.
A car is averaging 50 miles per hour. If the car maintains this speed, how many minutes less would a 450-mile trip take than a 475-mile trip?
Answer:
1/2 a minute (30 seconds)
Step-by-step explanation:
475/50=9.5
450/50=9
9-9.5=.5
I Need HELP PLEASE ANYONE U GET 5 STARS IF RIGHT ANSWER !
Answer:
4√(7^5) and (4√7)^5
Step-by-step explanation:
7^5/4
The above can be expressed as follow: Method 1:
7^5/4
(7^5)^1/4
Recall:
(a^m)^1/n = n√(a^m)
Therefore,
(7^5)^1/4 = 4√(7^5)
Method 2:
7^5/4
(7^1/4)^5
Recall:
(a^1/m)^n = (m√a)^n
Therefore,
(7^1/4)^5 = (4√7)^5
From the illustration above, we can see that 7^5/4 can be expressed as 4√(7^5) and (4√7)^5
Evaluate the following expression. −8 × (−10) −7× 1/−1
Answer:
87Step-by-step explanation:
[tex]-8\left(-10\right)-7 \times \frac{1}{-1}=87\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\\\=8\times \:10-7\times \frac{1}{-1}\\\\8\times \:10=80\\\\7\times \frac{1}{-1}=-7\\\\=80-\left(-7\right)\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\\\=80+7\\\\=87[/tex]
yoyoyo pls help with math
Answer:
C
Step-by-step explanation:
Calculate the ratio of corresponding sides, image to preimage, that is
scale factor = [tex]\frac{DE}{AB}[/tex] = [tex]\frac{14}{35}[/tex] = [tex]\frac{2}{5}[/tex] → C
Josh biked to the park at an average speed of 14 mph. He returned home at an average speed of 10 mph. If Josh spent a total of 2 1/2 hours for the roundtrip, how many total miles did he bike?
Answer:
Let the distance from home to the park be x
Going to the park
Distance=vt
x=14t¹ ——(1)
Going back home
x=10t² ——(2)
Total time=t¹+t²
2.5=t¹+t²
Solving equ. 1 and 2 simultaneously
10x=140t¹
14x=140t²
Adding
4x=140(t¹+t²)
24x=140(2.5)
x=14.58 miles
Total distance= 2x
= 29.16miles
Step-by-step explanation:
What is the scale factor in the dilation?
Answer Choices
2/5
1/2
2
2 1/2
Answer:
either 2 or 2 1/2
Step-by-step explanation:
Since the pre-image gets bigger, the scale factor is larger than 1.
Why do you think that when subtracting a negative
number, in reality you are adding it? (For example: 1-
(-1) = 1+1=2)
Answer:
See explanation
Step-by-step explanation:
When we have a positive number and a negative number, let's imagine it with a number line.
<-----------0----------->
If we have the positive number 1:
<-----------0--1-------->
And we want to subtract 1 from it, the number would move to the left
1 - 1 = 0
<-----------0----------->
However, if we were to subtract a negative number, they are opposites. It can't move to the left because that's what a positive number does. The only other way to go: right.
1 + -1 = 2
<-----------0--1--2----->
Hope this helped!
2 hours 40 minutes +11 hours 40 minutes
Answer:
14 hours 20 minutes
Step-by-step explanation:
→ Convert 2 hours and 40 minutes into minutes
2 hours + 40 minutes ⇒ 2 hours = 120 minutes + 40 minutes ⇒ 120 + 40 ⇒ 160 minutes
→ Convert 11 hours and 40 minutes into minutes
11 hours + 40 minutes ⇒ 11 hours = 660 minutes + 40 minutes ⇒ 660 + 40 ⇒ 700 minutes
→ Add the total minutes together
700 minutes + 160 minutes = 860 minutes
→ Convert 860 minutes into hours
860 minutes = 14 hours + 20 minutes
can u explain and answer this question for me thanks
Answer:
f(x)= x-6
g(x)= x^1/2 (x+3) =√x(x+3) = x √x + 3√x
g(x) × f(x)
=(x√x + 3√x) (x-6)
= x²√x -6x√x + 3x√x - 18√x
= x²√x -3x√x - 18 √x
= x^5/2 - 3x^3/2 - 18^1/2
= √x^5 - 3√x^3 - √18 (B)
Note:
√x = x^1/2
x √x = x^1 × √x= x^1+1/2= x^3/2
x²√x= x^2 × x^1/2 = x^2+1/2 = x^ 5/2
I hope this helps
if u have question let me know in comments ^_^
3.3. (08.01 LC) Find the circumference and area of a circle with a diameter of 10 inches. Leave your answers in terms of pi. (4 points) . 4. (08.01 MC) Given a cube with a volume of 27 cm3, what is the volume of a square pyramid that can fit perfectly inside the cube? (4 points)
Answer:
1. C = 10π, A = 25π
2. 9 cm³
Step-by-step explanation:
Formula for circumference = πd
Formula for area of a circle = πr²
1. Set up the equation for circumference
10π
2. Set up the equation for area (radius = 1/2diameter) and solve
π(5²) = 25π
Formula for volume of a square pyramid = 1/3s² · h
The volume of a square pyramid is equal to 1/3 of the volume of a cube. The formula for a volume of a cube is s³ which is equal to s² · h because a cube has the same side length for all sides. Therefore, the volume of a square pyramid that perfectly fits within a given cube would equal 1/3 the volume of the cube.
1. Set up the equation and solve
27 ÷ 3 = 9
Answer:
3. The fourth: C= 10π, A = 25π 4. The third: 9 cm³Step-by-step explanation:
3.
diameter is equal two radiuses
D = 10 = 2R ⇒ R = 5
circumference: C = 2πR = 2R•π = 10π
area: A = πR² = π•5² = 25π
4.
If square pyramid fit perfectly inside cube then its base is the same as a face of cube, and the height (H) of pyramid is equal to the edge (S) of its base.
[tex]A_p=\frac13S^2\cdot H =\frac13S^2\cdot S=\frac13S^3=\frac13A_c=\frac13\cdot27\,cm^3=9\,cm^3[/tex]
What is the answer that = n?
Answer:
n = 5
Step-by-step explanation:
To start off, we know that whenever the bases are the same, their exponents are equal to each other. Therefore, since both of the numbers bases are the same (both are z), we know that they will be equal.
The n can be distributed to the [tex]z^2[/tex] so that it now reads to be:
[tex]z^2^n = z^{10}[/tex]
Exponents are equal, so:
2n=10
Divide the 2 on both sides:
n=5
Answer:
n =5
Step-by-step explanation:
z^2^n
We know that a^b^c = a^ (b*c)
z^(2n)
This is equal to z^10
Since the bases are the same, the exponents are the same
2n = 10
Divide by 2
2n/2 = 10/2
n = 5
2 pts Question 1 Write an expression to model the phrase: Myles has $635 and is earning $120 each week as a lifeguard. (Use x as your variable) 2 pts Wuestion 2
Answer:
The equation is y= 120x+ 635Step-by-step explanation:
Hey there!!!,
in this problem we are expected to present an equation for the given scenario, and a way out is to model it after the equation of line
i.e y= mx+c
From the problem statement we can see that the constant amount Myles have is $635, and also earnings of $120 weekly.
Comparing the statement withe equation of line we have
y= 120x+ 635
as "x" is the number of weeks worked and $635 is the constant amount at hand.
Should you need further clarification on this, let me know
Find the missing probability. P(A)=1120,P(B|A)=1320,P(A∩B)=?
Explanation:
Assuming you meant to say
P(A) = 11/20
P(B|A) = 13/20
then,
P(A∩B) = P(A)*P(B|A)
P(A∩B) = (11/20)*(13/20)
P(A∩B) = (11*13)/(20*20)
P(A∩B) = 143/400
A to the power of 6 = a to he power 2
Answer:
a = 0, i, -i, 1, -1
Step-by-step explanation:
What we're basically looking for here is a number, that when multiplied by itself any amount of times, will get us with the same number.
We know that 0 times and number will be 0, so 0 works.
1 times any number will be 1, and -1 would also work as -1² = 1.
i would also work as it represents the square root of a negative, and -i would also work.
Hope this helped!
-K2 – (4k - 6n) + 9n; k = - 1 and n= - 4
For k= - 1 and n= -4, -K2 - (4k - 6n) + 9n =
(Simplify your answer.)
Answer:
The simplified answer of the given equation is -57.
Step-by-step explanation:
For this problem, we are given values for our variables.
k = -1
n = -4
So, let's plug these numbers into our expression so we can easily solve it.
-(-1)² - (4(-1) - 6(-4)) + 9(-4)
Simplify your parentheses.
-(-1)² - (-4 + 24) - 36
-(-1)² - 20 - 36
Now, simplify your exponents.
-1 - 20 - 36
Combine -1 and -20.
-21 - 36
Now, subtract -21 from 36.
-57
Answer:
-18
)())()()()()()()( ;)
Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles? ∠W ≅ ∠C ∠W ≅ ∠D ∠W ≅ ∠A
Answer:
The Answer would be ∠W ≅ ∠C
Step-by-step explanation:
Only one that is congruent
The measure of the angle ∠TWM is congruent to the measure of the angle ∠ADC. Therefore, the correct option is B.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
A triangle is a three-sided polygon with three edges and three vertices in geometry.
Given that the triangle ∆MTW is congruent to the triangle ∆CAD.
So, we have
∠MTW ≅ ∠CAD
∠WMT ≅ ∠DCA
∠TWM ≅ ∠ADC
If two triangles are equivalent, the ratio of matching sides will stay constant.
The proportion of the point ∠TWM is harmonious with the proportion of the point ∠ADC.
Therefore, at that point, the right choice is B.
Learn more about congruent triangles here:
brainly.com/question/4364353
#SPJ3
The pepper plant has \dfrac{2}{3} 3 2 start fraction, 2, divided by, 3, end fraction as many fruits on it as the tomato plant has. The tomato plant has 999 fruits on it.
Answer:
6 pepper fruits
Step-by-step explanation:
Given the following :
Fraction of pepper in terms of tomato = 2/3
Number of fruits on pepper plant = 9
Therefore number of pepper fruits on pepper plant:
2/3 * number of tomato fruits
2/3 * 9
(2 * 3) = 6
6 pepper fruits.
A group of 22 students participated in a math competition
what is the length of DI? A 1.4 B 4.4 C 5.6 D 17.6
[tex]\dfrac{DI}{DR}=\dfrac{DE}{DZ}\\\\\dfrac{DI}{6+2.8}=\dfrac{3}{6}\\\\6DI=26,4\\DI=4,4[/tex]
Please help me on this question
Answer:
you need to add 11 red circles
Step-by-step explanation:
1:3 one red and three blues
r=12 b=3
r:b =12:3
12:3 is the same as 4:1
you have to add 11 red circles
Find the value of x. A. -7 B. does not exist C. 35 D. 26
Answer:
C. 35
Step-by-step explanation:
x^2 + 12^2 = (x + 2)^2
x^2 + 144 = x^2 + 4x + 4
144 = 4x + 4
4x = 140
x = 35
Answer:
C
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem (a² + b² = c², in this case a = x, b = 12 and c = x + 2) to solve for x.
x² + 12² = (x + 2)²
x² + 144 = x² + 4x + 4
144 = 4x + 4
140 = 4x
x = 35
How would you write The difference of 9 and the square of a number
Answer:
9 - n^2
Step-by-step explanation:
Answer: 9-x^2
Step-by-step explanation:
no work needed
Determine if the event described is independent or dependent. Two people are standing in line at a movie theater trying to decide on which movies to see. a independent b dependent c neither d both
Answer:
c as in neither.
Step-by-step explanation:
the question does not give enough info because there are not two variables to be dependant on
Find the distance of (2,5) and (-1,3)
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
Use the distance formula:
[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Insert the values:
[tex](2_{x1},5_{y1})\\\\(-1_{x1},3_{y2})\\\\\\sqrt{(-1-2)^2+(3-5)^2}[/tex]
Simplify:
[tex]\sqrt{(-1-2)^2+(3-5)^2}\\\\ \sqrt{(-3)^2+(-2)^2}\\\\ \sqrt{9+4}\\\\\sqrt{13}[/tex]
The distance between the two points is the square root of 13.
:Done
Answer: [tex]\sqrt{13}[/tex] or 3.61
Step-by-step explanation:
[tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]\sqrt{\left(-1-2\right)^2+\left(3-5\right)^2}[/tex]
[tex]\sqrt{9+4}[/tex]
[tex]=\sqrt{13}[/tex]
Plz help: Round the numbers to estimate the quotient. 29 and one-fifth divided by 4 and StartFraction 6 over 7 EndFraction Which numbers should be used? ÷ The estimated quotient is...
Answer:
29 divided by 5
quotient is 5 4/5
Step-by-step explanation:
I just took that test from school
Answer: 29 divided by 5. 5 4/5
Step-by-step explanation:
I have proof plz mark me brainliest
Between which two integers does square root of /500 lie?
Answer:
22 and 23
Step-by-step explanation:
Step 1: Solve the square root
[tex] \sqrt{100 \times 5} [/tex]
[tex] \sqrt{ {10}^{2} \times 5 } [/tex]
We can move the 10² out because it matches the index of the root
[tex]10 \sqrt{5} [/tex]
Step 2: Input into calculator to find decimals
[tex]10 \sqrt{5} = 22.36[/tex]
Therefore the square root of 500 lies between 22 and 23
22 and 23
Because 5000 is between 222
(484) and 232 (529), the square root of 500 is in between 22 and 23..
Jack is 10 years old.
Kylie is 17 years old.
Vanessa is 23 years old.
Kylie and Vanessa share £16 in the ratio of their ages.
Kylie gives 20% of her share to Jack.
Vanessa gives a quarter of her share to Jack.
How much money does Jack receive?
plz answer me step by step plzz plz
Answer:
3.66
Step-by-step explanation:
calculate their shares and then add the amount they gave to Jack
The sum of the ages of Noi's and Noy's is 26 years. The different between four times Noi's age and two times Noy's age is 28 years. Find the age of Noi and Noy.
WRITE AS AN EQUATION
Answer:
The age of Noi is 13.333 Years and the age of Noy is 12.67 years
Step-by-step explanation:
The given information are;
The sum of the ages of Noi and Noy = 26 years
Four times Noi's age - Two times Noy's age = 28
Let the age of Noi = X and let the age of Noy = Y
We have;
X + Y = 26 years.................(1)
4X - 2Y = 28 years.............(2)
Divide equation (2) by 2 to get;
(4X - 2Y)/2 = (28 years)/2 which gives;
2X - Y = 14 years.................(3)
Add equation (3) to equation (1), to get;
X + Y + 2X - Y = 26 years + 14 years
3X = 40 years
X = 40/3 = 13.333 Years
From equation (1), X + Y = 26 years, therefore;
Y = 26 - X = 26 - 13.33 = 12.67 years
Therefore, the age of Noi = 13.333 Years and the age of Noy = 12.67 years.
the product of a number and five is eight
Answer:
Assuming x is the number, then [tex]x=1.6[/tex]
Step-by-step explanation:
If the product of a number and 5 is 8, the equation becomes:
[tex]5x=8[/tex] (assuming x is the unknown number).
We can isolate the variable x by dividing both sides by 5.
[tex]5x\div5 = 8\div5\\x = 1.6[/tex]
Hope this helped!